Morten Hjorth-Jensen
2025 lines
443 KiB
Plaintext
2025 lines
443 KiB
Plaintext
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"# Support Vector Machines, overarching aims\n",
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"\n",
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"A Support Vector Machine (SVM) is a very powerful and versatile\n",
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"Machine Learning method, capable of performing linear or nonlinear\n",
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"classification, regression, and even outlier detection. It is one of\n",
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"the most popular models in Machine Learning, and anyone interested in\n",
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"Machine Learning should have it in their toolbox. SVMs are\n",
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"particularly well suited for classification of complex but small-sized or\n",
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"medium-sized datasets. \n",
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"\n",
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"The case with two well-separated classes only can be understood in an\n",
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"intuitive way in terms of lines in a two-dimensional space separating\n",
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"the two classes (see figure below).\n",
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"\n",
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"The basic mathematics behind the SVM is however less familiar to most of us. \n",
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"It relies on the definition of hyperplanes and the\n",
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"definition of a **margin** which separates classes (in case of\n",
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"classification problems) of variables. It is also used for regression\n",
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"problems.\n",
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"\n",
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"With SVMs we distinguish between hard margin and soft margins. The\n",
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"latter introduces a so-called softening parameter to be discussed\n",
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"below. We distinguish also between linear and non-linear\n",
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"approaches. The latter are the most frequent ones since it is rather\n",
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"unlikely that we can separate classes easily by say straight lines.\n",
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"\n",
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"\n",
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"## Hyperplanes and all that\n",
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"\n",
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"The theory behind support vector machines (SVM hereafter) is based on\n",
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"the mathematical description of so-called hyperplanes. Let us start\n",
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"with a two-dimensional case. This will also allow us to introduce our\n",
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"first SVM examples. These will be tailored to the case of two specific\n",
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"classes, as displayed in the figure here based on the usage of the petal data.\n",
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"\n",
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"We assume here that our data set can be well separated into two\n",
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"domains, where a straight line does the job in the separating the two\n",
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"classes. Here the two classes are represented by either squares or\n",
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"circles."
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"text": [
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"LinearSVC: [0.28475098] [[1.05364854 1.09903804]]\n",
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"SVC: [0.31896852] [[1.1203284 1.02625193]]\n",
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"SGDClassifier(alpha=0.00200): [0.117] [[0.77714169 0.72981762]]\n"
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"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/svm/_classes.py:32: FutureWarning: The default value of `dual` will change from `True` to `'auto'` in 1.5. Set the value of `dual` explicitly to suppress the warning.\n",
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" warnings.warn(\n"
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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_1_2.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"from sklearn import datasets\n",
|
||
"from sklearn.svm import SVC, LinearSVC\n",
|
||
"from sklearn.linear_model import SGDClassifier\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"import matplotlib\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"plt.rcParams['axes.labelsize'] = 14\n",
|
||
"plt.rcParams['xtick.labelsize'] = 12\n",
|
||
"plt.rcParams['ytick.labelsize'] = 12\n",
|
||
"\n",
|
||
"\n",
|
||
"iris = datasets.load_iris()\n",
|
||
"X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n",
|
||
"y = iris[\"target\"]\n",
|
||
"\n",
|
||
"setosa_or_versicolor = (y == 0) | (y == 1)\n",
|
||
"X = X[setosa_or_versicolor]\n",
|
||
"y = y[setosa_or_versicolor]\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"C = 5\n",
|
||
"alpha = 1 / (C * len(X))\n",
|
||
"\n",
|
||
"lin_clf = LinearSVC(loss=\"hinge\", C=C, random_state=42)\n",
|
||
"svm_clf = SVC(kernel=\"linear\", C=C)\n",
|
||
"sgd_clf = SGDClassifier(loss=\"hinge\", learning_rate=\"constant\", eta0=0.001, alpha=alpha,\n",
|
||
" max_iter=100000, random_state=42)\n",
|
||
"\n",
|
||
"scaler = StandardScaler()\n",
|
||
"X_scaled = scaler.fit_transform(X)\n",
|
||
"\n",
|
||
"lin_clf.fit(X_scaled, y)\n",
|
||
"svm_clf.fit(X_scaled, y)\n",
|
||
"sgd_clf.fit(X_scaled, y)\n",
|
||
"\n",
|
||
"print(\"LinearSVC: \", lin_clf.intercept_, lin_clf.coef_)\n",
|
||
"print(\"SVC: \", svm_clf.intercept_, svm_clf.coef_)\n",
|
||
"print(\"SGDClassifier(alpha={:.5f}):\".format(sgd_clf.alpha), sgd_clf.intercept_, sgd_clf.coef_)\n",
|
||
"\n",
|
||
"# Compute the slope and bias of each decision boundary\n",
|
||
"w1 = -lin_clf.coef_[0, 0]/lin_clf.coef_[0, 1]\n",
|
||
"b1 = -lin_clf.intercept_[0]/lin_clf.coef_[0, 1]\n",
|
||
