FYS-STK4155/doc/src/LectureNotes/_build/jupyter_execute/chapter8.ipynb

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    "# Dimensionality Reduction\n",
    "\n",
    "\n",
    "## Reducing the number of degrees of freedom, overarching view\n",
    "\n",
    "Many Machine Learning problems involve thousands or even millions of\n",
    "features for each training instance. Not only does this make training\n",
    "extremely slow, it can also make it much harder to find a good\n",
    "solution, as we will see. This problem is often referred to as the\n",
    "curse of dimensionality.  Fortunately, in real-world problems, it is\n",
    "often possible to reduce the number of features considerably, turning\n",
    "an intractable problem into a tractable one.\n",
    "\n",
    "Here we will discuss some of the most popular dimensionality reduction\n",
    "techniques: the principal component analysis (PCA), Kernel PCA, and\n",
    "Locally Linear Embedding (LLE).  Furthermore, we will start by looking\n",
    "at some simple preprocessing of the data which allow us to rescale the\n",
    "data.\n",
    "\n",
    "Principal component analysis and its various variants deal with the\n",
    "problem of fitting a low-dimensional [affine\n",
    "subspace](https://en.wikipedia.org/wiki/Affine_space) to a set of of\n",
    "data points in a high-dimensional space. With its family of methods it\n",
    "is one of the most used tools in data modeling, compression and\n",
    "visualization.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## Preprocessing our data\n",
    "\n",
    "Before we proceed however, we will discuss how to preprocess our\n",
    "data. Till now and in connection with our previous examples we have\n",
    "not met so many cases where we are too sensitive to the scaling of our\n",
    "data. Normally the data may need a rescaling and/or may be sensitive\n",
    "to extreme values. Scaling the data renders our inputs much more\n",
    "suitable for the algorithms we want to employ.\n",
    "\n",
    "**Scikit-Learn** has several functions which allow us to rescale the\n",
    "data, normally resulting in much better results in terms of various\n",
    "accuracy scores.  The **StandardScaler** function in **Scikit-Learn**\n",
    "ensures that for each feature/predictor we study the mean value is\n",
    "zero and the variance is one (every column in the design/feature\n",
    "matrix).  This scaling has the drawback that it does not ensure that\n",
    "we have a particular maximum or minimum in our data set. Another\n",
    "function included in **Scikit-Learn** is the **MinMaxScaler** which\n",
    "ensures that all features are exactly between $0$ and $1$. The\n",
    "\n",
    "\n",
    "## More preprocessing\n",
    "\n",
    "\n",
    "The **Normalizer** scales each data\n",
    "point such that the feature vector has a euclidean length of one. In other words, it\n",
    "projects a data point on the circle (or sphere in the case of higher dimensions) with a\n",
    "radius of 1. This means every data point is scaled by a different number (by the\n",
    "inverse of it’s length).\n",
    "This normalization is often used when only the direction (or angle) of the data matters,\n",
    "not the length of the feature vector.\n",
    "\n",
    "The **RobustScaler** works similarly to the StandardScaler in that it\n",
    "ensures statistical properties for each feature that guarantee that\n",
    "they are on the same scale. However, the RobustScaler uses the median\n",
    "and quartiles, instead of mean and variance. This makes the\n",
    "RobustScaler ignore data points that are very different from the rest\n",
    "(like measurement errors). These odd data points are also called\n",
    "outliers, and might often lead to trouble for other scaling\n",
    "techniques.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## Simple preprocessing examples, Franke function and regression"
   ]
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      "MSE before scaling: 0.01\n",
      "R2 score before scaling 0.94\n",
      "Feature min values before scaling:\n",
      " [1.00000000e+00 2.52277631e-04 1.58998839e-03 6.36440033e-08\n",
      " 4.01118504e-07 2.52806307e-06 1.60559584e-11 1.01193226e-10\n",
      " 6.37773764e-10 4.01959093e-09 4.05055916e-15 2.55287874e-14\n",
      " 1.60896055e-13 1.01405288e-12 6.39110289e-12 1.02186547e-18\n",
      " 6.44034203e-18 4.05904756e-17 2.55822858e-16 1.61233230e-15\n",
      " 1.01617794e-14]\n",
      "Feature max values before scaling:\n",
      " [1.         0.99869632 0.999475   0.99739435 0.998172   0.99895027\n",
      " 0.99609407 0.99687071 0.99764796 0.99842581 0.99479548 0.99557111\n",
      " 0.99634735 0.99712419 0.99790164 0.99349859 0.99427321 0.99504844\n",
      " 0.99582426 0.99660069 0.99737773]\n",
      "Feature min values after scaling:\n",
      " [ 0.         -1.70327945 -1.70487638 -1.10269333 -1.11031464 -1.11779074\n",
      " -0.8675412  -0.87387845 -0.88025384 -0.88666051 -0.73621263 -0.74081963\n",
      " -0.74548023 -0.75019465 -0.75496285 -0.65064103 -0.65385832 -0.65711132\n",
      " -0.66040159 -0.66373067 -0.66710007]\n",
      "Feature max values after scaling:\n",
      " [0.         1.7648157  1.69590827 2.29614193 2.24159129 2.18630067\n",
      " 2.72674862 2.67767959 2.62822832 2.57838874 3.10180456 3.05384136\n",
      " 3.0057178  2.95743601 2.90899738 3.44157349 3.39262419 3.3436382\n",
      " 3.2946235  3.24558749 3.196537  ]\n",
      "MSE after  scaling: 0.00\n",
      "R2 score for  scaled data: 0.97\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "# Common imports\n",
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn.linear_model as skl\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import  train_test_split\n",
    "from sklearn.preprocessing import MinMaxScaler, StandardScaler, Normalizer\n",
    "from sklearn.svm import SVR\n",
    "\n",
    "# Where to save the figures and data files\n",
    "PROJECT_ROOT_DIR = \"Results\"\n",
    "FIGURE_ID = \"Results/FigureFiles\"\n",
    "DATA_ID = \"DataFiles/\"\n",
    "\n",
    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
    "    os.mkdir(PROJECT_ROOT_DIR)\n",
    "\n",
    "if not os.path.exists(FIGURE_ID):\n",
    "    os.makedirs(FIGURE_ID)\n",
    "\n",
    "if not os.path.exists(DATA_ID):\n",
    "    os.makedirs(DATA_ID)\n",
    "\n",
    "def image_path(fig_id):\n",
    "    return os.path.join(FIGURE_ID, fig_id)\n",
    "\n",
    "def data_path(dat_id):\n",
    "    return os.path.join(DATA_ID, dat_id)\n",
    "\n",
    "def save_fig(fig_id):\n",
    "    plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
    "\n",
    "\n",
    "def FrankeFunction(x,y):\n",
    "\tterm1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2))\n",
    "\tterm2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1))\n",
    "\tterm3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2))\n",
    "\tterm4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2)\n",
    "\treturn term1 + term2 + term3 + term4\n",
    "\n",
    "\n",
    "def create_X(x, y, n ):\n",
    "\tif len(x.shape) > 1:\n",
    "\t\tx = np.ravel(x)\n",
    "\t\ty = np.ravel(y)\n",
    "\n",
    "\tN = len(x)\n",
    "\tl = int((n+1)*(n+2)/2)\t\t# Number of elements in beta\n",
    "\tX = np.ones((N,l))\n",
    "\n",
    "\tfor i in range(1,n+1):\n",
    "\t\tq = int((i)*(i+1)/2)\n",
    "\t\tfor k in range(i+1):\n",
    "\t\t\tX[:,q+k] = (x**(i-k))*(y**k)\n",
    "\n",
    "\treturn X\n",
    "\n",
    "\n",
    "# Making meshgrid of datapoints and compute Franke's function\n",
    "n = 5\n",
    "N = 1000\n",
    "x = np.sort(np.random.uniform(0, 1, N))\n",
    "y = np.sort(np.random.uniform(0, 1, N))\n",
    "z = FrankeFunction(x, y)\n",
    "X = create_X(x, y, n=n)    \n",
    "# split in training and test data\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,z,test_size=0.2)\n",
    "\n",
    "\n",
    "svm = SVR(gamma='auto',C=10.0)\n",
    "svm.fit(X_train, y_train)\n",
    "\n",
    "# The mean squared error and R2 score\n",
    "print(\"MSE before scaling: {:.2f}\".format(mean_squared_error(svm.predict(X_test), y_test)))\n",
    "print(\"R2 score before scaling {:.2f}\".format(svm.score(X_test,y_test)))\n",
    "\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "\n",
    "print(\"Feature min values before scaling:\\n {}\".format(X_train.min(axis=0)))\n",
    "print(\"Feature max values before scaling:\\n {}\".format(X_train.max(axis=0)))\n",
    "\n",
    "print(\"Feature min values after scaling:\\n {}\".format(X_train_scaled.min(axis=0)))\n",
    "print(\"Feature max values after scaling:\\n {}\".format(X_train_scaled.max(axis=0)))\n",
    "\n",
    "svm = SVR(gamma='auto',C=10.0)\n",
    "svm.fit(X_train_scaled, y_train)\n",
    "\n",
    "print(\"MSE after  scaling: {:.2f}\".format(mean_squared_error(svm.predict(X_test_scaled), y_test)))\n",
    "print(\"R2 score for  scaled data: {:.2f}\".format(svm.score(X_test_scaled,y_test)))"
   ]
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    "## Simple preprocessing examples, breast cancer data and classification, Support Vector Machines\n",
    "\n",
    "We show here how we can use a simple regression case on the breast\n",
    "cancer data using support vector machines (SVM) as algorithm for\n",
    "classification."
   ]
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     "text": [
      "(426, 30)\n",
      "(143, 30)\n",
      "Test set accuracy: 0.94\n",
      "Feature min values before scaling:\n",
      " [6.981e+00 9.710e+00 4.379e+01 1.435e+02 5.263e-02 1.938e-02 0.000e+00\n",
      " 0.000e+00 1.060e-01 4.996e-02 1.115e-01 3.628e-01 7.570e-01 7.228e+00\n",
      " 1.713e-03 2.252e-03 0.000e+00 0.000e+00 7.882e-03 8.948e-04 7.930e+00\n",
      " 1.202e+01 5.041e+01 1.852e+02 7.117e-02 2.729e-02 0.000e+00 0.000e+00\n",
      " 1.565e-01 5.504e-02]\n",
      "Feature max values before scaling:\n",
      " [2.811e+01 3.381e+01 1.885e+02 2.501e+03 1.447e-01 3.114e-01 4.268e-01\n",
      " 2.012e-01 3.040e-01 9.744e-02 2.873e+00 4.885e+00 2.198e+01 5.422e+02\n",
      " 2.333e-02 1.064e-01 3.960e-01 5.279e-02 6.146e-02 2.984e-02 3.604e+01\n",
      " 4.954e+01 2.512e+02 4.254e+03 2.226e-01 1.058e+00 1.252e+00 2.903e-01\n",
      " 6.638e-01 2.075e-01]\n",
      "Feature min values before scaling:\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0.]\n",
      "Feature max values before scaling:\n",
      " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
      " 1. 1. 1. 1. 1. 1.]\n",
      "Test set accuracy scaled data with Min-Max scaling: 0.97\n",
      "Test set accuracy scaled data with Standar Scaler: 0.96\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.svm import SVC\n",
    "cancer = load_breast_cancer()\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "\n",
    "svm = SVC(C=100)\n",
    "svm.fit(X_train, y_train)\n",
    "print(\"Test set accuracy: {:.2f}\".format(svm.score(X_test,y_test)))\n",
    "\n",
    "from sklearn.preprocessing import MinMaxScaler, StandardScaler\n",
    "scaler = MinMaxScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "\n",
    "print(\"Feature min values before scaling:\\n {}\".format(X_train.min(axis=0)))\n",
    "print(\"Feature max values before scaling:\\n {}\".format(X_train.max(axis=0)))\n",
    "\n",
    "print(\"Feature min values before scaling:\\n {}\".format(X_train_scaled.min(axis=0)))\n",
    "print(\"Feature max values before scaling:\\n {}\".format(X_train_scaled.max(axis=0)))\n",
    "\n",
    "\n",
    "svm.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy scaled data with Min-Max scaling: {:.2f}\".format(svm.score(X_test_scaled,y_test)))\n",
    "\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "\n",
    "svm.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy scaled data with Standar Scaler: {:.2f}\".format(svm.score(X_test_scaled,y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More on Cancer Data, now with Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   },
   "outputs": [
    {
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     "output_type": "stream",
     "text": [
      "Test set accuracy: 0.95\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set accuracy scaled data: 0.96\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:762: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "cancer = load_breast_cancer()\n",
    "\n",
    "# Set up training data\n",
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
    "logreg = LogisticRegression()\n",
    "logreg.fit(X_train, y_train)\n",
    "print(\"Test set accuracy: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
    "\n",
    "# Scale data\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "logreg.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Why should we think of reducing the dimensionality\n",
    "\n",
    "In addition to the plot of the features, we study now also the covariance (and the correlation matrix).\n",
    "We use also **Pandas** to compute the correlation matrix."