"w2 = -svm_clf.coef_[0, 0]/svm_clf.coef_[0, 1]\n",
|
||
"b2 = -svm_clf.intercept_[0]/svm_clf.coef_[0, 1]\n",
|
||
"w3 = -sgd_clf.coef_[0, 0]/sgd_clf.coef_[0, 1]\n",
|
||
"b3 = -sgd_clf.intercept_[0]/sgd_clf.coef_[0, 1]\n",
|
||
"\n",
|
||
"# Transform the decision boundary lines back to the original scale\n",
|
||
"line1 = scaler.inverse_transform([[-10, -10 * w1 + b1], [10, 10 * w1 + b1]])\n",
|
||
"line2 = scaler.inverse_transform([[-10, -10 * w2 + b2], [10, 10 * w2 + b2]])\n",
|
||
"line3 = scaler.inverse_transform([[-10, -10 * w3 + b3], [10, 10 * w3 + b3]])\n",
|
||
"\n",
|
||
"# Plot all three decision boundaries\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.plot(line1[:, 0], line1[:, 1], \"k:\", label=\"LinearSVC\")\n",
|
||
"plt.plot(line2[:, 0], line2[:, 1], \"b--\", linewidth=2, label=\"SVC\")\n",
|
||
"plt.plot(line3[:, 0], line3[:, 1], \"r-\", label=\"SGDClassifier\")\n",
|
||
"plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\") # label=\"Iris-Versicolor\"\n",
|
||
"plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\") # label=\"Iris-Setosa\"\n",
|
||
"plt.xlabel(\"Petal length\", fontsize=14)\n",
|
||
"plt.ylabel(\"Petal width\", fontsize=14)\n",
|
||
"plt.legend(loc=\"upper center\", fontsize=14)\n",
|
||
"plt.axis([0, 5.5, 0, 2])\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The aim of the SVM algorithm is to find a hyperplane in a\n",
|
||
"$p$-dimensional space, where $p$ is the number of features that\n",
|
||
"distinctly classifies the data points.\n",
|
||
"\n",
|
||
"In a $p$-dimensional space, a hyperplane is what we call an affine subspace of dimension of $p-1$.\n",
|
||
"As an example, in two dimension, a hyperplane is simply as straight line while in three dimensions it is \n",
|
||
"a two-dimensional subspace, or stated simply, a plane. \n",
|
||
"\n",
|
||
"In two dimensions, with the variables $x_1$ and $x_2$, the hyperplane is defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"b+w_1x_1+w_2x_2=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $b$ is the intercept and $w_1$ and $w_2$ define the elements of a vector orthogonal to the line \n",
|
||
"$b+w_1x_1+w_2x_2=0$. \n",
|
||
"In two dimensions we define the vectors $\\boldsymbol{x} =[x1,x2]$ and $\\boldsymbol{w}=[w1,w2]$. \n",
|
||
"We can then rewrite the above equation as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}^T\\boldsymbol{w}+b=0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We limit ourselves to two classes of outputs $y_i$ and assign these classes the values $y_i = \\pm 1$. \n",
|
||
"In a $p$-dimensional space of say $p$ features we have a hyperplane defines as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"b+wx_1+w_2x_2+\\dots +w_px_p=0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"If we define a \n",
|
||
"matrix $\\boldsymbol{X}=\\left[\\boldsymbol{x}_1,\\boldsymbol{x}_2,\\dots, \\boldsymbol{x}_p\\right]$\n",
|
||
"of dimension $n\\times p$, where $n$ represents the observations for each feature and each vector $x_i$ is a column vector of the matrix $\\boldsymbol{X}$,"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_i = \\begin{bmatrix} x_{i1} \\\\ x_{i2} \\\\ \\dots \\\\ \\dots \\\\ x_{ip} \\end{bmatrix}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"If the above condition is not met for a given vector $\\boldsymbol{x}_i$ we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"b+w_1x_{i1}+w_2x_{i2}+\\dots +w_px_{ip} >0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"if our output $y_i=1$.\n",
|
||
"In this case we say that $\\boldsymbol{x}_i$ lies on one of the sides of the hyperplane and if"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"b+w_1x_{i1}+w_2x_{i2}+\\dots +w_px_{ip} < 0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"for the class of observations $y_i=-1$, \n",
|
||
"then $\\boldsymbol{x}_i$ lies on the other side. \n",
|
||
"\n",
|
||
"Equivalently, for the two classes of observations we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i\\left(b+w_1x_{i1}+w_2x_{i2}+\\dots +w_px_{ip}\\right) > 0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"When we try to separate hyperplanes, if it exists, we can use it to construct a natural classifier: a test observation is assigned a given class depending on which side of the hyperplane it is located.\n",
|
||
"\n",
|
||
"\n",
|
||
"### The two-dimensional case\n",
|
||
"\n",
|
||
"Let us try to develop our intuition about SVMs by limiting ourselves to a two-dimensional\n",
|
||
"plane. To separate the two classes of data points, there are many\n",
|
||
"possible lines (hyperplanes if you prefer a more strict naming) \n",
|
||
"that could be chosen. Our objective is to find a\n",
|
||
"plane that has the maximum margin, i.e the maximum distance between\n",
|
||
"data points of both classes. Maximizing the margin distance provides\n",
|
||
"some reinforcement so that future data points can be classified with\n",
|
||
"more confidence.\n",
|
||
"\n",
|
||
"What a linear classifier attempts to accomplish is to split the\n",
|
||
"feature space into two half spaces by placing a hyperplane between the\n",
|
||
"data points. This hyperplane will be our decision boundary. All\n",
|
||
"points on one side of the plane will belong to class one and all points\n",
|
||
"on the other side of the plane will belong to the second class two.\n",
|
||
"\n",
|
||
"Unfortunately there are many ways in which we can place a hyperplane\n",
|
||
"to divide the data. Below is an example of two candidate hyperplanes\n",
|
||
"for our data sample.\n",
|
||
"\n",
|
||
"\n",
|
||
"Let us define the function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"f(x) = \\boldsymbol{w}^T\\boldsymbol{x}+b = 0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"as the function that determines the line $L$ that separates two classes (our two features), see the figure here. \n",
|
||
"\n",
|
||
"\n",
|
||
"Any point defined by $\\boldsymbol{x}_i$ and $\\boldsymbol{x}_2$ on the line $L$ will satisfy $\\boldsymbol{w}^T(\\boldsymbol{x}_1-\\boldsymbol{x}_2)=0$. \n",
|
||
"\n",
|
||
"The signed distance $\\delta$ from any point defined by a vector $\\boldsymbol{x}$ and a point $\\boldsymbol{x}_0$ on the line $L$ is then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\delta = \\frac{1}{\\vert\\vert \\boldsymbol{w}\\vert\\vert}(\\boldsymbol{w}^T\\boldsymbol{x}+b).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"How do we find the parameter $b$ and the vector $\\boldsymbol{w}$? What we could\n",
|
||
"do is to define a cost function which now contains the set of all\n",
|
||