   ]
  },
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\n",
      "text/plain": [
       "<Figure size 720x1440 with 30 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/chapter8_7_0.png"
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/chapter8_7_1.png"
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.33026664e+01  5.69238112e+00  2.83259341e+00  1.99126621e+00\n",
      "  1.69095941e+00  1.19614372e+00  7.13037918e-01  5.77804918e-01\n",
      "  5.14549644e-01  4.30579019e-01  3.58977964e-01 -1.91269450e-01\n",
      "  2.86195387e-01 -1.59310961e-01 -1.38483045e-01  2.44786221e-01\n",
      " -8.79318674e-02  1.91811329e-01  1.70896266e-01 -7.17683028e-02\n",
      "  1.39860289e-01  1.18721828e-01 -4.83194721e-02  8.92983892e-02\n",
      "  6.81402316e-02  6.01968016e-02  3.31819744e-02  1.56432255e-02\n",
      " -1.61028757e-02 -6.50565973e-03]\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "cancer = load_breast_cancer()\n",
    "import pandas as pd\n",
    "# Making a data frame\n",
    "cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
    "\n",
    "fig, axes = plt.subplots(15,2,figsize=(10,20))\n",
    "malignant = cancer.data[cancer.target == 0]\n",
    "benign = cancer.data[cancer.target == 1]\n",
    "ax = axes.ravel()\n",
    "\n",
    "for i in range(30):\n",
    "    _, bins = np.histogram(cancer.data[:,i], bins =50)\n",
    "    ax[i].hist(malignant[:,i], bins = bins, alpha = 0.5)\n",
    "    ax[i].hist(benign[:,i], bins = bins, alpha = 0.5)\n",
    "    ax[i].set_title(cancer.feature_names[i])\n",
    "    ax[i].set_yticks(())\n",
    "ax[0].set_xlabel(\"Feature magnitude\")\n",
    "ax[0].set_ylabel(\"Frequency\")\n",
    "ax[0].legend([\"Malignant\", \"Benign\"], loc =\"best\")\n",
    "fig.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "import seaborn as sns\n",
    "correlation_matrix = cancerpd.corr().round(1)\n",
    "# use the heatmap function from seaborn to plot the correlation matrix\n",
    "# annot = True to print the values inside the square\n",
    "sns.heatmap(data=correlation_matrix, annot=True)\n",
    "plt.show()\n",
    "\n",
    "#print eigvalues of correlation matrix\n",
    "EigValues, EigVectors = np.linalg.eig(correlation_matrix)\n",
    "print(EigValues)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above example we note two things. In the first plot we display\n",
    "the overlap of benign and malignant tumors as functions of the various\n",
    "features in the Wisconsing breast cancer data set. We see that for\n",
    "some of the features we can distinguish clearly the benign and\n",
    "malignant cases while for other features we cannot. This can point to\n",
    "us which features may be of greater interest when we wish to classify\n",
    "a benign or not benign tumour.\n",
    "\n",
    "In the second figure we have computed the so-called correlation\n",
    "matrix, which in our case with thirty features becomes a $30\\times 30$\n",
    "matrix.\n",
    "\n",
    "We constructed this matrix using **pandas** via the statements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and then"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "correlation_matrix = cancerpd.corr().round(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Diagonalizing this matrix we can in turn say something about which\n",
    "features are of relevance and which are not. But before we proceed we\n",
    "need to define covariance and correlation matrices. This leads us to\n",
    "the classical Principal Component Analysis (PCA) theorem with\n",
    "applications.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## Basic ideas of the Principal Component Analysis (PCA)\n",
    "\n",
    "The principal component analysis deals with the problem of fitting a\n",
    "low-dimensional affine subspace $S$ of dimension $d$ much smaller than\n",
    "the totaldimension $D$ of the problem at hand (our data\n",
    "set). Mathematically it can be formulated as a statistical problem or\n",
    "a geometric problem.  In our discussion of the theorem for the\n",
    "classical PCA, we will stay with a statistical approach. This is also\n",
    "what set the scene historically which for the PCA.\n",
    "\n",
    "We have a data set defined by a design/feature matrix $\\boldsymbol{X}$ (see below for its definition) \n",
    "* Each data point is determined by $p$ extrinsic (measurement) variables\n",
    "\n",
    "* We may want to ask the following question: Are there fewer intrinsic variables (say $d << p$) that still approximately describe the data?\n",
    "\n",
    "* If so, these intrinsic variables may tell us something important and finding these intrinsic variables is what dimension reduction methods do. \n",
    "\n",
    "## Introducing the Covariance and Correlation functions\n",
    "\n",
    "Before we discuss the PCA theorem, we need to remind ourselves about\n",
    "the definition of the covariance and the correlation function. These are quantities \n",
    "\n",
    "Suppose we have defined two vectors\n",
    "$\\hat{x}$ and $\\hat{y}$ with $n$ elements each. The covariance matrix $\\boldsymbol{C}$ is defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{C}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n",
    "                              \\mathrm{cov}[\\boldsymbol{y},\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{y},\\boldsymbol{y}] \\\\\n",
    "             \\end{bmatrix},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where for example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] =\\frac{1}{n} \\sum_{i=0}^{n-1}(x_i- \\overline{x})(y_i- \\overline{y}).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this definition and recalling that the variance is defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{var}[\\boldsymbol{x}]=\\frac{1}{n} \\sum_{i=0}^{n-1}(x_i- \\overline{x})^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can rewrite the covariance matrix as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{C}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} \\mathrm{var}[\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n",
    "                              \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] & \\mathrm{var}[\\boldsymbol{y}] \\\\\n",
    "             \\end{bmatrix}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The covariance takes values between zero and infinity and may thus\n",
    "lead to problems with loss of numerical precision for particularly\n",
    "large values. It is common to scale the covariance matrix by\n",
    "introducing instead the correlation matrix defined via the so-called\n",
    "correlation function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}]=\\frac{\\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}]}{\\sqrt{\\mathrm{var}[\\boldsymbol{x}] \\mathrm{var}[\\boldsymbol{y}]}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation function is then given by values $\\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}]\n",
    "\\in [-1,1]$. This avoids eventual problems with too large values. We\n",
    "can then define the correlation matrix for the two vectors $\\boldsymbol{x}$\n",
    "and $\\boldsymbol{y}$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{K}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} 1 & \\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n",
    "                              \\mathrm{corr}[\\boldsymbol{y},\\boldsymbol{x}] & 1 \\\\\n",
    "             \\end{bmatrix},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above example this is the function we constructed using **pandas**.\n",
    "\n",
    "\n",
    "## Correlation Function and Design/Feature Matrix\n",
    "\n",
    "In our derivation of the various regression algorithms like **Ordinary Least Squares** or **Ridge regression**\n",
    "we defined the design/feature matrix $\\boldsymbol{X}$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{X}=\\begin{bmatrix}\n",
    "x_{0,0} & x_{0,1} & x_{0,2}& \\dots & \\dots x_{0,p-1}\\\\\n",
    "x_{1,0} & x_{1,1} & x_{1,2}& \\dots & \\dots x_{1,p-1}\\\\\n",
    "x_{2,0} & x_{2,1} & x_{2,2}& \\dots & \\dots x_{2,p-1}\\\\\n",
    "\\dots & \\dots & \\dots & \\dots \\dots & \\dots \\\\\n",
    "x_{n-2,0} & x_{n-2,1} & x_{n-2,2}& \\dots & \\dots x_{n-2,p-1}\\\\\n",
    "x_{n-1,0} & x_{n-1,1} & x_{n-1,2}& \\dots & \\dots x_{n-1,p-1}\\\\\n",
    "\\end{bmatrix},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$, with the predictors/features $p$  refering to the column numbers and the\n",
    "entries $n$ being the row elements.\n",
    "We can rewrite the design/feature matrix in terms of its column vectors as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{X}=\\begin{bmatrix} \\boldsymbol{x}_0 & \\boldsymbol{x}_1 & \\boldsymbol{x}_2 & \\dots & \\dots & \\boldsymbol{x}_{p-1}\\end{bmatrix},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with a given vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{x}_i^T = \\begin{bmatrix}x_{0,i} & x_{1,i} & x_{2,i}& \\dots & \\dots x_{n-1,i}\\end{bmatrix}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these definitions, we can now rewrite our $2\\times 2$\n",
    "correaltion/covariance matrix in terms of a moe general design/feature\n",
    "matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$. This leads to a $p\\times p$\n",
    "covariance matrix for the vectors $\\boldsymbol{x}_i$ with $i=0,1,\\dots,p-1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{C}[\\boldsymbol{x}] = \\begin{bmatrix}\n",
    "\\mathrm{var}[\\boldsymbol{x}_0] & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_1]  & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_{p-1}]\\\\\n",
    "\\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_0] & \\mathrm{var}[\\boldsymbol{x}_1]  & \\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_{p-1}]\\\\\n",
    "\\mathrm{cov}[\\boldsymbol{x}_2,\\boldsymbol{x}_0]   & \\mathrm{cov}[\\boldsymbol{x}_2,\\boldsymbol{x}_1] & \\mathrm{var}[\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{cov}[\\boldsymbol{x}_2,\\boldsymbol{x}_{p-1}]\\\\\n",
    "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
    "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
    "\\mathrm{cov}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_0]   & \\mathrm{cov}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_1] & \\mathrm{cov}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_{2}]  & \\dots & \\dots  & \\mathrm{var}[\\boldsymbol{x}_{p-1}]\\\\\n",
    "\\end{bmatrix},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the correlation matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{K}[\\boldsymbol{x}] = \\begin{bmatrix}\n",
    "1 & \\mathrm{corr}[\\boldsymbol{x}_0,\\boldsymbol{x}_1]  & \\mathrm{corr}[\\boldsymbol{x}_0,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{corr}[\\boldsymbol{x}_0,\\boldsymbol{x}_{p-1}]\\\\\n",
    "\\mathrm{corr}[\\boldsymbol{x}_1,\\boldsymbol{x}_0] & 1  & \\mathrm{corr}[\\boldsymbol{x}_1,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{corr}[\\boldsymbol{x}_1,\\boldsymbol{x}_{p-1}]\\\\\n",
    "\\mathrm{corr}[\\boldsymbol{x}_2,\\boldsymbol{x}_0]   & \\mathrm{corr}[\\boldsymbol{x}_2,\\boldsymbol{x}_1] & 1 & \\dots & \\dots & \\mathrm{corr}[\\boldsymbol{x}_2,\\boldsymbol{x}_{p-1}]\\\\\n",
    "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
    "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
    "\\mathrm{corr}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_0]   & \\mathrm{corr}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_1] & \\mathrm{corr}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_{2}]  & \\dots & \\dots  & 1\\\\\n",
    "\\end{bmatrix},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Covariance Matrix Examples\n",
    "\n",
    "\n",
    "The Numpy function **np.cov** calculates the covariance elements using\n",
    "the factor $1/(n-1)$ instead of $1/n$ since it assumes we do not have\n",
    "the exact mean values.  The following simple function uses the\n",
    "**np.vstack** function which takes each vector of dimension $1\\times n$\n",
    "and produces a $2\\times n$ matrix $\\boldsymbol{W}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{W} = \\begin{bmatrix} x_0 & y_0 \\\\\n",
    "                          x_1 & y_1 \\\\\n",
    "                          x_2 & y_2\\\\\n",
    "                          \\dots & \\dots \\\\\n",
    "                          x_{n-2} & y_{n-2}\\\\\n",
    "                          x_{n-1} & y_{n-1} & \n",
    "             \\end{bmatrix},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which in turn is converted into into the $2\\times 2$ covariance matrix\n",
    "$\\boldsymbol{C}$ via the Numpy function **np.cov()**. We note that we can also calculate\n",
    "the mean value of each set of samples $\\boldsymbol{x}$ etc using the Numpy\n",
    "function **np.mean(x)**. We can also extract the eigenvalues of the\n",
    "covariance matrix through the **np.linalg.eig()** function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07206099142503472\n",
      "4.125937788943556\n",
      "[[ 1.03889255  3.1254397 ]\n",
      " [ 3.1254397  10.77395298]]\n"
     ]
    }
   ],
   "source": [
    "# Importing various packages\n",
    "import numpy as np\n",
    "n = 100\n",
    "x = np.random.normal(size=n)\n",
    "print(np.mean(x))\n",
    "y = 4+3*x+np.random.normal(size=n)\n",
    "print(np.mean(y))\n",
    "W = np.vstack((x, y))\n",
    "C = np.cov(W)\n",
    "print(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlation Matrix\n",
    "\n",
    "The previous example can be converted into the correlation matrix by\n",
    "simply scaling the matrix elements with the variances.  We should also\n",
    "subtract the mean values for each column. This leads to the following\n",
    "code which sets up the correlations matrix for the previous example in\n",
    "a more brute force way. Here we scale the mean values for each column of the design matrix, calculate the relevant mean values and variances and then finally set up the $2\\times 2$ correlation matrix (since we have only two vectors)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07865526085644693\n",
      "1.4346285243728323\n",
      "[[1.         0.63566281]\n",
      " [0.63566281 1.        ]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "n = 100\n",
    "# define two vectors                                                                                           \n",
    "x = np.random.random(size=n)\n",
    "y = 4+3*x+np.random.normal(size=n)\n",
    "#scaling the x and y vectors                                                                                   \n",
    "x = x - np.mean(x)\n",
    "y = y - np.mean(y)\n",
    "variance_x = np.sum(x@x)/n\n",
    "variance_y = np.sum(y@y)/n\n",
    "print(variance_x)\n",
    "print(variance_y)\n",
    "cov_xy = np.sum(x@y)/n\n",
    "cov_xx = np.sum(x@x)/n\n",
    "cov_yy = np.sum(y@y)/n\n",
    "C = np.zeros((2,2))\n",
    "C[0,0]= cov_xx/variance_x\n",
    "C[1,1]= cov_yy/variance_y\n",
    "C[0,1]= cov_xy/np.sqrt(variance_y*variance_x)\n",
    "C[1,0]= C[0,1]\n",
    "print(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the matrix elements along the diagonal are one as they\n",
    "should be and that the matrix is symmetric. Furthermore, diagonalizing\n",
    "this matrix we easily see that it is a positive definite matrix.\n",
    "\n",
    "The above procedure with **numpy** can be made more compact if we use **pandas**.\n",
    "\n",
    "\n",
    "## Correlation Matrix with Pandas\n",
    "\n",
    "We whow here how we can set up the correlation matrix using **pandas**, as done in this simple code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.53680052  2.50858953]\n",
      " [-0.62753667 -1.74895806]\n",
      " [ 0.16570918  0.64706639]\n",
      " [-0.27228985 -0.08345099]\n",
      " [ 0.85643181  1.55737697]\n",
      " [-0.329196   -2.18391809]\n",
      " [ 0.92272798  2.91370357]\n",
      " [-0.37864859 -0.25719203]\n",
      " [-0.55226917 -1.4496257 ]\n",
      " [-0.32172921 -1.9035916 ]]\n",
      "          0         1\n",
      "0  0.536801  2.508590\n",
      "1 -0.627537 -1.748958\n",
      "2  0.165709  0.647066\n",
      "3 -0.272290 -0.083451\n",
      "4  0.856432  1.557377\n",
      "5 -0.329196 -2.183918\n",
      "6  0.922728  2.913704\n",
      "7 -0.378649 -0.257192\n",
      "8 -0.552269 -1.449626\n",
      "9 -0.321729 -1.903592\n",
      "          0         1\n",
      "0  1.000000  0.907143\n",
      "1  0.907143  1.000000\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "n = 10\n",
    "x = np.random.normal(size=n)\n",
    "x = x - np.mean(x)\n",
    "y = 4+3*x+np.random.normal(size=n)\n",
    "y = y - np.mean(y)\n",
    "X = (np.vstack((x, y))).T\n",
    "print(X)\n",
    "Xpd = pd.DataFrame(X)\n",
    "print(Xpd)\n",
    "correlation_matrix = Xpd.corr()\n",
    "print(correlation_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We expand this model to the Franke function discussed above.\n",
    "\n",
    "\n",
    "## Correlation Matrix with Pandas and the Franke function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     0         1         2         3         4         5         6         7   \\\n",
      "0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
      "1   0.0  0.076168  0.080935  0.078268  0.081921  0.085682  0.070727  0.073798   \n",
      "2   0.0  0.080935  0.086925  0.081766  0.086005  0.090410  0.072900  0.076302   \n",
      "3   0.0  0.078268  0.081766  0.085075  0.088305  0.091557  0.079623  0.082640   \n",
      "4   0.0  0.081921  0.086005  0.088305  0.091884  0.095514  0.082116  0.085368   \n",
      "5   0.0  0.085682  0.090410  0.091557  0.095514  0.099557  0.084565  0.088068   \n",
      "6   0.0  0.070727  0.072900  0.079623  0.082116  0.084565  0.076371  0.078937   \n",
      "7   0.0  0.073798  0.076302  0.082640  0.085368  0.088068  0.078937  0.081684   \n",
      "8   0.0  0.077019  0.079892  0.085767  0.088751  0.091725  0.081567  0.084509   \n",
      "9   0.0  0.080401  0.083686  0.089005  0.092271  0.095547  0.084258  0.087409   \n",
      "10  0.0  0.062426  0.063699  0.072024  0.073913  0.075721  0.070361  0.072486   \n",
      "11  0.0  0.065031  0.066507  0.074745  0.076802  0.078786  0.072797  0.075066   \n",
      "12  0.0  0.067773  0.069474  0.077585  0.079825  0.082002  0.075324  0.077748   \n",
      "13  0.0  0.070658  0.072612  0.080551  0.082990  0.085376  0.077944  0.080532   \n",
      "14  0.0  0.073697  0.075932  0.083645  0.086302  0.088919  0.080656  0.083422   \n",
      "\n",
      "          8         9         10        11        12        13        14  \n",
      "0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  \n",
      "1   0.077019  0.080401  0.062426  0.065031  0.067773  0.070658  0.073697  \n",
      "2   0.079892  0.083686  0.063699  0.066507  0.069474  0.072612  0.075932  \n",
      "3   0.085767  0.089005  0.072024  0.074745  0.077585  0.080551  0.083645  \n",
      "4   0.088751  0.092271  0.073913  0.076802  0.079825  0.082990  0.086302  \n",
      "5   0.091725  0.095547  0.075721  0.078786  0.082002  0.085376  0.088919  \n",
      "6   0.081567  0.084258  0.070361  0.072797  0.075324  0.077944  0.080656  \n",
      "7   0.084509  0.087409  0.072486  0.075066  0.077748  0.080532  0.083422  \n",
      "8   0.087542  0.090669  0.074644  0.077376  0.080221  0.083181  0.086261  \n",
      "9   0.090669  0.094040  0.076827  0.079721  0.082739  0.085887  0.089170  \n",
      "10  0.074644  0.076827  0.065759  0.067867  0.070042  0.072284  0.074590  \n",
      "11  0.077376  0.079721  0.067867  0.070098  0.072403  0.074782  0.077234  \n",
      "12  0.080221  0.082739  0.070042  0.072403  0.074845  0.077371  0.079979  \n",
      "13  0.083181  0.085887  0.072284  0.074782  0.077371  0.080053  0.082828  \n",
      "14  0.086261  0.089170  0.074590  0.077234  0.079979  0.082828  0.085781  \n"
     ]
    }
   ],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "def FrankeFunction(x,y):\n",
    "\tterm1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2))\n",
    "\tterm2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1))\n",
    "\tterm3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2))\n",
    "\tterm4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2)\n",
    "\treturn term1 + term2 + term3 + term4\n",
    "\n",
    "\n",
    "def create_X(x, y, n ):\n",
    "\tif len(x.shape) > 1:\n",
    "\t\tx = np.ravel(x)\n",
    "\t\ty = np.ravel(y)\n",
    "\n",
    "\tN = len(x)\n",
    "\tl = int((n+1)*(n+2)/2)\t\t# Number of elements in beta\n",
    "\tX = np.ones((N,l))\n",
    "\n",
    "\tfor i in range(1,n+1):\n",
    "\t\tq = int((i)*(i+1)/2)\n",
    "\t\tfor k in range(i+1):\n",
    "\t\t\tX[:,q+k] = (x**(i-k))*(y**k)\n",
    "\n",
    "\treturn X\n",
    "\n",
    "\n",
    "# Making meshgrid of datapoints and compute Franke's function\n",
    "n = 4\n",
    "N = 100\n",
    "x = np.sort(np.random.uniform(0, 1, N))\n",
    "y = np.sort(np.random.uniform(0, 1, N))\n",
    "z = FrankeFunction(x, y)\n",
    "X = create_X(x, y, n=n)    \n",
    "\n",
    "Xpd = pd.DataFrame(X)\n",
    "# subtract the mean values and set up the covariance matrix\n",
    "Xpd = Xpd - Xpd.mean()\n",
    "covariance_matrix = Xpd.cov()\n",
    "print(covariance_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note here that the covariance is zero for the first rows and\n",
    "columns since all matrix elements in the design matrix were set to one\n",
    "(we are fitting the function in terms of a polynomial of degree $n$).\n",
    "\n",
    "This means that the variance for these elements will be zero and will\n",
    "cause problems when we set up the correlation matrix.  We can simply\n",
    "drop these elements and construct a correlation\n",
    "matrix without these elements. \n",
    "\n",
    "\n",
    "\n",
    "## Rewriting the Covariance and/or Correlation Matrix\n",
    "\n",
    "We can rewrite the covariance matrix in a more compact form in terms of the design/feature matrix $\\boldsymbol{X}$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{C}[\\boldsymbol{x}] = \\frac{1}{n}\\boldsymbol{X}\\boldsymbol{X}^T= \\mathbb{E}[\\boldsymbol{X}\\boldsymbol{X}^T].\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see this let us simply look at a design matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{2\\times 2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{X}=\\begin{bmatrix}\n",
    "x_{00} & x_{01}\\\\\n",
    "x_{10} & x_{11}\\\\\n",
    "\\end{bmatrix}=\\begin{bmatrix}\n",
    "\\boldsymbol{x}_{0} & \\boldsymbol{x}_{1}\\\\\n",
    "\\end{bmatrix}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we then compute the expectation value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{E}[\\boldsymbol{X}\\boldsymbol{X}^T] = \\frac{1}{n}\\boldsymbol{X}\\boldsymbol{X}^T=\\begin{bmatrix}\n",
    "x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\\\\n",
    "x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\\\\n",
    "\\end{bmatrix},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which is just"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{C}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] = \\boldsymbol{C}[\\boldsymbol{x}]=\\begin{bmatrix} \\mathrm{var}[\\boldsymbol{x}_0] & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] \\\\\n",
    "                              \\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_0] & \\mathrm{var}[\\boldsymbol{x}_1] \\\\\n",
    "             \\end{bmatrix},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where we wrote $$\\boldsymbol{C}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] = \\boldsymbol{C}[\\boldsymbol{x}]$$ to indicate that this the covariance of the vectors $\\boldsymbol{x}$ of the design/feature matrix $\\boldsymbol{X}$.\n",
    "\n",
    "It is easy to generalize this to a matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$.\n",
    "\n",
    "\n",
    "\n",
    "## Towards the PCA theorem\n",
    "\n",
    "We have that the covariance matrix (the correlation matrix involves a simple rescaling) is given as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{C}[\\boldsymbol{x}] = \\frac{1}{n}\\boldsymbol{X}\\boldsymbol{X}^T= \\mathbb{E}[\\boldsymbol{X}\\boldsymbol{X}^T].\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now assume that we can perform a series of orthogonal transformations where we employ some orthogonal matrices $\\boldsymbol{S}$.\n",
    "These matrices are defined as $\\boldsymbol{S}\\in {\\mathbb{R}}^{p\\times p}$ and obey the orthogonality requirements $\\boldsymbol{S}\\boldsymbol{S}^T=\\boldsymbol{S}^T\\boldsymbol{S}=\\boldsymbol{I}$. The matrix can be written out in terms of the column vectors $\\boldsymbol{s}_i$ as $\\boldsymbol{S}=[\\boldsymbol{s}_0,\\boldsymbol{s}_1,\\dots,\\boldsymbol{s}_{p-1}]$ and $\\boldsymbol{s}_i \\in {\\mathbb{R}}^{p}$.\n",
    "\n",