"misclassified points $M$ and attempt to minimize this function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{w},b) = -\\sum_{i\\in M} y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We could now for example define all values $y_i =1$ as misclassified in case we have $\\boldsymbol{w}^T\\boldsymbol{x}_i+b < 0$ and the opposite if we have $y_i=-1$. Taking the derivatives gives us"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial C}{\\partial b} = -\\sum_{i\\in M} y_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial C}{\\partial \\boldsymbol{w}} = -\\sum_{i\\in M} y_ix_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We can now use the Newton-Raphson method or different variants of the gradient descent family (from plain gradient descent to various stochastic gradient descent approaches) to solve the equations"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"b \\leftarrow b +\\eta \\frac{\\partial C}{\\partial b},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{w} \\leftarrow \\boldsymbol{w} +\\eta \\frac{\\partial C}{\\partial \\boldsymbol{w}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\eta$ is our by now well-known learning rate. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"The equations we discussed above can be coded rather easily (the\n",
|
||
"framework is similar to what we developed for logistic\n",
|
||
"regression). We are going to set up a simple case with two classes only and we want to find a line which separates them the best possible way."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"There are however problems with this approach, although it looks\n",
|
||
"pretty straightforward to implement. When running the above code, we see that we can easily end up with many diffeent lines which separate the two classes.\n",
|
||
"\n",
|
||
"\n",
|
||
"For small\n",
|
||
"gaps between the entries, we may also end up needing many iterations\n",
|
||
"before the solutions converge and if the data cannot be separated\n",
|
||
"properly into two distinct classes, we may not experience a converge\n",
|
||
"at all.\n",
|
||
"\n",
|
||
"\n",
|
||
"### A better approach\n",
|
||
"\n",
|
||
"A better approach is rather to try to define a large margin between\n",
|
||
"the two classes (if they are well separated from the beginning).\n",
|
||
"\n",
|
||
"Thus, we wish to find a margin $M$ with $\\boldsymbol{w}$ normalized to\n",
|
||
"$\\vert\\vert \\boldsymbol{w}\\vert\\vert =1$ subject to the condition"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) \\geq M \\hspace{0.1cm}\\forall i=1,2,\\dots, p.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"All points are thus at a signed distance from the decision boundary defined by the line $L$. The parameters $b$ and $w_1$ and $w_2$ define this line. \n",
|
||
"\n",
|
||
"We seek thus the largest value $M$ defined by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{1}{\\vert \\vert \\boldsymbol{w}\\vert\\vert}y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) \\geq M \\hspace{0.1cm}\\forall i=1,2,\\dots, n,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"or just"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) \\geq M\\vert \\vert \\boldsymbol{w}\\vert\\vert \\hspace{0.1cm}\\forall i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"If we scale the equation so that $\\vert \\vert \\boldsymbol{w}\\vert\\vert = 1/M$, we have to find the minimum of \n",
|
||
"$\\boldsymbol{w}^T\\boldsymbol{w}=\\vert \\vert \\boldsymbol{w}\\vert\\vert$ (the norm) subject to the condition"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) \\geq 1 \\hspace{0.1cm}\\forall i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We have thus defined our margin as the invers of the norm of\n",
|
||
"$\\boldsymbol{w}$. We want to minimize the norm in order to have a as large as\n",
|
||
"possible margin $M$. Before we proceed, we need to remind ourselves\n",
|
||
"about Lagrangian multipliers.\n",
|
||
"\n",
|
||
"\n",
|
||
"## A quick Reminder on Lagrangian Multipliers\n",
|
||
"\n",
|
||
"Consider a function of three independent variables $f(x,y,z)$ . For the function $f$ to be an\n",
|
||
"extreme we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"df=0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"A necessary and sufficient condition is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial f}{\\partial x} =\\frac{\\partial f}{\\partial y}=\\frac{\\partial f}{\\partial z}=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"due to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"df = \\frac{\\partial f}{\\partial x}dx+\\frac{\\partial f}{\\partial y}dy+\\frac{\\partial f}{\\partial z}dz.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"In many problems the variables $x,y,z$ are often subject to constraints (such as those above for the margin)\n",
|
||
"so that they are no longer all independent. It is possible at least in principle to use each \n",
|
||
"constraint to eliminate one variable\n",
|
||
"and to proceed with a new and smaller set of independent varables.\n",
|
||
"\n",
|
||
"The use of so-called Lagrangian multipliers is an alternative technique when the elimination\n",
|
||
"of variables is incovenient or undesirable. Assume that we have an equation of constraint on \n",
|
||
"the variables $x,y,z$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\phi(x,y,z) = 0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"resulting in"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"d\\phi = \\frac{\\partial \\phi}{\\partial x}dx+\\frac{\\partial \\phi}{\\partial y}dy+\\frac{\\partial \\phi}{\\partial z}dz =0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Now we cannot set anymore"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial f}{\\partial x} =\\frac{\\partial f}{\\partial y}=\\frac{\\partial f}{\\partial z}=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"if $df=0$ is wanted\n",
|
||
"because there are now only two independent variables! Assume $x$ and $y$ are the independent \n",
|
||
"variables.\n",
|
||
"Then $dz$ is no longer arbitrary.\n",
|
||
"\n",
|
||
"\n",
|
||
"However, we can add to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"df = \\frac{\\partial f}{\\partial x}dx+\\frac{\\partial f}{\\partial y}dy+\\frac{\\partial f}{\\partial z}dz,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"a multiplum of $d\\phi$, viz. $\\lambda d\\phi$, resulting in"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"df+\\lambda d\\phi = (\\frac{\\partial f}{\\partial z}+\\lambda\n",
|
||
"\\frac{\\partial \\phi}{\\partial x})dx+(\\frac{\\partial f}{\\partial y}+\\lambda\\frac{\\partial \\phi}{\\partial y})dy+\n",
|
||
"(\\frac{\\partial f}{\\partial z}+\\lambda\\frac{\\partial \\phi}{\\partial z})dz =0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Our multiplier is chosen so that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial f}{\\partial z}+\\lambda\\frac{\\partial \\phi}{\\partial z} =0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We need to remember that we took $dx$ and $dy$ to be arbitrary and thus we must have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial f}{\\partial x}+\\lambda\\frac{\\partial \\phi}{\\partial x} =0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial f}{\\partial y}+\\lambda\\frac{\\partial \\phi}{\\partial y} =0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"When all these equations are satisfied, $df=0$. We have four unknowns, $x,y,z$ and\n",
|
||
"$\\lambda$. Actually we want only $x,y,z$, $\\lambda$ needs not to be determined, \n",
|
||
"it is therefore often called\n",
|
||
"Lagrange's undetermined multiplier.\n",
|
||
"If we have a set of constraints $\\phi_k$ we have the equations"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial f}{\\partial x_i}+\\sum_k\\lambda_k\\frac{\\partial \\phi_k}{\\partial x_i} =0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"In order to solve the above problem, we define the following Lagrangian function to be minimized"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\cal{L}(\\lambda,b,\\boldsymbol{w})=\\frac{1}{2}\\boldsymbol{w}^T\\boldsymbol{w}-\\sum_{i=1}^n\\lambda_i\\left[y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)-1\\right],\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\lambda_i$ is a so-called Lagrange multiplier subject to the condition $\\lambda_i \\geq 0$.\n",
|
||
"\n",
|
||
"Taking the derivatives with respect to $b$ and $\\boldsymbol{w}$ we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial \\cal{L}}{\\partial b} = -\\sum_{i} \\lambda_iy_i=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial \\cal{L}}{\\partial \\boldsymbol{w}} = 0 = \\boldsymbol{w}-\\sum_{i} \\lambda_iy_i\\boldsymbol{x}_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Inserting these constraints into the equation for $\\cal{L}$ we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\cal{L}=\\sum_i\\lambda_i-\\frac{1}{2}\\sum_{ij}^n\\lambda_i\\lambda_jy_iy_j\\boldsymbol{x}_i^T\\boldsymbol{x}_j,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"subject to the constraints $\\lambda_i\\geq 0$ and $\\sum_i\\lambda_iy_i=0$. \n",
|
||
"We must in addition satisfy the [Karush-Kuhn-Tucker](https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions) (KKT) condition"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\lambda_i\\left[y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) -1\\right] \\hspace{0.1cm}\\forall i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"1. If $\\lambda_i > 0$, then $y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1$ and we say that $x_i$ is on the boundary.\n",
|
||
"\n",
|
||
"2. If $y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)> 1$, we say $x_i$ is not on the boundary and we set $\\lambda_i=0$. \n",
|
||
"\n",
|
||
"When $\\lambda_i > 0$, the vectors $\\boldsymbol{x}_i$ are called support vectors. They are the vectors closest to the line (or hyperplane) and define the margin $M$. \n",
|
||
"\n",
|
||
"\n",
|
||
"We can rewrite"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\cal{L}=\\sum_i\\lambda_i-\\frac{1}{2}\\sum_{ij}^n\\lambda_i\\lambda_jy_iy_j\\boldsymbol{x}_i^T\\boldsymbol{x}_j,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and its constraints in terms of a matrix-vector problem where we minimize w.r.t. $\\lambda$ the following problem"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{1}{2} \\boldsymbol{\\lambda}^T\\begin{bmatrix} y_1y_1\\boldsymbol{x}_1^T\\boldsymbol{x}_1 & y_1y_2\\boldsymbol{x}_1^T\\boldsymbol{x}_2 & \\dots & \\dots & y_1y_n\\boldsymbol{x}_1^T\\boldsymbol{x}_n \\\\\n",
|
||
"y_2y_1\\boldsymbol{x}_2^T\\boldsymbol{x}_1 & y_2y_2\\boldsymbol{x}_2^T\\boldsymbol{x}_2 & \\dots & \\dots & y_1y_n\\boldsymbol{x}_2^T\\boldsymbol{x}_n \\\\\n",
|
||
"\\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
|
||
"\\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
|
||
"y_ny_1\\boldsymbol{x}_n^T\\boldsymbol{x}_1 & y_ny_2\\boldsymbol{x}_n^T\\boldsymbol{x}_2 & \\dots & \\dots & y_ny_n\\boldsymbol{x}_n^T\\boldsymbol{x}_n \\\\\n",
|
||
"\\end{bmatrix}\\boldsymbol{\\lambda}-\\mathbb{1}\\boldsymbol{\\lambda},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"subject to $\\boldsymbol{y}^T\\boldsymbol{\\lambda}=0$. Here we defined the vectors $\\boldsymbol{\\lambda} =[\\lambda_1,\\lambda_2,\\dots,\\lambda_n]$ and \n",
|
||
"$\\boldsymbol{y}=[y_1,y_2,\\dots,y_n]$. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"Solving the above problem, yields the values of $\\lambda_i$.\n",
|
||
"To find the coefficients of your hyperplane we need simply to compute"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{w}=\\sum_{i} \\lambda_iy_i\\boldsymbol{x}_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"With our vector $\\boldsymbol{w}$ we can in turn find the value of the intercept $b$ (here in two dimensions) via"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"resulting in"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"b = \\frac{1}{y_i}-\\boldsymbol{w}^T\\boldsymbol{x}_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"or if we write it out in terms of the support vectors only, with $N_s$ being their number, we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"b = \\frac{1}{N_s}\\sum_{j\\in N_s}\\left(y_j-\\sum_{i=1}^n\\lambda_iy_i\\boldsymbol{x}_i^T\\boldsymbol{x}_j\\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"With our hyperplane coefficients we can use our classifier to assign any observation by simply using"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i = \\mathrm{sign}(\\boldsymbol{w}^T\\boldsymbol{x}_i+b).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Below we discuss how to find the optimal values of $\\lambda_i$. Before we proceed however, we discuss now the so-called soft classifier. \n",
|
||
"\n",
|
||
"\n",
|
||
"## A soft classifier\n",
|
||
"\n",
|
||
"Till now, the margin is strictly defined by the support vectors. This defines what is called a hard classifier, that is the margins are well defined.\n",
|
||
"\n",
|
||
"Suppose now that classes overlap in feature space, as shown in the\n",
|
||
"figure here. One way to deal with this problem before we define the\n",
|
||
"so-called **kernel approach**, is to allow a kind of slack in the sense\n",
|
||
"that we allow some points to be on the wrong side of the margin.\n",
|
||
"\n",
|
||
"We introduce thus the so-called **slack** variables $\\boldsymbol{\\xi} =[\\xi_1,x_2,\\dots,x_n]$ and \n",
|
||
"modify our previous equation"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1-\\xi_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"with the requirement $\\xi_i\\geq 0$. The total violation is now $\\sum_i\\xi$. \n",
|
||