    "Assume also that there is a transformation $\\boldsymbol{S}\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{S}^T=\\boldsymbol{C}[\\boldsymbol{y}]$ such that the new matrix $\\boldsymbol{C}[\\boldsymbol{y}]$ is diagonal with elements $[\\lambda_0,\\lambda_1,\\lambda_2,\\dots,\\lambda_{p-1}]$.  \n",
    "\n",
    "That is we have"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{C}[\\boldsymbol{y}] = \\mathbb{E}[\\boldsymbol{S}\\boldsymbol{X}\\boldsymbol{X}^T\\boldsymbol{S}^T]=\\boldsymbol{S}\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{S}^T,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "since the matrix $\\boldsymbol{S}$ is not a data dependent matrix.   Multiplying with $\\boldsymbol{S}^T$ from the left we have"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{S}^T\\boldsymbol{C}[\\boldsymbol{y}] = \\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{S}^T,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and since $\\boldsymbol{C}[\\boldsymbol{y}]$ is diagonal we have for a given eigenvalue $i$ of the covariance matrix that"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{S}^T_i\\lambda_i = \\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{S}^T_i.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the derivation of the PCA theorem we will assume that the eigenvalues are ordered in descending order, that is\n",
    "$\\lambda_0 > \\lambda_1 > \\dots > \\lambda_{p-1}$. \n",
    "\n",
    "\n",
    "The eigenvalues tell us then how much we need to stretch the\n",
    "corresponding eigenvectors. Dimensions with large eigenvalues have\n",
    "thus large variations (large variance) and define therefore useful\n",
    "dimensions. The data points are more spread out in the direction of\n",
    "these eigenvectors.  Smaller eigenvalues mean on the other hand that\n",
    "the corresponding eigenvectors are shrunk accordingly and the data\n",
    "points are tightly bunched together and there is not much variation in\n",
    "these specific directions. Hopefully then we could leave it out\n",
    "dimensions where the eigenvalues are very small. If $p$ is very large,\n",
    "we could then aim at reducing $p$ to $l << p$ and handle only $l$\n",
    "features/predictors.\n",
    "\n",
    "\n",
    "## The Algorithm before theorem\n",
    "\n",
    "Here's how we would proceed in setting up the algorithm for the PCA, see also discussion below here. \n",
    "* Set up the datapoints for the design/feature matrix $\\boldsymbol{X}$ with $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$, with the predictors/features $p$  referring to the column numbers and the entries $n$ being the row elements."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{X}=\\begin{bmatrix}\n",
    "x_{0,0} & x_{0,1} & x_{0,2}& \\dots & \\dots x_{0,p-1}\\\\\n",
    "x_{1,0} & x_{1,1} & x_{1,2}& \\dots & \\dots x_{1,p-1}\\\\\n",
    "x_{2,0} & x_{2,1} & x_{2,2}& \\dots & \\dots x_{2,p-1}\\\\\n",
    "\\dots & \\dots & \\dots & \\dots \\dots & \\dots \\\\\n",
    "x_{n-2,0} & x_{n-2,1} & x_{n-2,2}& \\dots & \\dots x_{n-2,p-1}\\\\\n",
    "x_{n-1,0} & x_{n-1,1} & x_{n-1,2}& \\dots & \\dots x_{n-1,p-1}\\\\\n",
    "\\end{bmatrix},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Center the data by subtracting the mean value for each column. This leads to a new matrix $\\boldsymbol{X}\\rightarrow \\overline{\\boldsymbol{X}}$.\n",
    "\n",
    "* Compute then the covariance/correlation matrix $\\mathbb{E}[\\overline{\\boldsymbol{X}}\\overline{\\boldsymbol{X}}^T]$.\n",
    "\n",
    "* Find the eigenpairs of $\\boldsymbol{C}$ with eigenvalues $[\\lambda_0,\\lambda_1,\\dots,\\lambda_{p-1}]$ and eigenvectors $[\\boldsymbol{s}_0,\\boldsymbol{s}_1,\\dots,\\boldsymbol{s}_{p-1}]$.\n",
    "\n",
    "* Order the eigenvalue (and the eigenvectors accordingly) in order of decreasing eigenvalues.\n",
    "\n",
    "* Keep only those $l$ eigenvalues larger than a selected threshold value, discarding thus $p-l$ features since we expect small variations in the data here.\n",
    "\n",
    "## Writing our own PCA code\n",
    "\n",
    "We will use a simple example first with two-dimensional data\n",
    "drawn from a multivariate normal distribution with the following mean and covariance matrix:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mu = (-1,2) \\qquad \\Sigma = \\begin{bmatrix} 4 & 2 \\\\\n",
    "2 & 2\n",
    "\\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the mean refers to each column of data. \n",
    "We will generate $n = 1000$ points $X = \\{ x_1, \\ldots, x_N \\}$ from\n",
    "this distribution, and store them in the $1000 \\times 2$ matrix $\\boldsymbol{X}$.\n",
    "\n",
    "The following Python code aids in setting up the data and writing out the design matrix.\n",
    "Note that the function **multivariate** returns also the covariance discussed above and that it is defined by dividing by $n-1$ instead of $n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "n = 10000\n",
    "mean = (-1, 2)\n",
    "cov = [[4, 2], [2, 2]]\n",
    "X = np.random.multivariate_normal(mean, cov, n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are going to implement the PCA algorithm. We will break it down into various substeps.\n",
    "\n",
    "### Compute the sample mean and center the data\n",
    "\n",
    "The first step of PCA is to compute the sample mean of the data and use it to center the data. Recall that the sample mean is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mu_n = \\frac{1}{n} \\sum_{i=1}^n x_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the mean-centered data $\\bar{X} = \\{ \\bar{x}_1, \\ldots, \\bar{x}_n \\}$ takes the form"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\bar{x}_i = x_i - \\mu_n.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When you are done with these steps, print out $\\mu_n$ to verify it is\n",
    "close to $\\mu$ and plot your mean centered data to verify it is\n",
    "centered at the origin! Compare your code with the functionality from **Scikit-Learn** discussed above.\n",
    "The following code elements perform these operations using **pandas** or using our own functionality for doing so. The latter, using **numpy** is rather simple through the **mean()** function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = pd.DataFrame(X)\n",
    "# Pandas does the centering for us\n",
    "df = df -df.mean()\n",
    "# we center it ourselves\n",
    "X_centered = X - X.mean(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, we could use the functions we discussed\n",
    "earlier for scaling the data set.  That is, we could have used the\n",
    "**StandardScaler** function in **Scikit-Learn**, a function which ensures\n",
    "that for each feature/predictor we study the mean value is zero and\n",
    "the variance is one (every column in the design/feature matrix).  You\n",
    "would then not get the same results, since we divide by the\n",
    "variance. The diagonal covariance matrix elements will then be one,\n",
    "while the non-diagonal ones need to be divided by $2\\sqrt{2}$ for our\n",
    "specific case.\n",
    "\n",
    "### Compute the sample covariance\n",
    "\n",
    "Now we are going to use the mean centered data to compute the sample covariance of the data by using the following equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\Sigma_n = \\frac{1}{n-1} \\sum_{i=1}^n \\bar{x}_i^T \\bar{x}_i = \\frac{1}{n-1} \\sum_{i=1}^n (x_i - \\mu_n)^T (x_i - \\mu_n)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where the data points $x_i \\in \\mathbb{R}^p$ (here in this example $p = 2$) are column vectors and $x^T$ is the transpose of $x$.\n",
    "We can write our own code or simply use either the functionaly of **numpy** or that of **pandas**, as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          0         1\n",
      "0  3.884269  1.937050\n",
      "1  1.937050  1.951359\n",
      "[[3.88426936 1.93705016]\n",
      " [1.93705016 1.95135877]]\n"
     ]
    }
   ],
   "source": [
    "print(df.cov())\n",
    "print(np.cov(X_centered.T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the way we define the covariance matrix here has a factor $n-1$ instead of $n$. This is included in the **cov()** function by **numpy** and **pandas**. \n",
    "Our own code here is not very elegant and asks for obvious improvements. It is tailored to this specific $2\\times 2$ covariance matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Centered covariance using own code\n",
      "[[3.88426936 1.93705016]\n",
      " [1.93705016 1.95135877]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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sAEs5E/+av790Kuv31OPOdHLizDkWlLp47Xt3Dvl+1fpDlpnWAW+QxWVudtcFrH2B5Necn53Kx/4OHorV4Me7omWoGrkK5ArFBYjfJIw3jLrcteI3HE0p3ZcKsvlbc4gHZ+bz+qFGFpTmcqzpc8tIKqpLvnG7hwdmeiyZoK4bEsCobmT+Znt8/OUTZzqtcov5GuJLEGYm+7P/fYru/igAdg2mTcrkY7+RBQshkBJ0Ka2sO9Whcd+MSfzxI791HRgNScGuPl4/1MiMgiz8n/cmtNJPTHfyWWcvdptGQXYqda3nKMxJo+1cf0L5I/79Sk+xczrYRePZHvZ728id4KTtXD95WSm0dvSxvMLDX45/ZpWr/vk3VWyr8uOwCf6/7861jg2M2xZ+tdmpUFwCoznGK36tzQcbrHJK/NzKg74gfeEovzvazKPzCjnW9DmRqE5lQzsl7gwiUUmxO8Maq/bKyjn8h1kFrN9TbwVlsz3evGzTYFtVs5Htxr0Gmwb/aZPhA374kyAvbK8jEtVxxPrkIzrU+ju5MSuFSKyU8sP7ppFiPx82+iM6O2rO4Ihr3HHYBC/vq+dPx1qYUZBFTXMH+dmp1PpDViC12wSRqORcbyQWxFNpbO8hJ92RYIAV/94f/iTIb480sd/bxrRJmVaZp7WjD/cEJ9uq/FYD00FfGztqWlle4SHVYePJV4/ygc8o5yR3ql4LjOpmp0JxLZHckGNm0JdSXkleK3Cub4Ce22HTuOOmHA59chYbEldGCmBI9mZOzuaD+rP86rG5A/TmpsLD1E+b7fGPbTnCvTPyeLPKz5IyNwd9Z/lyyUSefPWoVZf+1pzJvLC9jpx0IxT0R6VRGom10IMRKDVhZOR/rm6hL3K+gVuX0BPWcdoEKXaNybHmn96wji7hdLCb5RUFbKtq5nhLByl2jU0r57C92m9tjqbaNRrbewFoO9fHgim5/N9v1tDY3sOWVXOs937V5kqisSd14kxnwnsXONdvbcDW+kOs31NvZfYHfW18d0vlqJ1VjUVURq5QDMFIG3QuZa34IQxmkDdldv9y3zT6o5J1u72sml/E1269kf3eINMmTRiw7kFfG6eDXazb5eWdmhYO+to4/EmQrYcamXVzDtuq/NyQ7uD9eiOIVza00xuO8uN3TnDP9DyWlXtw2jXauyPkTnACRiauS8hw2qzj6BL6IjpVjSHcmSnW9amx7DwjxY7TrnFn8UT6IzpFrnT6IzpzinL42bduZ0GpC11COCr5+W4vv64873LYG/tiEJz/8mhq78EWM9B6aa+PWr/xnpe6M4Z8j6M6fHNWQcLmrslIhzuPV1SNXKEYAcn1ZFO5Ej+78lI30Aazjn1sSyXhqEQTRvB7KFb/BaxsOifdgf/zHp5ZOpV1u7xEdUl/JIoujaAYjf1v/oV7slOJ6pLWzj4AllcU8Oe/tRCJSmbdfAOHG9oTMnGnXSMS0dEBmzDWi8fc3HRPcBI410+RK53TwW4emVdI8+e9FNyQyhsf+nlm6RTW7jxFiTuDGn+H9fjB1ixypdPa0cczS6cw3ZNtSQe3VTWzuMxNXlYqvz3SZGXmYJw9aELgsAkeqijggZmeATNFL8caeCyhauQKxWUQLx80NeBPvno0YXblSGWJyc1AZvA3r396axWbVs7hgZke+qMSh81oVzddDNft8nL3VDe+QBc9YZ0fv3OCNUtKueOmHCI6SHk+QJrhThPgD/VaQdweq5v3RXRuSLdz/Ewndk2gS5iQYmTi/RGdb1R4SHdoAwIuwJmOPvKyUgic6yfVJmgIdnNjVgpvfOjnrlIX79S0Mm3SBH6y4yTPLJ3C6bPd2E2fWgYGcYCGYDf3zpjE+j311PpDZKbY2VbVjNOu8b4vyO9iQVwTxmsA44vngZkeNq2cY0kWzfd0NM+qxjIqkCsUIyDZ+9rkA1/wojO84fTpZuAB2FFzhuUVBaQ4bLx1zM/8klw2rJjFlwqyrcYfMBwFf/TnOvZ72yhypTPYObYuh74c7AqTmWInzWmj1J3BuT5DtaIJeLPKT3dYJ8UmSEZg1M/tGvRGJTZhXC65MYN1u7zcMz2PW/OzEAIa2rqIRHUisSA8FDnpDv78txYmpjt4cXsdzZ8bJltISapDIxJ74s9+vYybXRnW8/zTMT+1fmOv4P/aVmNtlgJWJm66PV6LPixqs1OhuADxpQ+zrX15hYfPOvoG9Q1PLpWY0r4D3qA1x9Jsf793xqSEjsN4vxPzumffqOZ3R5po7ejlewuLqTvTyYLSXPZ725juyeR4S6dVTvGHekf0mvS4souZrafaNbyxDUiA7DQH7d1hBNA3SPpsXmPufUYlZKfZqWnuwKYJq8Tx97MKeP1QI3ZN4LRrllVtMp7sVPyhXgTgDXShCWNt07OlvzuCJrBUM41ne6wN1qxUOy9sryPFrnFXqYvHtlQSlbBl1ZwBXbPXIiojVygugJlBb9znizkLenizys+Hn7aPaI6l6aNdcEOqtc76PfWxzciBHYcft3QQ1aXlI17sziCiS/5aF2DV5kpunpjGfm8bKXaNk2fOWdm1xCiHDJfxxiOBJWVuq9zRmxRg27vDAJTEbTBeaOlQT8RYW0q2V/s5/EmQ3x1pJifdQUSXgwZxc01/qNdq689Jd6BLQ8de4++wXtOdxS42rZzD2p2n+ObsApx2jZZQL8fPdOKwCfoiOv0RSW9YxyYu7YxpPKI2OxWKEbBxn48Xt9fxUEUBfzneSiSqY0+aBB8fLJJdBE0Xv5smpvOxv4O7Sl3s9wZZUOri45ZO67Hf+MV+Ah19tHf3I4RAl0bwiy+FmEHNoQn6opJ0h0Z3eMiZLheNAIRILL84NEFYl6TYNbJS7QRiGu6hcGU4CHYZ2bwWa04ymeC00dUfTajfm8cSwI2xBh/Tx3xCio1zfVGWVxSwo+aMtRFq+qevfOWw1XE6bVImJ850srzCQ2FO+jUnORxqs1OVVhSKERDV4aGYHnp+iYunF5cC51Ur8T7YgGVgZQaS6Z5swlGdWn8H0yZNiAXxXD5u6bDMsVYvKqa2uYOILnHajMJH/yAlDTPomeWOSHIB/BIwyxdgZMRSQopNWMeYkGonzWHDH+q9YBAHo+5urhUfxDMcGuf6o2hAmtNGil2zMn8B2DVBa0cfqQ6NxvYeUmyCc31RKgqzmTYpk9s8mby4vY6vlrn53sJiav0h6z3SMPTlk3PS2FFzBrvtvClYZpp9wIi4awkVyBWKEVA+OZuX36tPsIGNn12ZPMcSsLodX95Xz8Z99cjYeLP93iAzPFl83NLBzRPT+Mm7J5lblMOP3znBV6bmsu9k26ABPBmzxh0ewX2T0Uicy2hazsZ/KcTXxdu7w7QTvujjxOPQoCusWxn2HTfdwIeffm7dLoTxD7D8W/qikorCbE6f7UnYd/jJjpPs9wbpj+ikOTRK3BOsEkygs4++iE4acGeJi8w0Oy9ur+O5ZWWX9fzHMiqQKxTDYG5Urt9Tn2AD+9iWI0Naoho68CM8s3QKnT0Ra/CCK8PBfm/Q0lOXujOoajRkcPu9QYpc6QCER5hhS4yGnOTa9kjQwfIoMRlhaX1IBtOFxxPWwakZGfaMgiz2e4O4MhzckOagJdSLLhnwBTZtUianz/ZYdrUAjy8sSXhf87JSqfF3sKTMzeGGdm7MTKEl1IuUkl/s9nL8TKfly36tomrkiuuWkfiNxwflxxeebzBZvah40FP1lZsPown4comLn+w4id0muDEzhYagIaMzNxbjjafiSbFrIOUAlYgmjHJH/LWpDs3KXK80yRn9xeLKcJCT7kxQySQzOSeN5vYeHplXSOHEDEu/b05EctiE9UW0vKKAn33rdjbu81nqoF/s9nLAF7wuauRKtaK4bhmJ3/j8klw2rZzN+j31rN15wtrUfHxhyaD11rtKXeyuC/CBL4jdJujuj9IQ7MauYZUuIvrgQRyMNvjBpH56LIgLjI5K4AsL4qXuDNIdw4eGSz2yM6ZHD3aFLa8VE5F0v3+cfzOpDo2thxoxPbmiumR3XYDb8jPp6Alb93239gzf3XKY9XvqeeIrxQAcP9M5KmZn4wEVyBXXLfFNPvFBOlkTDnDrpExrLBoYmffGfT7rdjC+CKI6PDqvkF11AVwZTus2ieEKmJd13qfkQpgdliZCwO2F2ZyJK4d8EXgDXaOqgoknvnSS/HUlgTSHhtMmKJyYzrpdXr5c4sJhE7z2/qc8+epRpuRNYIbHKMtEJTy/rAybJugNR/lrXYDVi4wgbv4uRzISbrixe+MFFcgV1zXJE+mTa97m6fyHn7aT6tDYuK+eJ189SsENqby4vc7KFOOz+ReWlzNtUiaN7T3WOlHdqOW2XkQQNjssTexCUNUYuuxa9lgkXvu+YEouN8f2CwA0TXD6bDc9/VECHX2xgc5p9Ed0PvZ3Eo4aZzgPVXiI6gPb8uPdIU3iA/W1MNtT1cgV1zXmH+2tkzKpbg4lDBx49o1qDn9yFv/nPdhtGl+79Ua2VfnRhKFIuavURWVDuzUkYdPKObx1zE9dS4e1iTlaaEm67gttLI5HHp1XyJ+OtVga/TVLSlm3y0t3f8SYPRr3mp9fVsbHfmNYBjBAjx/PSIyzRnMS1BeJ0pErFEkkt26bRlhmk8/b1S309kex2wRfuzWPbVXNltVq6Y0T+N7CYg76Kjl91tjI3F7t5w9Hm87rmsVAj5NLJXmdayWIp9oFvRHjxegS5sT8Y/KyUlm3y0tXXwRdYjksOm2Cb842PNRtMa2iXRP801cNXf9g5bH4EtpQgTr+zCzZcmE8oEoriuuW+FNw05CqP6LzwvbjPL21ivvL8/lv901Dl4ZToC3WPi5ik99r/YlljtcPNSZMykmxada0HcVA3BOc9EYkZXkTcNo1Wjt6qWxop7KhnQdmenBlOC1PmLZz/ZaBWEuoF7smiErJtEmZ/OqxuTy9tQpgSGfDC5XQRnMS1NVABXLFdY3pZwLGH/ucohxq/cZosgdmeli786Q1EScqz8sAe8NRXtheRzgqrWAugK7+KNlpdgTQE9GJXoXS5VhkEPNEAuf6meHJ4vTZHn5wz1QqG9qtjHzFpkM0BLut2vkj8wrZezLAmiWl7DvVRkSXzC3K4eSZTmr9oYTO2sHURMMF6vgzs5Fsjo5FVCBXXLeUT842/FA2V7Jxn8/SIGtArb+DF7YfHyDxS7FrVBRmW92UEV1aDoISSLELQj0RJMaQhNEqrYx3hioF1fg7ePgOD+t2eYlEdfKyUvnarTdazTtfLnbx3LIy3vjQz30z8njfFyQclSwuc/Nf/m4qXy1z8+L2Omr9Qw/1uFCgvhY8yy97s1MIUQj8CpiEIS99WUr5P4d7jNrsVIwVzGk8PbGAnebQePgOw3YVEifswOCbjLYkUyjF+elByZiNRKamXhNGsK483c70/EzK8rP4w4fNSCljAyQEv3psLrX+EGt3nsJzQyoA355baHXb1vpDvF3dwn0z8gcN5iNp/BovfJENQRHg+1LKW4E7gf8shLhtFNZVKC6ZkWqD55fk8vjCYuvylwqy+dOxFtKdtgF2sOb4tPjLTptgsFzoeq+MD6V1N7/vzCD+jds9HPAFyUl3UNUY4g9Hm0DCP8yeTKrDRkSXPLalkvd9QcomTaA+0EV+dhovbq/jvhl5VDeFmO7JpjHmxTIYT91dMqAmfq0Nl7jsQC6lbJFSfhj7uRM4DhRc7roKxeUwnDY4Psgf9LWx+WADTruGAA43tHOuN8LyCg+35mchMbLHDKeW2B5v16zJ8oMFclVRMfBkpw55m00IS87Z2tGHK8OBBObeksPrhxpZXuHh0XmF9EV09pwIUNUY4mZXOvu9bdxVmsvWQ42cONNxXfiNX4hR1ZELIYqA94AZUsqOpNueAJ4AuOmmm2adPn161I6rUJjEn0abwfvuqW5rCk91U8gywTI9wvsjOlFdDvA/MTNy8zqzrHKpRlWKoSlypfPp2W7LT8Y09DLPbOKj1NyiHCob2rnZlUZDsOea8lK5EF+414oQYgLwB+C/JAdxACnly1LK2VLK2W63e7QOq1AkYGbiz75RDWBNYC92Z1DrD3E62GUF8X979yR2zZgq47AJ/uPcQgRYPiO6TAhAXWEAACAASURBVNRvR6XxB9MX0clKtQ08uGLE2OMiz+ScNJo/70nwkzE7YCWJQXxBqYvDDe3YNEFDsIflFZ4RywWvhVb8oRiVQC6EcGAE8dellG+MxpoKxaVgtmO/Xd3CP75ymDermllQmsvJ1k5e2F5HsTuDnz9SYagkdJ327jB5mSk8s3QqLywvp9idMcBnxJTO5aQ7EJpAAh290YEHV4yY+BOaMzHLWTAmEYlBNhicNoFDE+z3Bg0NuS5ZUuamvTs8IrmgaUccf7+N+3w8tuXIuGrFH4rLDuRCCAFsAo5LKdde/lNSKEaGaVwVT+PZLv51xwlmTjYkgpoGR06fNSbe2DXW7fLygS9IXzhKVDeywe5wlJ+8e5KN+3x8e27hgONEJdbMSaGq36NGRWE2MzxZlhvkkjI30UHsfdMcGv1Rafm0F+Sk8ci8QnbXBbir1DUiuWD55GzrTOzprVX8828+4sXtdTyzdMo1UVsfDfnhAmAf8DfOb0o/J6X881CPUfJDxeVg1sFr/SFr8st0Tza/3FfPX+sCLC5zs6suwLRJEzhx5hwAyys8/OX4Z9w0MZ3a2EgzuwZpTjtrlpSydudJesI6di0xW1SMPhWF2Xy9PJ/N+xvwh3qtMXPJgy7iMWeAOmwCmyZwxLxYLmZ8m7lnUurO4HBDu+VhPp74wmrkUsr9UkohpSyXUt4e+zdkEFcoLhezDj7dk81zy8p4cXsdKzYd4q91AR6ZV0hVY4jlFQWcOHMOp02Q6tD4y/HPeHBmPrVxE9mddhtrlpSyfk89D99RgGBkQbw0bqq84uL5qDHEL/d9gj/Ui12D55bdyoJSlxXETftegZGNe7JTCXaFKXVn4MlOozesE47qTPdk89TdJRclNb17ai6HG9qZW5TD3pOBcdW9ORyqs1Mx7og3QfprXQAhjIacOUU5FE7M4L4Zefz5by2kOjRSHDa+v3Qqc4oMSVteZgq6hOmeTKSU/OuOE2Sl2vl1ZRMAGc7zm5jJpVrTRiV5IILi4pBgDVjWNI3HtlSy3xu0bnfGumcl4LkhjamTMqkozMbX1sVnnb3ML3HhsGm8dcwPjNyGduM+H29W+Vle4cEb6LLKLNdCMFeBXDGuMLMv0wTpoC+ILiF3gtMwXPokyNZDjUzOSaPghjQenJnP+j315GWlUlGYTWtnHxOcNj4920M4KolEJQ3BbqKxVvvu/vObmMlFR7N7U1XJR4fesM7CUpfVVasJw54WBGX5WUbwDnRZI+GcNo2oDk8vLmXDilm8W9tqfRYuNCDkoK+NtTtP8dyyMn72rQp+/kiFVTMfT634Q6ECuWJcYWZfhjdKvXV9V1+Eu0pd7IrVyP/7QzNoCfXy+qFG7puRR2tHr+URfq4/ys0T0y2flHhUkL6y7K4LWD+bm5w/f6SC1o5ePmoMMSkrhW1VzaTaNfoiOj+4dypw3h/FDMIXcjesbgqxaeVsHl9YYt3/549UXFSNfSyjBksoxjQv7fVxOtjFAzM91h/n89uqef1QIxNSbOgS/vnvpvDjd04Q0SULSl3YbRpbVs1l4z4f/7rjhOVQKDGGF/z74UZlZjUGMf1XllcUsKPmDDnpDvyhXut3N8OTxY1ZKbzvO8umlbMHZNyD+Y1fSz4roIYvK8YppkPhyphD4UFfG78/2oxdM0ah3V54A9M92ThsArsmONYU4omvFHPQ18b6PfVMzcsEsFrti3IzBuiUr3dflCvNYBbtFYXG71AThvd7iTsjIYgLDKfE3XWBAZLB4dwNr4UxbiNBZeSKMU+8Q6EmjIBst2no0nDHk1LyUEUBD8z08OSrR+npj+K0a/zz303h3941/MSTXQwVV48JKbaEeaSFOak0tp8P2tlpdkI9EUrdGXgDXQmTljQBr31v3oAB2cNl3eNljNtIUBm5YtwS71CoS2MSu5SSV1bO4c7iiVaAn1+Sy6r5RUR0SXd/lBe319EX0S0zJsXVxaYZGXfyUOnG9l7jB2F0cIZ6IiwodeENdDGjIOu8141mNHWZahVz4zve3dCUHca7G16ofn4toAK5YsxjOhSmOjSrLBKV8IEvyEeNIR6dV8gbH/pjG6CfUBSbwG4OfOjsjVy9J6+wiOqJXZsOTVCYk2ZdtglIcdhYs7iUyoZ2St0ZnDjTCRiSRKdN48slLkutMtKyyXgf4zYSVCBXjGkO+tpYtbmSSFTn+0unMiHFjtMm6I/orNvtpWxSJsvKPTyzdAovbq9j1s030BDsth5vZvCKq4NdE1QUDqxHawKiUtLY3kNKzMwmosOGFbO4s8SFlBJvoItwVPLovEK2rJqD3aZR2dDOfTPyePm9+hHLDsf7GLeRoGrkijHNS3t9HP4kyPu+IHabxv3l+XzW0cuuuoCVwUkpmTopk+LcCWyrasZpE0SlkQEqxiYiNvs0J91Be3c4QZly8rNzRHUdpLHZffpsD6sXFVMf6KK1o3eAamXtzhOs2+0d1M72elGtqECuGBd84xf7+bi5g2mTMqnxd/DovEKKcjMsvw6nTaDL87Mzk0/jFWMDc3i1xGi/B8HDd3j43ZFmIrpu/A4xbn9uWRmPLyxh4z4fL26v46EKD3tPtiVk3dfSRuZIUJudinHDYN4Z95fnE5WSGn8HMzxZ/OlYC//jnRP4Q70sKXOjS2IuehK7JlQQHyM4kiJMZord2LvAKHnNL5nIOzWtfHN2AVpsA0QH7irNZf2eetbuPMH6PfU8VOFhW5U/YbPyeimbjAQVyBVXhIsx9R9sE2vdLi+pDhtOm6DG38G53ghRXeKwGcayNk2Q5tCI6Fgt30MxmI5ZMfoIIPlXEeqN4J7gJMWhkZViZ1ddgIpCY06qLfaLsWuC/d42bsvPZN1uL3dPdbP3ZNuAzUqzu9MM7COxs71WUaUVxRUhPnuaX5LLs29U88aHzfzXe6YS1bGUBm8d83OzKwObBmt3nuLxhbfw0t56JJL/du80OnsirNvtBSDVLojoRiYOhi1t8lQfxdjCrIWbdsELSl287zuLEMbvcXGZmy+XuCz9/4JSFwe8Qb5a5mbuLS5rTJ/5ORrP9e5LQdXIFVed+Hrm5oMNRKI69piv9LpdXqK6xKaJmD/4KfKyUmgIdjPdk0V94Bz9Ed0aB2YS3yxi1wTZaXaCXeGr8voUg2M2AAnAbhPW/kWRK51gV7/lEb+8wsNtnix+suMkdpvgzuKJBLv6OXmm0/qcmEZX5pf/9TZ4WdXIFVeUwUopAGWTjNPlVfOL2LRyDgA/3WlkX939Ub52642s3XmK+SUTaQh2Y9fg07PdlE3KJBoXxJ0xyZoZxPOyUojoUgXxMYJZvTIbgPKyUhACwjEp6O2F2WSnO4jqMhbEC/jL8c9Yt8vLgikubJpghiebxrM9bFo5hw0rZhHVsVwLu/si110QHw4VyBVfCIPVuZ989Sh/aw5ZtU6AVfOL6A3r9Ed05hblsK3Kz6ybb2B3XYAlZW4iutHQYzoXmiRrw4eaLKO4ssRPva8ozMauaaQ5NKZ7sshIsVtnUMvK8/nhvWXYNEG600ZrR6+1xvcWFrNqflFCJ6bZqXk9dGleCvar/QQU1ybxzRq3Tsrkw0/bsds0NqyYxfySXDLT7KzaXIkmINWhoUti47c87Khp5ZF5hbxT00phThqN7T3WujZhdHUOdVlxdYmvgVc3d/Av9xm6bkM+WMBfjrcypyiH9XvquWd6HhtWzOIDX9DSgd9Z4uKtY37erW21vvDvLHElKFXiuzTjb7ueURm5YlSJL6mY2dMBX5C+iM6aJaXWBtW6XV6klEQlfH/pVIgNR/7L8c94ZukU3qlpxWETCUEcBgbtqFTuhWMF9wQn8SKVIlc6Ud0YyHFXqYttVc2sml/EKyvn8vNHKrjZZYzMiw/Mtf4Q79a2DiopVHLDoVEZueKSGKpj7p2aFn7xVy8bVswCYPPBBpw2w2d67c6TdPZEeO3Qp9xfnk9rRy95WalEdfjBvVNZt8vLnKIcorpxWr4rbujAcKiE/MpjNmBF4iRCgXP91pDkiA7fnltoNfQc8AZZXlEwIIuOr3PfWeLisS1HEmxqkyWFQ8kNr/esXKlWFJdEspzQvLx6UTHrdnmJRHXLR9pu03hwZj6vH2oEsE6hn95axT3T83hgpofqppAlOSxxZ1Dj7yDdodE9jCY8xS7oi6gwfjUwJ95nOG10xcbjmfVvc0BEutPGPdPzeLPKb3Vpxn9uqptC11T7/JVAyQ8Vo85Q7dEHfW1855eH0KVR/15eUUCxO4N/e/ck4aiO066hCcE3bvfwwEwPT2+tIifdQUuol+JcI4jnZaUQPNefkPElEy89VFx5BEbWvfdEAH+o19KGO2yC6Z4s2rvDnA52s7zCw8++VWE9TgXrS0fJDxWXxYXkhKaC4KW9Pn65r/683awu+ayjlxe21xHVJd+4vYDesCE1LHZnML8kl3um53E62EV3f5QafwfuCU5aO/qGDeKggvjVxm4TFLsz6OyLYNdAIlhe4SESlXzs7+BsVz9rFpey92Rbwmcn3itcMTqMSiAXQtwrhDghhPAKIf5lNNZUjC0GkxOufKWSjxo/T2idbjzbxe66ANFY1144Kq1at00TvFPTYmnA3/cFASh2ZxCJq6AEzvVf2RenuGg0YOEUww+l1J1BVIcHZxqmVo/MKyQclcwpyiE9xc7thdk8+erRhM/Os29UD7BnuBgbB0Uil11aEULYgJPA3wFNQCXwH6WUHw/1GFVaGZ8kd2aanZjmxqY5Zs10IATQdcN3Oi8rhfbuMP0RnTWLS8lMs/Pi9jpui3Vt9oZ1tWk5TjA7MgHWLCnlgDdITrqTbVXNrFlcSnqKHZuG1X355KtHiUT1hHF8gCVFNRlq30U1/ZzniyytzAW8Usp6KWU/8GvgG6OwrmKMEd+MUV6QzS//cTYbVszi6a1V/GK3scE5vSCLLd+dy9S8TMJRSVRKpk3KJNDZR39Ep8iVzv/aY2RYt3myqPV30BPWuX2Q4QOKsckN6Q42rJhFJKrzdnULd5W6eLvab6lSTge7mO7JpnxyNtVNIe4vz0eX8LsjTXx3SyVgfAEkm1uNZFCEYnBGI5AXAI1xl5ti1ymuMeKbMY7HRnDFa8Ul8MN7ywA42dppPe5Ua6dVz/6ss49vzZnMi9vrOHmm09KAJ3duKsYmNs1wHaz1hxBCEOjo48XtdfzD7MnsPRlg9aJi3viwmZWvHObJV49SPjmbYncGfRGdiC7pDet87dY81u+pH3SSvercvDRGI5AP1o8x4CxZCPGEEOKIEOJIIDAyfbBi7BB/mpueYmf1omKe3lrFxn0+Xjv0KcsrPOgSHttSycrNlYSjkiVlbsuR0OTO4oksK/fgsAnCuiTVPvKPoGr8uXpownj/BQK7Jnhhex3hqE7gXB9fLXPzwvJyywdlTtFE+qOSSFTnA1+QtTtPWuvYNcG2qmZWLyoeNEhfD/M1vwhGI5A3AYVxlycD/uQ7SSlfllLOllLOdrvdo3BYxZUk3vv5dLCLdbu83Dcjj7U7T7F6UTF/Of4ZhTlp9EcM35TlFQXcmJVKfPgVwL5Tbfzzbz7CbtNw2AQ9keG9w+NRNfSrgybAYdN4ZF4hEV3SH5WG13jU2CP53sJi4Hw2vd/bxvKKAiSwbreXnrBOmkMzFC26MfjjJ++eHHRjU3VuXhqjEcgrgSlCiFuEEE7g28CfRmFdxRjiqbtLqG4KcdDXxgMzPQD87kgzeVkp/PidE4CRbZv2pNurW/j90SbrD9ccABGOSlo7+ugNR7FrgryslKv4qhQjQZfw8B0FLCv34IydQUnOZ+kmB31tbD7YwPwSF3853powM3V+iYu9J9tYXuEhqkum52cOqJGrQRGXzmUHcillBHgaeBc4DvxWSll7uesqxh6mBBEMxQECGoLdRHTJgzPzeeNDP4vL3JwOdpOT7iAcNYK4JgT3l3sS1tIl9EV05Vo4RkkODHUtHazYdBhd17HHJvloQhCO6jy68RDPb6u21ChfLXPTF44SjkqWV3iwaYJddQFuy89k78k2nltWhjfQxelgV8IxTHfDeJTmfGSMio5cSvlnKeVUKWWJlPKF0VhTMfaIVxW8sP04/bGyiNMm+N2RZrJSjdFdN2al0NrZR15mClFd4rQbdVGzSSjZSzwn3XE1Xo5iGMyClzkWr6oxhEAS0UGX0iqTRHSj7v3vhxuJRHU2rJjF+74g/bE9kmmTsrh7qhGc93uDlE3KZLpHKZRGG9XZqbgo5pfkcvdUN7X+DgCWVxSQ4rAR0XVaO/vQhOENrglo7TSy7XN9hheHlIYZVrKXeHu3GgYxVtGE4NF5hdg0QVHMrVCX0BxzpbRrgvtneqzJTR/4grzvO8uj8wqpajS8VL63sJiUWEnmSMNZnnz1KBtWzOJHD5dfrZd1zaECueKiOOhrY3t1C067hl0T7KhpwZXhtLJrPWYra142jbNMlMxw7BL/ezI2OI29jT8da+HBmR4+CXaxuMzN5Jw0Dje0M7cohx/eN40dNWdYXlFAJCpZt9vL4wtvsVQsT756lO9uqcRpNzx3+qOScHTkG9yKkaECuWLEmKqC/zCrgC2r5vDD+6bRE9ZpCHYnBIFkdYk55V4xton/vZlfxM8snUo4qrOtqhmHTSM/O5Xm9h5smjEIZO3OkzyzdAp/OW74x6c6NDYfbOCgr435JbmUF2THtOM3svdkgDWLS3HYNN46NkDYprgMlB+5YsQkqwrAOLU2sm7JcErCqHK4GvOY033iL//sf59CjymPdF2y9VAjzy0rY7onm/+06TA9YZ2f7DhBisNmzWB965jfsjQ+fqaT5RWeBCtb08L4gZltquFnlFCBXDFiTPXAys2HCXX34w108avH5lqjuhTjG/PMSQBOu8a0vAn8rbmDiC4NF8NTAU6e6WS6x/AQ/6dFJazb7SXdaed/feeOBNlgsdvH2p2n2LRyNtVNIZ5blsX6PfXWY9VAiNFFBXLFiDGnAt1V6uKF7XVoAjbtq2fvSdWwMV6xa4I7iyey3xtEYJw5mYM/Vr5i1Lb/acEtlt88YOm64zswk4nqsGnlbGtwMsB0T7YVvOOvV1w+arCEYsSYNfJ7puehCayJP8mogQ/jA3OSD0BepiEZXVCay8ctHdakpzlFOcy9xWX1EJjBXLkUXh3UYAnFiBnKF9qskb9d3cIfPmwe0vukfHK2pRVPRn3grizDbTF/qSDL+jlwrg9PdioHvG2W9cKDM/M54A1y+JNgQjnkrWN+7pmepzowxxDq70oxgMGGSDy9tcqar7hqfpHlHx4fKPKyUlhc5qa6KcTEDOegwVwJz64sEmPARzICQwpaUZiNw2Z0365aUESqQ+P3R5u5d8Ykfn+0GU1AZUP7eRXK5GzerW21bBpMVAfm1UXVyBUDiO/gHGwe58Z99dZ9Tc8NXRqNQF+7NRV3ZgpnOvqsTk7F1SMz1cah+rOA8XtKsWtkpTqsZq1jTSEyUuzWkIfpnmy+u6UyJjcUbF41FzBKKXdPzWVHTatV+1aMHVRGrhiUwXyhzcx86qRMKgqzMR1ozSYggK2HGi3/FCnPt3gPxlDlF8XooAmsM6c0h8azXy9DCEFrZ5/1+9IlrJpfNGhgDkcltf5QrJs3l21Vfu6dkaeC+BhEZeSKAby018fhT4JUNrRbqoTMNDtvV7dwz/Q8HphpTL6fXpDNp8Fu2rvDlnTN1IubWfpwm57JrfqK0UVKuGliOv/9oRmAMYovHNWxCdBiMsP+qGTjvnruLHFZ93HYNJ5YWMzGffW8uL2OvScCHPAGWV7hsQYpq2A+tlAZucLC3OS0abC7LkB/RCczzU5OuoMXttfxccxfpbopxO2F2XT1RmjvDltZd3zTj1KtXH0k8O25hZbU76aJ6YaHuE0j1WFjy3fn8vyyMnRpBPBfxkpmG1bM4pml09i0cg42zTC7eqiigJ99q0J5hI9RVCBXWJibnG9Xt1AaG8/1wvY6y27U8BLvpXxyNge8QbyBLjzZqSpoj2HW7/HF9jV81Po7yEl3oOvGhPuX36unoa2Lh+8osOZqPjgzn5ffO78HYtM0pnuy2HsyYGXiSqEy9lA6ckUCB31tPPnqUfpik36ScdoEmibQJSwsdbGrTo3tu5LYBAxXkUrW8GsC7DaN/ohu/ByzVEh12Ch1Z1DVGOLReYW8sLycjft8vLi9zmrBV1rxsYfSkV/nDKUNf2mvL+E6U144WBBfUJpLf9QYoPvUV4rZtHLuRc3cVFw+QwXx+M3LGZ4s6zpdkvC77I8N+5g5OZuqxhBLytxsPdTIP7x00Arijy8sUdN6xhnqr/A6YThteDzmuC7HIIqS/d42HDaB067x0t56nt9WTe9FzNxUXB7mb8SmCRxJf7kTM84P56jxd/DovELSnLaE++jSOKP6UkE2+2Obl5tWzmVOUQ6HG9qZU5TD4wsNLbia1jO+UIH8OiFeG75254lBT5PN4H5/eT7TPVmDrnPzxHRS7Boi1qKfYlcSwiuFELBmcSkgCcd9f2oCgl3nN501Ab+pbKK3P5rweC1WljG9xPeebOP5bdVUxi5XNrSzcV/iGZpifKAC+XXEYNrweKqbQtwzPY9idwbHWzpJc2g8v6wMT3YqYAQCb6CLB2fm8/AdBZS4M+iLyGHbwBWjh8OmEezqw5zL8Oi8QlLs2vkhHtKY2CSloSCKP1ea4clCj12vCfioyejqfP1QI4/MK+S3T83nuWVlvLi9TgXzcYgK5GOUC9W0R1rzTr493rEu+fFP3V3CAzM9rN15irtKXWxaOYf6QBedfREWlLrQJRS50nj9UCPVTZ9zOthNRWH2gEESii+Gwpw0fl3ZhMDY9NQlPPmVYuv2m11p7D0Z4JF5hdbvxMzS6850WpdTHTYWlBpT7ZeUuSmcaIxwe3xhCc8tK+OAN3gFX5ViNFCBfIxyoZr2SGveZsCPdy7MTLNzz/Q86/HxXwDVTSGeWTqFjxpDfOAL8oejzfSGoxz+pJ27Sly0xlrva/2dlNxoqB40ATlpaoDyF0H8VsWnZ7uxCcMr/F++Xsbb1S2s3+uz1CgNwR6+M+8mdGl0ct48MZ2MFDsLSl1EdIl7gpOMFDvfuN3DKyvn8qvH5jLnFhdP3V1ifU4eX1jCllhb/rNvVPPsG9UJz+dCyYLi6qDkh2MYM/gm+52M9Pb4+5gdmbX+UILE7Mc76jju7+QH904lqoNNg3W7vLgynDQEuylypdMQ7CbFrvH1L+Wzrao5YX0R+6e2PL8YnHaNcERPOOtZXOYmPzuVfz/ciC4NNdHR02cJRyUOm8Bu0yzvFFNSOHXSBE6cOcfyigJ+9q3bBxwnWV5oylABay0lQbz6KPnhOORCNe0L3W7e5+ePVPBubSsf+IKs31PPc8vKWL+nng98QeoDXdhtgnW7vFYQ7+2P0hDsJjvNTkOsfCIEA4I4GN2DKoiPPnlZKTjthv47fhPCrsEBb5DXD50P4vu9bQgh+OF905g6KdO670FfG+v31PPIvEI+DfawvKKAN6uaB62BD7YZvmHFLDasmDXsBrlibKC8VsYwyTXtO0tcAzLy4W43iQ/4axaX8vjCEjp7ItblwLk+/viRn5/uPEkkKq3T8MC5fuya4G/NHQnrJc92VFw+8e9pkSudYFe/sXuJ9Z9hMiYEfTHJp10T6FKS7rRZw63vm5FP+eRsS++9elEx6/fUW46Ft3kyWbvzlDVyLZ7kz4l5+2DXKcYWlxXIhRA/AR4A+gEfsEpK+floPLHrneTTWHNgrVkigfNTWsAYDDBUxpQc8DPT7AmXVy8qRpdGow9AhlMjcK6fsrwJnD7bTU/serNrcLAgroL75RH/3rWEeglHdXRpZOatHX04bIK5txgj2eD89Qd9QdYsLiUzzW7NyIwfo/bSXl9CI8/jC0uskWtg7ImY2vDBEgNgRMmC4upyWTVyIcRSYLeUMiKE+DGAlPKHF3qcqpFfGHM+ZnIG/tYxP+/Wtg4Z0OP/MM3HxAf4+DbsxxeWWLXQ/ohOX6yNW5dG00m600aJO4OPGo0/enMwb0SZq4waKTZBX1y7pic7lTMdvbHfgZGN35qfhfezc/RFdJx2DZuAL5e4eN8XpCes47AJUh02q5Y9GIPVwC90WdXIxx5D1cgvKyOXUu6Mu/gB8PeXs57iPIN10JmZ1gMzjT8o94SUAZucg2nD42+P6lgSs+me7Nh1EilhRkEWNc0daMI4jY/q0src0hyalZnHozLxy8MM4hWF2VQ3h/CHenFoAvcEpzX8ISfdSV/ECNg/uGcq7/uC/LUuwHPLyvjY38G2Kj9C6Lx1zD9kgB1uWAgM/JzML8nl/vJ86+f4NcwByoqxw6ipVoQQbwG/kVK+NsTtTwBPANx0002zTp8+PSrHvV5Zu/OEVbd8Zum0i358vJoFsIYpz/BkUevvID87FaddoyHYjU0TfHvO5CGHLSsuD01ARoqdNUtK+cmOE/RHJdM9WdQHzhGNeaUsryjgm7Mn8/J79TSe7abxbDcLpuTyUWOI2/Kz2O9to8Sdwa7vLxr2WJf7uVFcXS5ZtSKE+IsQomaQf9+Iu8/zQAR4fah1pJQvSylnSylnu93uS30dCi7c2DMU8U1E1U0hVi8q5u3qFqqbQmw91Mij8wq5f6aH55aV4Q/10hDsxq4JnDZhZH1J66mOzsvHNLYKR3X+WhcgxWFjeuzL9N4Z+aTYNe4qcbG9uoVf7qvnia8U81lnH0IIdtcFyEq1s9/bRopd47POvmE/C5f6uVGMfS4YyKWUX5NSzhjk3x8BhBD/CNwPPCqvhij9OiO+TvnM0mkXZfQf30RUPjnbkBqGo9T6O7jZlcbvjzZj02C6J9saw6ZLSVaqg+7+KLcXZieMZ5Og3A8vEwlM9xiSwYO+IF+7NY9Pz3bjtGtsq2pmzZJS/vPiUuw2I3DX+kNsWDHLGuLREDTuu3nVjL1mogAAIABJREFUHDasmDWkO+HlfG4UY5/L3ey8F1gL3C2lHLExtdrsvHSG2gRN3uQc6nGAVSfd8F49fRHdMkzSNHDaNL5c4uKD+rNEoro1jm1BaS6HG86SYte4aWIatf5Oa+0Mp42uJIMmhSEPHMnGsDPWxBOJ6oSjkueWlVEf6OKPH/nRpcQRa/Cp9YdYu/MUjy+8hfV7fYRjv5tUh8YrK+cMW7e+1M+NYmwxVGnlcgO5F0gBTHOGD6SUT13ocSqQX1le2uvDpsH6PfX8/JEKPvAFWbfbC5zf4FxeUcCOmhZrQ9NhE2gxzbJNE+i6tDI/gO/88pCaDDQM5sR6c/hxPGa3rF07P9d0cZmbvKxUWjt6qYxZyvaGdQ76gswvcbH18TuB8zVuMLo+NQGaENg0MaxqRXFt8IV0dkopS6WUhVLK22P/LhjEFSPjUkyxhqJ8cjbr99SzelExKzdX8os9RiCwCaht7mBBqYu3q/3ML3FZde9wVNIX0Vlc5uZf7puGENAX0dle7Wd7tV8F8QugS+iJBXHTuEoAyys8dPRGeHReIdMLsrklNwOHTVDZ0M4DMz18b2ExUV3y3sk2/tYcYs3iUurOdFqeOJsPNljr/eCeqbyyco419PqtY/6r9XIVVxnltTJGuZDO92J59o1q/viRn95wNOZimM5nnX30hqNICTfnptPQ1m0FCTNQPx/zZHnrmJ9fH25McNWTQzQHXc8sKHVZTTtwvuxkfkF+tczY6K9saE/wQ/nXHSeQEuw2Q6tv+qVUN4WwafBv755EE/BQRQGtHb3WGveX5/PATA9vHfNzsytDlUmucb4QHbnii+NCut+L5YGZHn5TafhzFOak0hDstixNb8xMsYK4GcDNn//Hn+tIT7EzpygHTcPywlYZ+UAEcCxps7GrP0qGQ6M3Kvn2nMnU+DuoD3TR0x+1ptav2+VFAGHdsEeY7snk+WW3Ud0U4vAnQd73BXFlOGnr6kcTsP9UkAVTXNYx4js5FdcnSnIwhhmJKdZIqfWHkNII0K2d/VagznDaOB3sJi8zBZsQcVNmBHlZKUQlSF3yvi9oBfFkslNtg99wnSGBzt4IABNSzr8nXWGdW1zpvFPTym35WaxZUorTrrG7LsDKzZX0xc6SwNggrfV3UusPUT452+rebO/uZ27RxJhZlrQy+h89XH4VXqlirKEC+RhmtHS/B31trN15iq+WuZlf4qI/Yvh4ZKfZCZzrB2DSDam4M1MsRz0JtHb0oQk41x+1NkEH046HepViJZlzfVFSYlJN48uzj9WLjCEQ6/fUc8/0SYDR7NMfMyp7flkZv3psLulOGy9sr+N3R5qw2zTSHBrhqGS/tw2bMCwSVs0vUlm4wkIF8jHKaOp+q5tCbFo5my+XuDjgDWKPpd2hHiN7lMCnwW78oV4yU+109YUx9050mfghuZYqKskDjC+GwR6qJX3L9UWNMXgOm8aaJaVEdfjRw+WsXlTMm1WGZt9kQamLxxcaA49/+Y+zme7JYltVM6vmF3HvjHxLxhiVxoapauhRxKMC+RhlMO+LeBe7wRhK6WKyfk89xe4MbNr5EsqC0lyKXOm0d4fJy0qhszdCVWPICODmxmfSccwvAtsg6bnG+On4DOvGa7iY52sThmQz+T1Jc2jc5EofcH+JMaKtPtDFU3cbJmXrdnmt/QaHTeC0a+z3BhN8wltCvaxZXMrGffVsq2q23vMUu8Zfjn/G6kXFqqFHYaEC+RjlqbtLBvWLHk6VMNz4t5ffq+f2wmy+PbeQiC5jm55pHPC20RDsZoYni9aOPtLj0lTXBOegx/lSQRae7FTiTPsSgv54ytqjI1TemMFel1Af6EoI/k6bobdvaOsmJz1x5J1DE3gDXbxZ1Ww14JS6M6wgnuqw8YN7prK4zM3anafYuM9nnYndWeIiEnuTvzI1l+eXleG0a0R1SX2g64Jf7IrrByU/vMaIH/+2cd8nPLN0imVXu2pzpeVzHd91aNPg1f+/vbOPjro+E/3nmZm8kJAghBgyEMUkQDTcYATBIixUWBDxBdxr28XrrWtF5LTL3eW0pwrn7Nmzntptu2vP8dhl1VtfLrVdd/cKbdUKKxarUFFiIIIGSFIwJAFDiAkQSDIz3/3j98JkmCEhmUzens85czKZ33fm9+SZyTPP7/k+L9+aw5NvfMaB+lay0pOtwQYReGzv1THgqUlWwYvTAdEpdBmuhGf1wMXOj05v8JzMFDwIX5y5QNBY4ZIz7QEqG84waewomts6WTA1m63ldeRnp/PEiulA1zbEz/3B6qcyt2A8//puNceazpFvG37Ho9dUw5GLph+OEMIzXVaW+tm0s8adBjOvMIsdlY22Abpokb5xcx4/eauSA/WtTPdnuhPXHUrzxnCDP5NX9tR2Kcd3BlEYe015bQvpyR7OdQyu4W+RBjgSxyDPnjyWD482x1zj83pI9Qmt9ubuX99WyHtHGimvbWFsWhKdQcONeZmcPRpg8fU5vHXgBOuXTKGm8RyzrxtH9ugUnn6nimSv8MSK6e4Vl+NZR16FXa6VsaKEo4Z8mBGZ6eLEUosmZFB2rNktyQ+GLAPn9Qgf1JzmT6fOcf+cPCaPT+fgG5V4BPLHp9PWEaS8toUb/JnkjR1FbfP5LudL9grGQHltC2NG+dwN1HiT4hPaA727euyJEfd5pIsR9wh4Rei0n+z0Av/hm5WAVR7/LzurCISsOZrXZKVxZ0lul6Ed982yro7WLSrk6R1VdAZDpCZ5SPJ2jWiqcVb6isbIhxHRMl027axhwdRsdlc3ETKGIyfPuutDBr42axK1p8+TmuRleYmfX+2p5baibJK81ubd7scXsagom1f21HYx4k6M2Of1MH/qeAT6zYg7Z8xIvXK/w/mAh+d1O6T6PIxO9VGaN8adfuQQMjAubI+gI2j4yVuHSE3ycltRNhiDPTqT7y8r4tffnucO7XDy7Z0N6prGc3QGQ1zoDPHI/Hx3oLFuVCrxQg35MCJapsvahfm8deAEK0v9bv8Un8fyMAFe/eg4982ayD03+vnOL8uZkXcV71Q2ckNuBvtqW3j+vWp2V18sOfd57PJ8rJh4IGjYVdXUZcMwM44FQl6xztkeCHGhs+f56s7mq8H6kJ9tDzLdn8m0CaPdNRcCIQqz01k6PZfvLp1Kir3Rm5OZYuV+t7aT7BV+uXoOG5cXWRujxjBmVJLbFTLZ56Gm8RxghUJWzy/oEhJx3oskr8e9SgJ0o1KJK2rIhxGRMVanEGj9kilMm5BJaZ7VxjYQgqk5GWxcXgTAf5ZZm29FEzLYUl5HktfKtFgwNZsn36gkNckyzF471uzzCNP9mRxtamP+lCw6g9asz5zMFAA3hhwPMlOT8Hg8lOaNIWRMl6yQtG4SwRcVZTM2PQkDjE1L4kB9K4dOnCU7zNPeV9vC+0ca+adth11j+2Vbp3vcY38jFPvH8LVZk8jPHs2W8nqSvMK62wpJ8Xl4vaIhpne9u/oU2w6e5NkHZnapB4DoMfDLEc9GasrwQg35EKC3/8AVx1tYv2QKm3bWUDJpDEW5maTYw3s/rW8F4L5Zk7ghN4MfvFHJnj+ddntjXzMujS3ldUwam0pzWycrS/08dkcRIWOFGaobz7JxeRF/OHKKkIHH7yhiz4bFrjGPRk/ztT0C98/JA6D5fCezJ49jy7fn8e2FhTTbRnbMKB9tUWaIdtVRE+c7gqQmeTh74WLYp/FsB0l2KOXa8Wm8X9VEIBji2QdmupPjnQrXJK+Hh1/ey5rNZeRnp3Pki7Nu2uAtBVk8+8BMgJidB3tTDxCLy6WXKiMbNeRDgJ7+A0ca/EcXFFDsH8PS4hzWbC5jS3kdyT4Pmx+ew4blRTz5RiW1p9sor23BZ7dCNVjDmD+1M1hqmy8w3Z/Ju4dPUdN4jpWlfsBqc3vmfABBKMhOp9g/ht3Vp+gMmqiFQhA7XzvyQxgysKfmNGB50h/UWMUyL+4+SrLdHbDlfOCSnO1IAiFDZ9DQETR0hgzT/Zm4A40Eiv2ZbrOwFPuq47f760n2ebh/Th5lx5pZfP3VtHUEKchOZ9POGv7ipom8/NBsN84N1pT5a7PSo8rQm3qAWIQ3Untq+yGdaK+4aB75ECE8PzxWJ8TLtb792TtV7Kpu6jJ0929fLWdLeb2b/x2efjfdn8mB+lbun5PHax/Xc+9Nfn6zvwGAv5o72Z1Qs+62Qm4pyGLN5jIA7p6R22VIc6pXuBBWOSR2+9twnMyRJI9gsAqRTra2s6gom/LaFpZNz+GXe2q5MW8MlSfO0B4IIULMJl7Oa6bYee5wMbUwNcnDsukT2FJuedBJXuHlh2YD8K2X9vKVgnE8PN/K43aGOBT7M8jOSHXzu8P1PRATdnSA8silXwZLKImjJ50QY3lsAJ+dONOl+dbu6lO8e/gUK0v9HGtqY15hFh8ebabYn4nXIxyot6YG/WBlCeuXTOFXH9Zy9kKAmyePJWOUj4DdR+RnO6v57f567izJpSMQ4pU9tQi4nnO4ER+bloQxXUv7nY3T++fk8fK3ZuPxCCdb25lXmMXN12XxzKpSXvu4nlsLs/ikrpWvFGTx+B1FpCX7SE++dFN1kd3v22Dlufs8Vgn8h0eb8Xkcb77TlSFkpxfOLRjP+iVT+GO1dSXgDHFITfLw+enzlxhxsMImkVdF/R2z1gHKSjTUkA8RevoPHGnwgUtSEtdsLmPN5jKeWVXKtAmZrJqTx66qJlaWTuTz021gLCO97eAJdlefothvGSsD/L6ykSffqGTVnDy3XPzX++q5a4afq0ZZoY6rM1K4b9YkvGFdpJw+LqNTvG7VozNBfro/k7ovL3CwvoWOQIicjGQ+bTjjzphcPf863q9q4q4ZueyrbaHYP4a7Z+RGnRP6+0MXR8d6xPK4rcwXsUMtId6pbMTn9ZDsFTweYc3mMnZXn2L1/AJ+/uAs1mwu46GXPgLghQdvjpkumOiYtQ5QVmKhoZUhwJVMC4oMwSwtzuGuGf4u6x5/rQKwOvE562+0M1o+OtpMwC7jd+Z1JnsFEaEjECRgFxIl+zxuV7+nd1Rxzbg0Pq1vZUXY7E+fx8qQcUInY9OSaG7rtNMfPXQEQm65vxPeSfF5uPemieRnp7sZN5t21rh/z9qF+Ty1/TDnO0NuxWa0ys1ifyY1jWfxXzWKL860s/j6q/nt/gZCxuARax7pSw9Z80fXbC7jzpJct7f3quc/YHe19cX206/f6Oo1Wml8T0Je8UIHKCsaWhnC9DTzIZrHtu3gyUte74f3lrhG67k/WLM8H56fzx+rT7NuUSHrl0xl0thRgLXx2R4IYYxhVLKP2ZPHEjJW2OKv5k5m9fwCFl9/NQfrW1lR6uenX7+Rr9iZH4HQxd7mgNVhMSOF7y8r4nxniMxRFzcrnYlFAJUNrTy9o4p7b/Lz1PYjrF2YT+PZdpYW57BpZw2ZqdbzvB4hNcmDz+O5pOCnvTNIIGhsI57DlvJ67pqRS97YNAIhw6ML8t2KyvDNyt3Vp6g8cYaVpRPZWl7XpSPhtoMnL/G24zn8ozviuXGqDC/UIx9G9MZjc4z/0uIc8rPT3VJyT5gHDpbRfGzZNJ7eUcWFziCddox8w/Iintp+hNun5/Du4VPuF8y2Aw1U1LUSDBmyM5JpPNPh9uYu9mew/3iLneLXdcals8maluzlnhv9rkxgZYccrG/hn7YdRmwv/HtLp/JmRQPltS2MTvFytj3oev5JXuFrsybx2sf13D49h63l9aQmeVg9Pz+q9/z4axW8XtHQZZbmD96opNifQUNLe4+ugDSLROlPYnnkasgVdlefYs3mMqszYshK13PCIsleq9+IsQuBRiV7KchOZ19tixvSCB/QvO3gSXeDdc3mMto6ggRDxl3rGOoUn4c7/oeVPeLEr5018wrHs//4l3TaaSlJ9iBiwP3SuWuGv8s5SiZmUnniLNeOG0XlybNMzkrD6xFqGs+xonQib392kkAw5A41dl4r3PBGGvLd1ad48MWP6AiEomaIxHtAtqJ0hxryEUS4Z+7cB1zP3PHSAXedk9IGFye/J3uFl+zUvPuf3+MOSahtPk9aspdpOaNpvRBg9nXjuhjw3+6vZ2u5lbL46kfH3Xa52aOTaTxrzQv9+s1Wwc9rH9fREQhxa6E1vcgaeiEsL7mYIugY0WhXHOHxfiedsihnNMdOn2dFqZ8LnSG2lNcxtyCL79xWGFUPsWLeL+4+CljpltG8bY1ZK4lGY+TDnPBiICeb4vn3rH7WTpZKyaQxXTIrwte9uPsoyXa1zLmOIJOz0twimbkF49mwvAgBapvPM3vyWP72z6ewr7aFkklXuUbciTlfm5XO+iVT+I+9VgHSutsK8XqExrMdZKb68Hk9rked7POwak4eZce+ZMPyIkYleyn2Z7Cl3CrMSU3y8OLuo+yuPhU1RuzE+59/r5qt5fWsLPXzxdkO1i+ZwusVDbz92UnW3VbotuYNjylHiy+Hx7w77WrP9UumuUVV4RkiJZPGXLJPoTFrZSCIiyEXke+KiBERvZ4cIMJT4SqOW0U0T75R6TaaCgRD/Oydqi6X/k5TrSffqOSacWl4xRpZlprkoelcB+sWFV5iqLwe+PBoM09tP8yK0olsKa/rssnnDEMAqyDH6xFe/ajWDa8YrLj2ms1lfNrQyrMPzCRvXDo/f3AWq+cXsG5RIQcbzpCW7OUvbprICw9ezCy5XD+Tp7YfYcPyIn769VKeWVXK0zuqCIYMd5bkXlGqnpPmObcgq0u7WeeLxynF1/J4ZTDR537kIpIH/Dnwed/FUXpLxfEWt/f4gqnj2Vpebw/wrWdeYRZ7jzW7lZ1gGdxHFxQQDOEa5NQkj2s4f/RWJU/vqOLZB2by/HvVbu740VNt7Kpu4nxniDc/aXDz2p0eJceazvF6RQPtgRDfWzqVVz743J0a9Jez8wgZeGr7YQIhww25mZf04t5V1cS8wiy3uhJg3aJCXq9ooOJ4S9TYszNcOjyr586SXAA3Oyc80ydW/Lq7mLeTT549+pBubCqDij7HyEXkP4EngF8Ds4wx3VYnaIw8/jhGZ8HUbLaU17mbik5MO9krPLqgwI37hm/oOYMnPqlr6fK4k1/d0HKBiVeluiX6i6+/mi3l9XgEfvHwHAC3RN/ZSFyzuYz2zqDb7jXF5yHZ52Hx9TlsLa/jq0XZvPDg7Jh/x0BsIPYk5q3l8cpA0i8xchG5G6gzxuzvwdpHRGSviOxtbGzsbrnSA5y4uFMSvnZhPlvL68gencyB+lZyMlOobT6Pz2M1uYqc7hNuJH+5+pYuFYwVx1tYt6jQyp2eOIbf7G8gEAxxZ0ku0yZksnF5EekpPtZsLuMDu1/5nSW5roe9+Poc14ivLPWT7PPQ1hFgS3kdK0onRjXiMLCNobrL09byeGWw0q1HLiJvAxOiHNoIbACWGGNaROQo6pEnFMcQr12Yz9M7qggEQ27HP6/dzbDYn8nnp9uYMekq3q865Ta5qjjewgc1TdxamMXq+Rc35x566UOaznXw/duLunj4OZkptHUEXY/dOf8z71SxO6IZlzPo2RiDxyMkeT3u+SeNHUVbR7Bb4zzYPF9NNVQGA732yI0xi40x0yNvQA1wHbDfNuKTgI9FJJrRV/oBx3vdtLOGa8alcd6eaO/0QLl/Th53zfCzblEhu6qsBlnOhJpHFxTwyJ/ls2lnTZdeIR8dbXYn3jgevtcDX7S2s25R4SVGq9JuxvX8e3+ypwlZIZlkn4fv3T6NaRMyuNAR5P2qU8wrHE9bR5Bl03P41kt7L7t5+Ys9n3NrQZabsRJ+bCAGKcSzr7iixJu45ZGrR55YwuO5jvfqFNTMLcjiq0XZbNppld87P4Ohi9ktkZ5leGUi4BYIBW0Pf2Wp363cjOaROhuiXy3KJiczlXy7f/ey6Tm8sqeWwux0/uesPLwe3I3TvHHpl6Tqhb+uIwcQs4hHUUYSmkc+zAjPAf/Fns+ZnJXmlrxXnjhDsX8Mz6wqZVdVE8+sKnVnSUZ6kuF509dPyHAfK5k4xu3lfWtBFu8ePsXahfnu8yI91GAIVs3J44/Vp8keneJ+edR9eYGNy4s43dZJW3uATTtr2LC8KKoRj3xdJ1ME4JmI1ElFUS6ilZ0JJp7VgI4X7FRFrpqTx+8OnHS98HCjF+u8Tll9eCWj09Hwgt14aoNdgn85QxqZNbOydCLvHm501/cl5j3Y4uWKMlCoRz5IiGcPaysH3M/7VU2sKPXzg5UlPLOqlGDo0int0c67ZnMZr1c0uN0Sn31gJoFgyC0QSk3ysmF5EZt21gCXn/zuFBdtLa9j9uSxbC2vY+3CfDcM09tsD80UUZTuUY98AIhXx7wrfZ2e9iqvON7CwfpW1wPuyRXDRY98PFvsUnknHBN+dXAl2R6aKaIoXVGPfBARjx7WvZkWE3neH95bcsm575rhp6HlQhcPuCf9Q5zK0ncPWymOjhF3YvS9yfbQTBFF6SHGmITfZs6caUYyu6oaTek/bDf/vK3SlP7DdrOrqvGKX2PTzqpLnrerqtFs2lnV6/M6x53HI3/vyd/Um+cqitIzgL0mik1VQ55gBsrg9eS8vflyiMdzFUXpGbEMucbIE8xA9bDW3tmKMvTRwRKKoihDHN3sVPqN8KEWDgNVSq8oIxE15EqfiWduvKIoV06fB0soSnjrWZ0mryiJRz1yJS7EIzdeUZTeoYZciQtaSq8oA4cacqXP9KbKVFGU+KGGXOkzWkqvKAOL5pEriqIMETSPXFEUZZiihlxRFGWIo4ZcURRliKOGfISiZfWKMnxQQz5C0bJ6RRk+aIn+CEXL6hVl+KAe+QhGy+oVZXighnwEo2X1ijI8UEM+QtGyekUZPvTZkIvIX4vIIRE5KCI/jodQSv+jZfWKMnzo02aniHwVuAcoMca0i8jV8RFL6W+izemcWzBe4+SKMgTpq0e+FvhHY0w7gDHmi76LpCiKolwJfTXkU4H5IrJHRN4VkZtjLRSRR0Rkr4jsbWxs7ONpFUVRFIduQysi8jYwIcqhjfbzxwK3ADcD/y4i+SZKS0VjzHPAc2B1P+yL0IqiKMpFujXkxpjFsY6JyFrgNdtwfygiIWA8oC63oihKguhraGUrcBuAiEwFkgHNX1MURUkgfS3RfwF4QUQOAB3AN6OFVRRFUZT+o0+G3BjTAfyvOMmiKIqi9IJhVdmprVkVRRmJDCtDrq1ZFUUZiQyrNrbamlVRlJHIsPLIQVuzKooy8hh2hlxbsyqKMtIYVoZcW7MqijISGVaGXFuzKooyEpGBqN+ZNWuW2bt3b8LPqyiKMpQRkTJjzKzIx4eVR64oijISUUOuKIoyxFFDriiKMsRRQ64oijLEUUOuKIoyxBmQrBURaQSO9cNLj2fw90NXGePDYJdxsMsHKmO8SKSM1xpjsiMfHBBD3l+IyN5oqTmDCZUxPgx2GQe7fKAyxovBIKOGVhRFUYY4asgVRVGGOMPNkD830AL0AJUxPgx2GQe7fKAyxosBl3FYxcgVRVFGIsPNI1cURRlxqCFXFEUZ4gwpQy4i94nIQREJicisiGOPi0iViBwSkaUxnj9ORP5LRI7YP8cmQOZXRWSffTsqIvtirDsqIp/Y6xLWGlJE/l5E6sJkvCPGuttt3VaJyGOJks8+909EpFJEKkRki4hcFWNdwnXYnV7E4mn7eIWI3JQIucLOnycivxeRz+z/nf8TZc1CEWkJ+wz8XSJltGW47Hs3CPQ4LUw/+0SkVUT+JmLNwOnRGDNkbsD1wDRgJzAr7PEbgP1ACnAdUA14ozz/x8Bj9v3HgB8lWP5/Bv4uxrGjwPgB0OnfA9/tZo3X1mk+kGzr+oYEyrgE8Nn3fxTrfUu0DnuiF+AO4HeAALcAexL8/uYCN9n3M4DDUWRcCLye6M/elbx3A63HKO/7CazinEGhxyHlkRtjPjPGHIpy6B7g34wx7caYPwFVwOwY6162778MrOgfSS9FRAT4GvCrRJ0zjswGqowxNcaYDuDfsHSZEIwx240xAfvXD4BJiTp3N/REL/cA/89YfABcJSK5iRLQGNNgjPnYvn8G+AyYmKjzx5EB1WMEi4BqY0x/VKf3iiFlyC/DRKA27PfjRP+w5hhjGsD6gANXJ0A2h/nASWPMkRjHDbBdRMpE5JEEygXwHfty9YUY4aae6jcRPITlmUUj0TrsiV4Gje5EZDJQCuyJcvgrIrJfRH4nIsUJFcyiu/du0OgR+AaxHbIB0aMvUSfqKSLyNjAhyqGNxphfx3palMcSllfZQ5n/kst747caY+pF5Grgv0Sk0hjzh/6WD9gEPIGlryewwj8PRb5ElOfGVb890aGIbAQCwCsxXqbfdBiDnuhlQD+brhAio4H/D/yNMaY14vDHWGGCs/YeyVZgSoJF7O69Gyx6TAbuBh6PcnjA9DjoDLkxZnEvnnYcyAv7fRJQH2XdSRHJNcY02JdlX/RGxki6k1lEfMC9wMzLvEa9/fMLEdmCddkeFyPUU52KyPPA61EO9VS/vaYHOvwmcCewyNgBySiv0W86jEFP9NLvuusOEUnCMuKvGGNeizwebtiNMW+KyL+IyHhjTMKaVfXgvRtwPdosAz42xpyMPDCQehwuoZXfAN8QkRQRuQ7rW/DDGOu+ad//JhDLw483i4FKY8zxaAdFJF1EMpz7WJt7BxIhWESccWWM834ETBGR62yP5BtYukwIInI78H3gbmNMW4w1A6HDnujlN8D/trMubgFanPBeIrD3Zn4OfGaMeSrGmgn2OkRkNpZdaEqgjD157wZUj2HEvLIeUD0OxA5rb29YhuY40A6cBLaFHduIlUFwCFgW9vj/xc5wAbKAHcAR++e4BMn9EvBoxGN+4E37fj5WxsN+4CBWOCFROt0MfAJUYP2z5EbKZ/9+B1bGQ3Ui5bPPXYUVH91n3/51sOgwml6AR53R1ND7AAAAd0lEQVT3Gysk8DP7+CeEZVslSL55WCGIijD93REh43dsne3H2kyem2AZo753g0mPtgxpWIZ5TNhjg0KPWqKvKIoyxBkuoRVFUZQRixpyRVGUIY4ackVRlCGOGnJFUZQhjhpyRVGUIY4ackVRlCGOGnJFUZQhzn8DY+w+bSRIuBwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/chapter8_77_1.png"
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extract the relevant columns from the centered design matrix of dim n x 2\n",
    "x = X_centered[:,0]\n",
    "y = X_centered[:,1]\n",
    "Cov = np.zeros((2,2))\n",
    "Cov[0,1] = np.sum(x.T@y)/(n-1.0)\n",
    "Cov[0,0] = np.sum(x.T@x)/(n-1.0)\n",
    "Cov[1,1] = np.sum(y.T@y)/(n-1.0)\n",
    "Cov[1,0]= Cov[0,1]\n",
    "print(\"Centered covariance using own code\")\n",
    "print(Cov)\n",
    "plt.plot(x, y, 'x')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Depending on the number of points $n$, we will get results that are close to the covariance values defined above.\n",
    "The plot shows how the data are clustered around a line with slope close to one. Is this expected?\n",
    "\n",
    "### Diagonalize the sample covariance matrix to obtain the principal components\n",
    "\n",
    "Now we are ready to solve for the principal components! To do so we\n",