"The value $\\xi_i$ in the constraint the last constraint corresponds to the amount by which the prediction\n",
|
||
"$y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1$ is on the wrong side of its margin. Hence by bounding the sum $\\sum_i \\xi_i$,\n",
|
||
"we bound the total amount by which predictions fall on the wrong side of their margins.\n",
|
||
"\n",
|
||
"Misclassifications occur when $\\xi_i > 1$. Thus bounding the total sum by some value $C$ bounds in turn the total number of\n",
|
||
"misclassifications.\n",
|
||
"\n",
|
||
"\n",
|
||
"This has in turn the consequences that we change our optmization problem to finding the minimum of"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\cal{L}=\\frac{1}{2}\\boldsymbol{w}^T\\boldsymbol{w}-\\sum_{i=1}^n\\lambda_i\\left[y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)-(1-\\xi_)\\right]+C\\sum_{i=1}^n\\xi_i-\\sum_{i=1}^n\\gamma_i\\xi_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"subject to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1-\\xi_i \\hspace{0.1cm}\\forall i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"with the requirement $\\xi_i\\geq 0$.\n",
|
||
"\n",
|
||
"Taking the derivatives with respect to $b$ and $\\boldsymbol{w}$ we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial \\cal{L}}{\\partial b} = -\\sum_{i} \\lambda_iy_i=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial \\cal{L}}{\\partial \\boldsymbol{w}} = 0 = \\boldsymbol{w}-\\sum_{i} \\lambda_iy_i\\boldsymbol{x}_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\lambda_i = C-\\gamma_i \\hspace{0.1cm}\\forall i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Inserting these constraints into the equation for $\\cal{L}$ we obtain the same equation as before"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\cal{L}=\\sum_i\\lambda_i-\\frac{1}{2}\\sum_{ij}^n\\lambda_i\\lambda_jy_iy_j\\boldsymbol{x}_i^T\\boldsymbol{x}_j,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"but now subject to the constraints $\\lambda_i\\geq 0$, $\\sum_i\\lambda_iy_i=0$ and $0\\leq\\lambda_i \\leq C$. \n",
|
||
"We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"5\n",
|
||
"0\n",
|
||
" \n",
|
||
"<\n",
|
||
"<\n",
|
||
"<\n",
|
||
"!\n",
|
||
"!\n",
|
||
"M\n",
|
||
"A\n",
|
||
"T\n",
|
||
"H\n",
|
||
"_\n",
|
||
"B\n",
|
||
"L\n",
|
||
"O\n",
|
||
"C\n",
|
||
"K"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\gamma_i\\xi_i = 0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) -(1-\\xi_) \\geq 0 \\hspace{0.1cm}\\forall i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Kernels and non-linearity\n",
|
||
"\n",
|
||
"The cases we have studied till now, were all characterized by two classes\n",
|
||
"with a close to linear separability. The classifiers we have described\n",
|
||
"so far find linear boundaries in our input feature space. It is\n",
|
||
"possible to make our procedure more flexible by exploring the feature\n",
|
||
"space using other basis expansions such as higher-order polynomials,\n",
|
||
"wavelets, splines etc.\n",
|
||
"\n",
|
||
"If our feature space is not easy to separate, as shown in the figure\n",
|
||
"here, we can achieve a better separation by introducing more complex\n",
|
||
"basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to \n",
|
||
"obtain a separation between the classes which is almost linear. \n",
|
||
"\n",
|
||
"The change of basis, from $x\\rightarrow z=\\phi(x)$ leads to the same type of equations to be solved, except that\n",
|
||
"we need to introduce for example a polynomial transformation to a two-dimensional training set."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_109_0.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import os\n",
|
||
"\n",
|
||
"np.random.seed(42)\n",
|
||
"\n",
|
||
"# To plot pretty figures\n",
|
||
"import matplotlib\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"plt.rcParams['axes.labelsize'] = 14\n",
|
||
"plt.rcParams['xtick.labelsize'] = 12\n",
|
||
"plt.rcParams['ytick.labelsize'] = 12\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn import datasets\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"X1D = np.linspace(-4, 4, 9).reshape(-1, 1)\n",
|
||
"X2D = np.c_[X1D, X1D**2]\n",
|
||
"y = np.array([0, 0, 1, 1, 1, 1, 1, 0, 0])\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"\n",
|
||
"plt.subplot(121)\n",
|
||
"plt.grid(True, which='both')\n",
|
||
"plt.axhline(y=0, color='k')\n",
|
||
"plt.plot(X1D[:, 0][y==0], np.zeros(4), \"bs\")\n",
|
||
"plt.plot(X1D[:, 0][y==1], np.zeros(5), \"g^\")\n",
|
||
"plt.gca().get_yaxis().set_ticks([])\n",
|
||
"plt.xlabel(r\"$x_1$\", fontsize=20)\n",
|
||
"plt.axis([-4.5, 4.5, -0.2, 0.2])\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plt.grid(True, which='both')\n",
|
||
"plt.axhline(y=0, color='k')\n",
|
||
"plt.axvline(x=0, color='k')\n",
|
||
"plt.plot(X2D[:, 0][y==0], X2D[:, 1][y==0], \"bs\")\n",
|
||
"plt.plot(X2D[:, 0][y==1], X2D[:, 1][y==1], \"g^\")\n",
|
||
"plt.xlabel(r\"$x_1$\", fontsize=20)\n",
|
||
"plt.ylabel(r\"$x_2$\", fontsize=20, rotation=0)\n",
|
||
"plt.gca().get_yaxis().set_ticks([0, 4, 8, 12, 16])\n",
|
||
"plt.plot([-4.5, 4.5], [6.5, 6.5], \"r--\", linewidth=3)\n",
|
||
"plt.axis([-4.5, 4.5, -1, 17])\n",
|
||
"plt.subplots_adjust(right=1)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with $x_i$ and $y_i$ as variables)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"z = \\phi(x_i) =\\left(x_i^2, y_i^2, \\sqrt{2}x_iy_i\\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"With our new basis, the equations we solved earlier are basically the same, that is we have now (without the slack option for simplicity)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\cal{L}=\\sum_i\\lambda_i-\\frac{1}{2}\\sum_{ij}^n\\lambda_i\\lambda_jy_iy_j\\boldsymbol{z}_i^T\\boldsymbol{z}_j,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"subject to the constraints $\\lambda_i\\geq 0$, $\\sum_i\\lambda_iy_i=0$, and for the support vectors"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"y_i(\\boldsymbol{w}^T\\boldsymbol{z}_i+b)= 1 \\hspace{0.1cm}\\forall i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"from which we also find $b$.\n",
|
||
"To compute $\\boldsymbol{z}_i^T\\boldsymbol{z}_j$ we define the kernel $K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=\\boldsymbol{z}_i^T\\boldsymbol{z}_j= \\phi(\\boldsymbol{x}_i)^T\\phi(\\boldsymbol{x}_j).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"For the above example, the kernel reads"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=[x_i^2, y_i^2, \\sqrt{2}x_iy_i]^T\\begin{bmatrix} x_j^2 \\\\ y_j^2 \\\\ \\sqrt{2}x_jy_j \\end{bmatrix}=x_i^2x_j^2+2x_ix_jy_iy_j+y_i^2y_j^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We note that this is nothing but the dot product of the two original\n",
|
||
"vectors $(\\boldsymbol{x}_i^T\\boldsymbol{x}_j)^2$. Instead of thus computing the\n",
|
||
"product in the Lagrangian of $\\boldsymbol{z}_i^T\\boldsymbol{z}_j$ we simply compute\n",
|
||
"the dot product $(\\boldsymbol{x}_i^T\\boldsymbol{x}_j)^2$.\n",
|
||
"\n",
|
||
"\n",
|
||
"This leads to the so-called\n",
|
||
"kernel trick and the result leads to the same as if we went through\n",
|
||
"the trouble of performing the transformation\n",
|
||
"$\\phi(\\boldsymbol{x}_i)^T\\phi(\\boldsymbol{x}_j)$ during the SVM calculations.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"Using our definition of the kernel We can rewrite again the Lagrangian"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\cal{L}=\\sum_i\\lambda_i-\\frac{1}{2}\\sum_{ij}^n\\lambda_i\\lambda_jy_iy_j\\boldsymbol{x}_i^T\\boldsymbol{z}_j,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"subject to the constraints $\\lambda_i\\geq 0$, $\\sum_i\\lambda_iy_i=0$ in terms of a convex optimization problem"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{1}{2} \\boldsymbol{\\lambda}^T\\begin{bmatrix} y_1y_1K(\\boldsymbol{x}_1,\\boldsymbol{x}_1) & y_1y_2K(\\boldsymbol{x}_1,\\boldsymbol{x}_2) & \\dots & \\dots & y_1y_nK(\\boldsymbol{x}_1,\\boldsymbol{x}_n) \\\\\n",
|
||
"y_2y_1K(\\boldsymbol{x}_2,\\boldsymbol{x}_1) & y_2y_2(\\boldsymbol{x}_2,\\boldsymbol{x}_2) & \\dots & \\dots & y_1y_nK(\\boldsymbol{x}_2,\\boldsymbol{x}_n) \\\\\n",
|
||
"\\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
|
||
"\\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
|
||
"y_ny_1K(\\boldsymbol{x}_n,\\boldsymbol{x}_1) & y_ny_2K(\\boldsymbol{x}_n\\boldsymbol{x}_2) & \\dots & \\dots & y_ny_nK(\\boldsymbol{x}_n,\\boldsymbol{x}_n) \\\\\n",
|
||
"\\end{bmatrix}\\boldsymbol{\\lambda}-\\mathbb{1}\\boldsymbol{\\lambda},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"subject to $\\boldsymbol{y}^T\\boldsymbol{\\lambda}=0$. Here we defined the vectors $\\boldsymbol{\\lambda} =[\\lambda_1,\\lambda_2,\\dots,\\lambda_n]$ and \n",
|
||
"$\\boldsymbol{y}=[y_1,y_2,\\dots,y_n]$. \n",
|
||
"If we add the slack constants this leads to the additional constraint $0\\leq \\lambda_i \\leq C$.\n",
|
||
"\n",
|
||
"We can rewrite this (see the solutions below) in terms of a convex optimization problem of the type"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
" &\\mathrm{min}_{\\lambda}\\hspace{0.2cm} \\frac{1}{2}\\boldsymbol{\\lambda}^T\\boldsymbol{P}\\boldsymbol{\\lambda}+\\boldsymbol{q}^T\\boldsymbol{\\lambda},\\\\ \\nonumber\n",
|
||
" &\\mathrm{subject\\hspace{0.1cm}to} \\hspace{0.2cm} \\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq \\boldsymbol{h} \\hspace{0.2cm} \\wedge \\boldsymbol{A}\\boldsymbol{\\lambda}=f.\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Below we discuss how to solve these equations. Here we note that the matrix $\\boldsymbol{P}$ has matrix elements $p_{ij}=y_iy_jK(\\boldsymbol{x}_i,\\boldsymbol{x}_j)$.\n",
|
||
"Given a kernel $K$ and the targets $y_i$ this matrix is easy to set up. The constraint $\\boldsymbol{y}^T\\boldsymbol{\\lambda}=0$ leads to $f=0$ and $\\boldsymbol{A}=\\boldsymbol{y}$. How to set up the matrix $\\boldsymbol{G}$ is discussed later. Here note that the inequalities $0\\leq \\lambda_i \\leq C$ can be split up into\n",
|
||
"$0\\leq \\lambda_i$ and $\\lambda_i \\leq C$. These two inequalities define then the matrix $\\boldsymbol{G}$ and the vector $\\boldsymbol{h}$.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## Different kernels and Mercer's theorem\n",
|
||
"\n",
|
||
"There are several popular kernels being used. These are\n",
|
||
"1. Linear: $K(\\boldsymbol{x},\\boldsymbol{y})=\\boldsymbol{x}^T\\boldsymbol{y}$,\n",
|
||
"\n",
|
||
"2. Polynomial: $K(\\boldsymbol{x},\\boldsymbol{y})=(\\boldsymbol{x}^T\\boldsymbol{y}+\\gamma)^d$,\n",
|
||
"\n",
|
||
"3. Gaussian Radial Basis Function: $K(\\boldsymbol{x},\\boldsymbol{y})=\\exp{\\left(-\\gamma\\vert\\vert\\boldsymbol{x}-\\boldsymbol{y}\\vert\\vert^2\\right)}$,\n",
|
||
"\n",
|
||
"4. Tanh: $K(\\boldsymbol{x},\\boldsymbol{y})=\\tanh{(\\boldsymbol{x}^T\\boldsymbol{y}+\\gamma)}$,\n",
|
||
"\n",
|
||
"and many other ones.\n",
|
||
"\n",
|
||
"An important theorem for us is [Mercer's\n",
|
||
"theorem](https://en.wikipedia.org/wiki/Mercer%27s_theorem). The\n",
|
||
"theorem states that if a kernel function $K$ is symmetric, continuous\n",
|
||
"and leads to a positive semi-definite matrix $\\boldsymbol{P}$ then there\n",
|
||
"exists a function $\\phi$ that maps $\\boldsymbol{x}_i$ and $\\boldsymbol{x}_j$ into\n",
|
||
"another space (possibly with much higher dimensions) such that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=\\phi(\\boldsymbol{x}_i)^T\\phi(\\boldsymbol{x}_j).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"So you can use $K$ as a kernel since you know $\\phi$ exists, even if\n",
|
||
"you don’t know what $\\phi$ is. \n",
|
||
"\n",
|
||
"Note that some frequently used kernels (such as the Sigmoid kernel)\n",
|
||
"don’t respect all of Mercer’s conditions, yet they generally work well\n",
|
||
"in practice.\n",
|
||
"\n",
|
||
"\n",
|
||
"## The moons example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_0.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/svm/_classes.py:32: FutureWarning: The default value of `dual` will change from `True` to `'auto'` in 1.5. Set the value of `dual` explicitly to suppress the warning.\n",
|
||
" warnings.warn(\n",
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/svm/_base.py:1242: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
|
||
" warnings.warn(\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_2.png"
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",
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||
"text/plain": [
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||
"<Figure size 1100x400 with 2 Axes>"
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]
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},
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"metadata": {
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"filenames": {
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"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_3.png"
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}
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},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_4.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Phi(-1.0, -2) = [0.74081822]\n",
|
||
"Phi(-1.0, 1) = [0.30119421]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x700 with 4 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_6.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from __future__ import division, print_function, unicode_literals\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"np.random.seed(42)\n",
|
||
"\n",
|
||
"import matplotlib\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"plt.rcParams['axes.labelsize'] = 14\n",
|
||
"plt.rcParams['xtick.labelsize'] = 12\n",
|
||
"plt.rcParams['ytick.labelsize'] = 12\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn import datasets\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.pipeline import Pipeline\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"from sklearn.svm import LinearSVC\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"X, y = make_moons(n_samples=100, noise=0.15, random_state=42)\n",
|
||
"\n",
|
||
"def plot_dataset(X, y, axes):\n",
|
||
" plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n",
|
||
" plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")\n",
|
||
" plt.axis(axes)\n",
|
||
" plt.grid(True, which='both')\n",
|
||
" plt.xlabel(r\"$x_1$\", fontsize=20)\n",
|
||
" plt.ylabel(r\"$x_2$\", fontsize=20, rotation=0)\n",
|
||
"\n",
|
||
"plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"from sklearn.pipeline import Pipeline\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"\n",
|
||
"polynomial_svm_clf = Pipeline([\n",
|
||
" (\"poly_features\", PolynomialFeatures(degree=3)),\n",
|
||
" (\"scaler\", StandardScaler()),\n",
|
||
" (\"svm_clf\", LinearSVC(C=10, loss=\"hinge\", random_state=42))\n",
|
||
" ])\n",
|
||
"\n",
|
||
"polynomial_svm_clf.fit(X, y)\n",
|
||
"\n",
|
||
"def plot_predictions(clf, axes):\n",
|
||
" x0s = np.linspace(axes[0], axes[1], 100)\n",
|
||
" x1s = np.linspace(axes[2], axes[3], 100)\n",
|
||
" x0, x1 = np.meshgrid(x0s, x1s)\n",
|
||
" X = np.c_[x0.ravel(), x1.ravel()]\n",
|
||
" y_pred = clf.predict(X).reshape(x0.shape)\n",
|
||
" y_decision = clf.decision_function(X).reshape(x0.shape)\n",
|
||
" plt.contourf(x0, x1, y_pred, cmap=plt.cm.brg, alpha=0.2)\n",
|
||
" plt.contourf(x0, x1, y_decision, cmap=plt.cm.brg, alpha=0.1)\n",
|
||
"\n",
|
||
"plot_predictions(polynomial_svm_clf, [-1.5, 2.5, -1, 1.5])\n",
|
||
"plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
|
||
"\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"\n",
|
||
"poly_kernel_svm_clf = Pipeline([\n",
|
||
" (\"scaler\", StandardScaler()),\n",
|
||
" (\"svm_clf\", SVC(kernel=\"poly\", degree=3, coef0=1, C=5))\n",
|
||
" ])\n",
|
||
"poly_kernel_svm_clf.fit(X, y)\n",
|
||
"\n",
|
||
"poly100_kernel_svm_clf = Pipeline([\n",
|
||
" (\"scaler\", StandardScaler()),\n",
|
||
" (\"svm_clf\", SVC(kernel=\"poly\", degree=10, coef0=100, C=5))\n",
|
||
" ])\n",
|
||
"poly100_kernel_svm_clf.fit(X, y)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_predictions(poly_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])\n",
|
||
"plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
|
||
"plt.title(r\"$d=3, r=1, C=5$\", fontsize=18)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_predictions(poly100_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])\n",
|
||
"plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
|
||
"plt.title(r\"$d=10, r=100, C=5$\", fontsize=18)\n",
|
||
"\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"def gaussian_rbf(x, landmark, gamma):\n",
|
||
" return np.exp(-gamma * np.linalg.norm(x - landmark, axis=1)**2)\n",
|
||
"\n",
|
||
"gamma = 0.3\n",
|
||
"\n",
|
||
"x1s = np.linspace(-4.5, 4.5, 200).reshape(-1, 1)\n",
|
||
"x2s = gaussian_rbf(x1s, -2, gamma)\n",
|
||
"x3s = gaussian_rbf(x1s, 1, gamma)\n",
|
||
"\n",
|
||
"XK = np.c_[gaussian_rbf(X1D, -2, gamma), gaussian_rbf(X1D, 1, gamma)]\n",
|
||
"yk = np.array([0, 0, 1, 1, 1, 1, 1, 0, 0])\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"\n",
|
||
"plt.subplot(121)\n",
|
||
"plt.grid(True, which='both')\n",
|
||
"plt.axhline(y=0, color='k')\n",
|
||
"plt.scatter(x=[-2, 1], y=[0, 0], s=150, alpha=0.5, c=\"red\")\n",
|
||
"plt.plot(X1D[:, 0][yk==0], np.zeros(4), \"bs\")\n",
|
||
"plt.plot(X1D[:, 0][yk==1], np.zeros(5), \"g^\")\n",
|
||
"plt.plot(x1s, x2s, \"g--\")\n",
|
||
"plt.plot(x1s, x3s, \"b:\")\n",
|
||
"plt.gca().get_yaxis().set_ticks([0, 0.25, 0.5, 0.75, 1])\n",
|
||
"plt.xlabel(r\"$x_1$\", fontsize=20)\n",
|
||
"plt.ylabel(r\"Similarity\", fontsize=14)\n",
|
||
"plt.annotate(r'$\\mathbf{x}$',\n",
|
||
" xy=(X1D[3, 0], 0),\n",
|
||
" xytext=(-0.5, 0.20),\n",
|
||
" ha=\"center\",\n",
|
||
" arrowprops=dict(facecolor='black', shrink=0.1),\n",
|
||
" fontsize=18,\n",
|
||
" )\n",
|
||
"plt.text(-2, 0.9, \"$x_2$\", ha=\"center\", fontsize=20)\n",
|
||
"plt.text(1, 0.9, \"$x_3$\", ha=\"center\", fontsize=20)\n",
|
||
"plt.axis([-4.5, 4.5, -0.1, 1.1])\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plt.grid(True, which='both')\n",
|
||
"plt.axhline(y=0, color='k')\n",
|
||
"plt.axvline(x=0, color='k')\n",
|
||
"plt.plot(XK[:, 0][yk==0], XK[:, 1][yk==0], \"bs\")\n",
|
||
"plt.plot(XK[:, 0][yk==1], XK[:, 1][yk==1], \"g^\")\n",
|
||
"plt.xlabel(r\"$x_2$\", fontsize=20)\n",
|
||
"plt.ylabel(r\"$x_3$ \", fontsize=20, rotation=0)\n",
|
||
"plt.annotate(r'$\\phi\\left(\\mathbf{x}\\right)$',\n",
|
||
" xy=(XK[3, 0], XK[3, 1]),\n",
|
||
" xytext=(0.65, 0.50),\n",
|
||
" ha=\"center\",\n",
|
||
" arrowprops=dict(facecolor='black', shrink=0.1),\n",
|
||
" fontsize=18,\n",
|
||
" )\n",
|
||
"plt.plot([-0.1, 1.1], [0.57, -0.1], \"r--\", linewidth=3)\n",
|
||
"plt.axis([-0.1, 1.1, -0.1, 1.1])\n",
|
||
" \n",
|
||
"plt.subplots_adjust(right=1)\n",
|
||
"\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"\n",
|
||
"x1_example = X1D[3, 0]\n",
|
||
"for landmark in (-2, 1):\n",
|
||
" k = gaussian_rbf(np.array([[x1_example]]), np.array([[landmark]]), gamma)\n",
|
||
" print(\"Phi({}, {}) = {}\".format(x1_example, landmark, k))\n",
|
||
"\n",
|
||
"rbf_kernel_svm_clf = Pipeline([\n",
|
||
" (\"scaler\", StandardScaler()),\n",
|
||
" (\"svm_clf\", SVC(kernel=\"rbf\", gamma=5, C=0.001))\n",
|
||
" ])\n",
|
||
"rbf_kernel_svm_clf.fit(X, y)\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"\n",
|
||
"gamma1, gamma2 = 0.1, 5\n",
|
||
"C1, C2 = 0.001, 1000\n",
|
||
"hyperparams = (gamma1, C1), (gamma1, C2), (gamma2, C1), (gamma2, C2)\n",
|
||
"\n",
|
||
"svm_clfs = []\n",
|
||
"for gamma, C in hyperparams:\n",
|
||
" rbf_kernel_svm_clf = Pipeline([\n",
|
||
" (\"scaler\", StandardScaler()),\n",
|
||
" (\"svm_clf\", SVC(kernel=\"rbf\", gamma=gamma, C=C))\n",
|
||
" ])\n",
|
||
" rbf_kernel_svm_clf.fit(X, y)\n",
|
||
" svm_clfs.append(rbf_kernel_svm_clf)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 7))\n",
|
||
"\n",
|
||
"for i, svm_clf in enumerate(svm_clfs):\n",
|
||
" plt.subplot(221 + i)\n",
|
||
" plot_predictions(svm_clf, [-1.5, 2.5, -1, 1.5])\n",
|
||
" plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n",
|
||
" gamma, C = hyperparams[i]\n",
|
||
" plt.title(r\"$\\gamma = {}, C = {}$\".format(gamma, C), fontsize=16)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Mathematical optimization of convex functions\n",