    "diagonalize the sample covariance matrix $\\Sigma$. We can use the\n",
    "function **np.linalg.eig** to do so. It will return the eigenvalues and\n",
    "eigenvectors of $\\Sigma$. Once we have these we can perform the \n",
    "following tasks:\n",
    "\n",
    "* We compute the percentage of the total variance captured by the first principal component\n",
    "\n",
    "* We plot the mean centered data and lines along the first and second principal components\n",
    "\n",
    "* Then we project the mean centered data onto the first and second principal components, and plot the projected data. \n",
    "\n",
    "* Finally, we approximate the data as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "x_i \\approx \\tilde{x}_i = \\mu_n + \\langle x_i, v_0 \\rangle v_0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $v_0$ is the first principal component. \n",
    "\n",
    "Collecting all these steps we can write our own PCA function and\n",
    "compare this with the functionality included in **Scikit-Learn**.  \n",
    "\n",
    "The code here outlines some of the elements we could include in the\n",
    "analysis. Feel free to extend upon this in order to address the above\n",
    "questions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues of Covariance matrix\n",
      "5.082577137078103\n",
      "0.7530509884519185\n",
      "First eigenvector\n",
      "[0.85042593 0.5260948 ]\n",
      "Second eigenvector\n",
      "[-0.5260948   0.85042593]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvector of largest eigenvalue\n",
      "[-0.85042593 -0.5260948 ]\n"
     ]
    }
   ],
   "source": [
    "# diagonalize and obtain eigenvalues, not necessarily sorted\n",
    "EigValues, EigVectors = np.linalg.eig(Cov)\n",
    "# sort eigenvectors and eigenvalues\n",
    "#permute = EigValues.argsort()\n",
    "#EigValues = EigValues[permute]\n",
    "#EigVectors = EigVectors[:,permute]\n",
    "print(\"Eigenvalues of Covariance matrix\")\n",
    "for i in range(2):\n",
    "    print(EigValues[i])\n",
    "FirstEigvector = EigVectors[:,0]\n",
    "SecondEigvector = EigVectors[:,1]\n",
    "print(\"First eigenvector\")\n",
    "print(FirstEigvector)\n",
    "print(\"Second eigenvector\")\n",
    "print(SecondEigvector)\n",
    "#thereafter we do a PCA with Scikit-learn\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components = 2)\n",
    "X2Dsl = pca.fit_transform(X)\n",
    "print(\"Eigenvector of largest eigenvalue\")\n",
    "print(pca.components_.T[:, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This code does not contain all the above elements, but it shows how we can use **Scikit-Learn** to extract the eigenvector which corresponds to the largest eigenvalue. Try to address the questions we pose before the above code.  Try also to change the values of the covariance matrix by making one of the diagonal elements much larger than the other. What do you observe then? \n",
    "\n",
    "\n",
    "## Classical PCA Theorem\n",
    "\n",
    "We assume now that we have a design matrix $\\boldsymbol{X}$ which has been\n",
    "centered as discussed above. For the sake of simplicity we skip the\n",
    "overline symbol. The matrix is defined in terms of the various column\n",
    "vectors $[\\boldsymbol{x}_0,\\boldsymbol{x}_1,\\dots, \\boldsymbol{x}_{p-1}]$ each with dimension\n",
    "$\\boldsymbol{x}\\in {\\mathbb{R}}^{n}$.\n",
    "\n",
    "We assume also that we have an orthogonal transformation $\\boldsymbol{W}\\in {\\mathbb{R}}^{p\\times p}$.  We define the reconstruction error (which is similar to the mean squared error we have seen before) as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "J(\\boldsymbol{W},\\boldsymbol{Z}) = \\frac{1}{n}\\sum_i (\\boldsymbol{x}_i - \\overline{\\boldsymbol{x}}_i)^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with $\\overline{\\boldsymbol{x}}_i = \\boldsymbol{W}\\boldsymbol{z}_i$, where $\\boldsymbol{z}_i$ is a row vector with dimension ${\\mathbb{R}}^{n}$ of the matrix\n",
    "$\\boldsymbol{Z}\\in{\\mathbb{R}}^{p\\times n}$.  When doing PCA we want to reduce this dimensionality. \n",
    "\n",
    "The PCA theorem states that minimizing the above reconstruction error\n",
    "corresponds to setting $\\boldsymbol{W}=\\boldsymbol{S}$, the orthogonal matrix which\n",
    "diagonalizes the empirical covariance(correlation) matrix. The optimal\n",
    "low-dimensional encoding of the data is then given by a set of vectors\n",
    "$\\boldsymbol{z}_i$ with at most $l$ vectors, with $l << p$, defined by the\n",
    "orthogonal projection of the data onto the columns spanned by the\n",
    "eigenvectors of the covariance(correlations matrix).\n",
    "\n",
    "The proof which follows will be updated by mid January 2020.\n",
    "\n",
    "\n",
    "## Proof of the PCA Theorem\n",
    "\n",
    "To show the PCA theorem let us start with the assumption that there is one vector $\\boldsymbol{w}_0$ which corresponds to a solution which minimized the reconstruction error $J$. This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of $\\boldsymbol{w}_0$ and $\\boldsymbol{z}_0$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "J(\\boldsymbol{w}_0,\\boldsymbol{z}_0)= \\frac{1}{n}\\sum_i (\\boldsymbol{x}_i - z_{i0}\\boldsymbol{w}_0)^2=\\frac{1}{n}\\sum_i (\\boldsymbol{x}_i^T\\boldsymbol{x}_i - 2z_{i0}\\boldsymbol{w}_0^T\\boldsymbol{x}_i+z_{i0}^2\\boldsymbol{w}_0^T\\boldsymbol{w}_0),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which we can rewrite due to the orthogonality of $\\boldsymbol{w}_i$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "J(\\boldsymbol{w}_0,\\boldsymbol{z}_0)=\\frac{1}{n}\\sum_i (\\boldsymbol{x}_i^T\\boldsymbol{x}_i - 2z_{i0}\\boldsymbol{w}_0^T\\boldsymbol{x}_i+z_{i0}^2).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Minimizing $J$ with respect to the unknown parameters $z_{0i}$ we obtain that"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "z_{i0}=\\boldsymbol{w}_0^T\\boldsymbol{x}_i,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where the vectors on the rhs are known. \n",
    "\n",
    "\n",
    "\n",
    "## PCA Proof continued\n",
    "\n",
    "We have now found the unknown parameters $z_{i0}$. These correspond to the projected coordinates and we can write"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "J(\\boldsymbol{w}_0)= \\frac{1}{p}\\sum_i (\\boldsymbol{x}_i^T\\boldsymbol{x}_i - z_{i0}^2)=\\mathrm{const}-\\frac{1}{n}\\sum_i z_{i0}^2.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can show that the variance of the projected coordinates defined by $\\boldsymbol{w}_0^T\\boldsymbol{x}_i$ are given by"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{var}[\\boldsymbol{w}_0^T\\boldsymbol{x}_i] = \\frac{1}{n}\\sum_i z_{i0}^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "since the expectation value of"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{E}[\\boldsymbol{w}_0^T\\boldsymbol{x}_i] = \\mathbb{E}[z_{i0}]= \\boldsymbol{w}_0^T\\mathbb{E}[\\boldsymbol{x}_i]=0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where we have used the fact that our data are centered.\n",
    "\n",
    "Recalling our definition of the covariance as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{C}[\\boldsymbol{x}] = \\frac{1}{n}\\boldsymbol{X}\\boldsymbol{X}^T=\\mathbb{E}[\\boldsymbol{X}\\boldsymbol{X}^T],\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we have thus that"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{var}[\\boldsymbol{w}_0^T\\boldsymbol{x}_i] = \\frac{1}{n}\\sum_i z_{i0}^2=\\boldsymbol{w}_0^T\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are almost there, we have obtained a relation between minimizing\n",
    "the reconstruction error and the variance and the covariance\n",
    "matrix. Minimizing the error is equivalent to maximizing the variance\n",
    "of the projected data.\n",
    "\n",
    "\n",
    "## The final step\n",
    "\n",
    "We could trivially maximize the variance of the projection (and\n",
    "thereby minimize the error in the reconstruction function) by letting\n",
    "the norm-2 of $\\boldsymbol{w}_0$ go to infinity. However, this norm since we\n",
    "want the matrix $\\boldsymbol{W}$ to be an orthogonal matrix, is constrained by\n",
    "$\\vert\\vert \\boldsymbol{w}_0 \\vert\\vert_2^2=1$. Imposing this condition via a\n",
    "Lagrange multiplier we can then in turn maximize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "J(\\boldsymbol{w}_0)= \\boldsymbol{w}_0^T\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0+\\lambda_0(1-\\boldsymbol{w}_0^T\\boldsymbol{w}_0).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taking the derivative with respect to $\\boldsymbol{w}_0$ we obtain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{\\partial J(\\boldsymbol{w}_0)}{\\partial \\boldsymbol{w}_0}= 2\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0-2\\lambda_0\\boldsymbol{w}_0=0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "meaning that"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0=\\lambda_0\\boldsymbol{w}_0.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The direction that maximizes the variance (or minimizes the construction error) is an eigenvector of the covariance matrix**! If we left multiply with $\\boldsymbol{w}_0^T$ we have the variance of the projected data is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{w}_0^T\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0=\\lambda_0.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to maximize the variance (minimize the construction error)\n",
    "we simply pick the eigenvector of the covariance matrix with the\n",
    "largest eigenvalue. This establishes the link between the minimization\n",
    "of the reconstruction function $J$ in terms of an orthogonal matrix\n",
    "and the maximization of the variance and thereby the covariance of our\n",
    "observations encoded in the design/feature matrix $\\boldsymbol{X}$.\n",
    "\n",
    "The proof\n",
    "for the other eigenvectors $\\boldsymbol{w}_1,\\boldsymbol{w}_2,\\dots$ can be\n",
    "established by applying the above arguments and using the fact that\n",
    "our basis of eigenvectors is orthogonal, see [Murphy chapter\n",
    "12.2](https://mitpress.mit.edu/books/machine-learning-1).  The\n",
    "discussion in chapter 12.2 of Murphy's text has also a nice link with\n",
    "the Singular Value Decomposition theorem. For categorical data, see\n",
    "chapter 12.4 and discussion therein.\n",
    "\n",
    "Additional part of the proof for the other eigenvectors will be added by mid January 2020.\n",
    "\n",
    "\n",
    "## Geometric Interpretation and link with Singular Value Decomposition\n",
    "\n",
    "This material will be added by mid January 2020.\n",
    "\n",
    "\n",
    "\n",
    "## Principal Component Analysis\n",
    "\n",
    "Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.\n",
    "First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.\n",
    "\n",
    "The following Python code uses NumPy’s **svd()** function to obtain all the principal components of the\n",
    "training set, then extracts the first two principal components. First we center the data using either **pandas** or our own code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.574465</td>\n",
       "      <td>0.259153</td>\n",
       "      <td>1.197370</td>\n",
       "      <td>0.147400</td>\n",
       "      <td>0.649382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.689519</td>\n",
       "      <td>0.137652</td>\n",
       "      <td>-1.025709</td>\n",
       "      <td>0.210340</td>\n",
       "      <td>-0.076938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.282727</td>\n",
       "      <td>0.351636</td>\n",
       "      <td>-0.539261</td>\n",
       "      <td>1.216683</td>\n",
       "      <td>0.340782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.070889</td>\n",
       "      <td>-0.614808</td>\n",
       "      <td>1.074067</td>\n",
       "      <td>-0.038300</td>\n",
       "      <td>-1.450257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.794282</td>\n",
       "      <td>1.458078</td>\n",
       "      <td>-0.207545</td>\n",
       "      <td>-0.442600</td>\n",
       "      <td>-0.147420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.112383</td>\n",
       "      <td>0.647473</td>\n",
       "      <td>1.405890</td>\n",
       "      <td>0.073598</td>\n",
       "      <td>-0.276263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.397700</td>\n",
       "      <td>-1.526744</td>\n",
       "      <td>-0.712018</td>\n",
       "      <td>1.216290</td>\n",
       "      <td>0.418506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.280647</td>\n",
       "      <td>1.106095</td>\n",
       "      <td>-1.646283</td>\n",
       "      <td>-0.956563</td>\n",
       "      <td>-1.564374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.369139</td>\n",
       "      <td>-0.751699</td>\n",
       "      <td>0.051649</td>\n",
       "      <td>-0.213103</td>\n",
       "      <td>0.967809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-1.557795</td>\n",
       "      <td>-1.066837</td>\n",
       "      <td>0.401842</td>\n",
       "      <td>-1.213743</td>\n",
       "      <td>1.138775</td>\n",
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       "          0         1         2         3         4\n",
       "0 -1.574465  0.259153  1.197370  0.147400  0.649382\n",
       "1  0.689519  0.137652 -1.025709  0.210340 -0.076938\n",
       "2 -0.282727  0.351636 -0.539261  1.216683  0.340782\n",
       "3  0.070889 -0.614808  1.074067 -0.038300 -1.450257\n",
       "4  1.794282  1.458078 -0.207545 -0.442600 -0.147420\n",
       "5  1.112383  0.647473  1.405890  0.073598 -0.276263\n",
       "6  0.397700 -1.526744 -0.712018  1.216290  0.418506\n",
       "7 -0.280647  1.106095 -1.646283 -0.956563 -1.564374\n",
       "8 -0.369139 -0.751699  0.051649 -0.213103  0.967809\n",
       "9 -1.557795 -1.066837  0.401842 -1.213743  1.138775"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     0    1    2    3    4\n",
      "0  0.0  0.0  0.0  0.0  0.0\n",
      "1  0.0  0.0  0.0  0.0  0.0\n",
      "2  0.0  0.0  0.0  0.0  0.0\n",
      "3  0.0  0.0  0.0  0.0  0.0\n",
      "4  0.0  0.0  0.0  0.0  0.0\n",
      "5  0.0  0.0  0.0  0.0  0.0\n",
      "6  0.0  0.0  0.0  0.0  0.0\n",
      "7  0.0  0.0  0.0  0.0  0.0\n",
      "8  0.0  0.0  0.0  0.0  0.0\n",
      "9  0.0  0.0  0.0  0.0  0.0\n",
      "[[-1.5378811  -0.94639099]\n",
      " [ 0.86145244  0.89288636]\n",
      " [-0.00445655  0.81633628]\n",
      " [ 0.07145103 -1.00433417]\n",
      " [ 2.03707133 -0.48476997]\n",
      " [ 0.72174172 -1.4557763 ]\n",
      " [-0.55854694  1.60673226]\n",
      " [ 1.6999536   0.43766686]\n",
      " [-1.10405456  0.31718909]\n",
      " [-2.18673098 -0.17953942]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from IPython.display import display\n",
    "np.random.seed(100)\n",
    "# setting up a 10 x 5 vanilla matrix \n",
    "rows = 10\n",
    "cols = 5\n",
    "X = np.random.randn(rows,cols)\n",
    "df = pd.DataFrame(X)\n",
    "# Pandas does the centering for us\n",
    "df = df -df.mean()\n",
    "display(df)\n",
    "\n",
    "# we center it ourselves\n",
    "X_centered = X - X.mean(axis=0)\n",
    "# Then check the difference between pandas and our own set up\n",
    "print(X_centered-df)\n",
    "#Now we do an SVD\n",
    "U, s, V = np.linalg.svd(X_centered)\n",
    "c1 = V.T[:, 0]\n",
    "c2 = V.T[:, 1]\n",
    "W2 = V.T[:, :2]\n",
    "X2D = X_centered.dot(W2)\n",
    "print(X2D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA assumes that the dataset is centered around the origin. Scikit-Learn’s PCA classes take care of centering\n",
    "the data for you. However, if you implement PCA yourself (as in the preceding example), or if you use other libraries, don’t\n",
    "forget to center the data first.\n",
    "\n",
    "Once you have identified all the principal components, you can reduce the dimensionality of the dataset\n",
    "down to $d$ dimensions by projecting it onto the hyperplane defined by the first $d$ principal components.\n",
    "Selecting this hyperplane ensures that the projection will preserve as much variance as possible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "W2 = V.T[:, :2]\n",
    "X2D = X_centered.dot(W2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA and scikit-learn\n",
    "\n",
    "Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The\n",
    "following code applies PCA to reduce the dimensionality of the dataset down to two dimensions (note\n",
    "that it automatically takes care of centering the data):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.5378811  -0.94639099]\n",
      " [-0.86145244  0.89288636]\n",
      " [ 0.00445655  0.81633628]\n",
      " [-0.07145103 -1.00433417]\n",
      " [-2.03707133 -0.48476997]\n",
      " [-0.72174172 -1.4557763 ]\n",
      " [ 0.55854694  1.60673226]\n",
      " [-1.6999536   0.43766686]\n",
      " [ 1.10405456  0.31718909]\n",
      " [ 2.18673098 -0.17953942]]\n"
     ]
    }
   ],
   "source": [
    "#thereafter we do a PCA with Scikit-learn\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components = 2)\n",
    "X2D = pca.fit_transform(X)\n",
    "print(X2D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After fitting the PCA transformer to the dataset, you can access the principal components using the\n",
    "components variable (note that it contains the PCs as horizontal vectors, so, for example, the first\n",
    "principal component is equal to"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-19-17314f270d45>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-19-17314f270d45>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    pca.components_.T[:, 0].\u001b[0m\n\u001b[0m                            ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "pca.components_.T[:, 0]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another very useful piece of information is the explained variance ratio of each principal component,\n",
    "available via the $explained\\_variance\\_ratio$ variable. It indicates the proportion of the dataset’s\n",
    "variance that lies along the axis of each principal component. \n",
    "\n",
    "\n",
    "## Back to the Cancer Data\n",
    "We can now repeat the above but applied to real data, in this case our breast cancer data.\n",
    "Here we compute performance scores on the training data using logistic regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "cancer = load_breast_cancer()\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
    "\n",
    "logreg = LogisticRegression()\n",
    "logreg.fit(X_train, y_train)\n",
    "print(\"Train set accuracy from Logistic Regression: {:.2f}\".format(logreg.score(X_train,y_train)))\n",
    "# We scale the data\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "# Then perform again a log reg fit\n",
    "logreg.fit(X_train_scaled, y_train)\n",
    "print(\"Train set accuracy scaled data: {:.2f}\".format(logreg.score(X_train_scaled,y_train)))\n",
    "#thereafter we do a PCA with Scikit-learn\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components = 2)\n",
    "X2D_train = pca.fit_transform(X_train_scaled)\n",
    "# and finally compute the log reg fit and the score on the training data\t\n",
    "logreg.fit(X2D_train,y_train)\n",
    "print(\"Train set accuracy scaled and PCA data: {:.2f}\".format(logreg.score(X2D_train,y_train)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that our training data after the PCA decomposition has a performance similar to the non-scaled data. \n",
    "\n",
    "\n",
    "## More on the PCA\n",
    "\n",
    "Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to\n",
    "choose the number of dimensions that add up to a sufficiently large portion of the variance (e.g., 95%).\n",
    "Unless, of course, you are reducing dimensionality for data visualization — in that case you will\n",
    "generally want to reduce the dimensionality down to 2 or 3.\n",
    "The following code computes PCA without reducing dimensionality, then computes the minimum number\n",
    "of dimensions required to preserve 95% of the training set’s variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pca = PCA()\n",
    "pca.fit(X)\n",
    "cumsum = np.cumsum(pca.explained_variance_ratio_)\n",
    "d = np.argmax(cumsum >= 0.95) + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You could then set $n\\_components=d$ and run PCA again. However, there is a much better option: instead\n",
    "of specifying the number of principal components you want to preserve, you can set $n\\_components$ to be\n",
    "a float between 0.0 and 1.0, indicating the ratio of variance you wish to preserve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pca = PCA(n_components=0.95)\n",
    "X_reduced = pca.fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Incremental PCA\n",
    "\n",
    "One problem with the preceding implementation of PCA is that it requires the whole training set to fit in\n",
    "memory in order for the SVD algorithm to run. Fortunately, Incremental PCA (IPCA) algorithms have\n",
    "been developed: you can split the training set into mini-batches and feed an IPCA algorithm one minibatch\n",
    "at a time. This is useful for large training sets, and also to apply PCA online (i.e., on the fly, as new\n",
    "instances arrive).\n",
    "\n",
    "\n",
    "## Randomized PCA\n",
    "\n",
    "Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic\n",
    "algorithm that quickly finds an approximation of the first d principal components. Its computational\n",
    "complexity is $O(m \\times d^2)+O(d^3)$, instead of $O(m \\times n^2) + O(n^3)$, so it is dramatically faster than the\n",
    "previous algorithms when $d$ is much smaller than $n$.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## Kernel PCA\n",
    "\n",
    "The kernel trick is a mathematical technique that implicitly maps instances into a\n",
    "very high-dimensional space (called the feature space), enabling nonlinear classification and regression\n",
    "with Support Vector Machines. Recall that a linear decision boundary in the high-dimensional feature\n",
    "space corresponds to a complex nonlinear decision boundary in the original space.\n",
    "It turns out that the same trick can be applied to PCA, making it possible to perform complex nonlinear\n",
    "projections for dimensionality reduction. This is called Kernel PCA (kPCA). It is often good at\n",
    "preserving clusters of instances after projection, or sometimes even unrolling datasets that lie close to a\n",
    "twisted manifold.\n",
    "For example, the following code uses Scikit-Learn’s KernelPCA class to perform kPCA with an"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import KernelPCA\n",
    "rbf_pca = KernelPCA(n_components = 2, kernel=\"rbf\", gamma=0.04)\n",
    "X_reduced = rbf_pca.fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LLE\n",
    "\n",
    "Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction\n",
    "(NLDR) technique. It is a Manifold Learning technique that does not rely on projections like the previous\n",
    "algorithms. In a nutshell, LLE works by first measuring how each training instance linearly relates to its\n",
    "closest neighbors (c.n.), and then looking for a low-dimensional representation of the training set where\n",
    "these local relationships are best preserved (more details shortly). \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## Other techniques\n",
    "\n",
    "\n",
    "There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.\n",
    "\n",
    "Here are some of the most popular:\n",
    "* **Multidimensional Scaling (MDS)** reduces dimensionality while trying to preserve the distances between the instances.\n",
    "\n",
    "* **Isomap** creates a graph by connecting each instance to its nearest neighbors, then reduces dimensionality while trying to preserve the geodesic distances between the instances.\n",
    "\n",
    "* **t-Distributed Stochastic Neighbor Embedding** (t-SNE) reduces dimensionality while trying to keep similar instances close and dissimilar instances apart. It is mostly used for visualization, in particular to visualize clusters of instances in high-dimensional space (e.g., to visualize the MNIST images in 2D).\n",
    "\n",
    "* Linear Discriminant Analysis (LDA) is actually a classification algorithm, but during training it learns the most discriminative axes between the classes, and these axes can then be used to define a hyperplane onto which to project the data. The benefit is that the projection will keep classes as far apart as possible, so LDA is a good technique to reduce dimensionality before running another classification algorithm such as a Support Vector Machine (SVM) classifier discussed in the SVM lectures."
   ]
  }
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