|
||
"\n",
|
||
"A mathematical (quadratic) optimization problem, or just optimization problem, has the form"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
" &\\mathrm{min}_{\\lambda}\\hspace{0.2cm} \\frac{1}{2}\\boldsymbol{\\lambda}^T\\boldsymbol{P}\\boldsymbol{\\lambda}+\\boldsymbol{q}^T\\boldsymbol{\\lambda},\\\\ \\nonumber\n",
|
||
" &\\mathrm{subject\\hspace{0.1cm}to} \\hspace{0.2cm} \\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq \\boldsymbol{h} \\wedge \\boldsymbol{A}\\boldsymbol{\\lambda}=f.\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"subject to some constraints for say a selected set $i=1,2,\\dots, n$.\n",
|
||
"In our case we are optimizing with respect to the Lagrangian multipliers $\\lambda_i$, and the\n",
|
||
"vector $\\boldsymbol{\\lambda}=[\\lambda_1, \\lambda_2,\\dots, \\lambda_n]$ is the optimization variable we are dealing with.\n",
|
||
"\n",
|
||
"In our case we are particularly interested in a class of optimization problems called convex optmization problems. \n",
|
||
"In our discussion on gradient descent methods we discussed at length the definition of a convex function. \n",
|
||
"\n",
|
||
"Convex optimization problems play a central role in applied mathematics and we recommend strongly [Boyd and Vandenberghe's text on the topics](http://web.stanford.edu/~boyd/cvxbook/).\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"If we use Python as programming language and wish to venture beyond\n",
|
||
"**scikit-learn**, **tensorflow** and similar software which makes our\n",
|
||
"lives so much easier, we need to dive into the wonderful world of\n",
|
||
"quadratic programming. We can, if we wish, solve the minimization\n",
|
||
"problem using say standard gradient methods or conjugate gradient\n",
|
||
"methods. However, these methods tend to exhibit a rather slow\n",
|
||
"converge. So, welcome to the promised land of quadratic programming.\n",
|
||
"\n",
|
||
"The functions we need are contained in the quadratic programming package **CVXOPT** and we need to import it together with **numpy** as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy\n",
|
||
"import cvxopt"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"This will make our life much easier. You don't need t write your own optimizer.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"We remind ourselves about the general problem we want to solve"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
" &\\mathrm{min}_{x}\\hspace{0.2cm} \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{P}\\boldsymbol{x}+\\boldsymbol{q}^T\\boldsymbol{x},\\\\ \\nonumber\n",
|
||
" &\\mathrm{subject\\hspace{0.1cm} to} \\hspace{0.2cm} \\boldsymbol{G}\\boldsymbol{x} \\preceq \\boldsymbol{h} \\wedge \\boldsymbol{A}\\boldsymbol{x}=f.\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
" &\\mathrm{min}_{x}\\hspace{0.2cm} \\frac{1}{2}x^2+5x+3y \\\\ \\nonumber\n",
|
||
" &\\mathrm{subject to} \\\\ \\nonumber\n",
|
||
" &x, y \\geq 0 \\\\ \\nonumber\n",
|
||
" &x+3y \\geq 15 \\\\ \\nonumber\n",
|
||
" &2x+5y \\leq 100 \\\\ \\nonumber\n",
|
||
" &3x+4y \\leq 80. \\\\ \\nonumber\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The minimization problem can be rewritten in terms of vectors and matrices as (with $x$ and $y$ being the unknowns)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{1}{2}\\begin{bmatrix} x\\\\ y \\end{bmatrix}^T \\begin{bmatrix} 1 & 0\\\\ 0 & 0 \\end{bmatrix} \\begin{bmatrix} x \\\\ y \\end{bmatrix} + \\begin{bmatrix}3\\\\ 4 \\end{bmatrix}^T \\begin{bmatrix}x \\\\ y \\end{bmatrix}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Similarly, we can now set up the inequalities (we need to change $\\geq$ to $\\leq$ by multiplying with $-1$ on bot sides) as the following matrix-vector equation"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{bmatrix} -1 & 0 \\\\ 0 & -1 \\\\ -1 & -3 \\\\ 2 & 5 \\\\ 3 & 4\\end{bmatrix}\\begin{bmatrix} x \\\\ y\\end{bmatrix} \\preceq \\begin{bmatrix}0 \\\\ 0\\\\ -15 \\\\ 100 \\\\ 80\\end{bmatrix}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We have collapsed all the inequalities into a single matrix $\\boldsymbol{G}$. We see also that our matrix"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{P} =\\begin{bmatrix} 1 & 0\\\\ 0 & 0 \\end{bmatrix}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"is clearly positive semi-definite (all eigenvalues larger or equal zero). \n",
|
||
"Finally, the vector $\\boldsymbol{h}$ is defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{h} = \\begin{bmatrix}0 \\\\ 0\\\\ -15 \\\\ 100 \\\\ 80\\end{bmatrix}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Since we don't have any equalities the matrix $\\boldsymbol{A}$ is set to zero\n",
|
||
"The following code solves the equations for us"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"ename": "SyntaxError",
|
||
"evalue": "invalid character '’' (U+2019) (3974140161.py, line 5)",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[0;36m Cell \u001b[0;32mIn[5], line 5\u001b[0;36m\u001b[0m\n\u001b[0;31m P = matrix(numpy.diag([1,0]), tc=’d’)\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid character '’' (U+2019)\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Import the necessary packages\n",
|
||
"import numpy\n",
|
||
"from cvxopt import matrix\n",
|
||
"from cvxopt import solvers\n",
|
||
"P = matrix(numpy.diag([1,0]), tc=’d’)\n",
|
||
"q = matrix(numpy.array([3,4]), tc=’d’)\n",
|
||
"G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)\n",
|
||
"h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)\n",
|
||
"# Construct the QP, invoke solver\n",
|
||
"sol = solvers.qp(P,q,G,h)\n",
|
||
"# Extract optimal value and solution\n",
|
||
"sol[’x’] \n",
|
||
"sol[’primal objective’]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We are now ready to return to our setup of the optmization problem for a more realistic case. Introducing the **slack** parameter $C$ we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{1}{2} \\boldsymbol{\\lambda}^T\\begin{bmatrix} y_1y_1K(\\boldsymbol{x}_1,\\boldsymbol{x}_1) & y_1y_2K(\\boldsymbol{x}_1,\\boldsymbol{x}_2) & \\dots & \\dots & y_1y_nK(\\boldsymbol{x}_1,\\boldsymbol{x}_n) \\\\\n",
|
||
"y_2y_1K(\\boldsymbol{x}_2,\\boldsymbol{x}_1) & y_2y_2K(\\boldsymbol{x}_2,\\boldsymbol{x}_2) & \\dots & \\dots & y_1y_nK(\\boldsymbol{x}_2,\\boldsymbol{x}_n) \\\\\n",
|
||
"\\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
|
||
"\\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
|
||
"y_ny_1K(\\boldsymbol{x}_n,\\boldsymbol{x}_1) & y_ny_2K(\\boldsymbol{x}_n\\boldsymbol{x}_2) & \\dots & \\dots & y_ny_nK(\\boldsymbol{x}_n,\\boldsymbol{x}_n) \\\\\n",
|
||
"\\end{bmatrix}\\boldsymbol{\\lambda}-\\mathbb{I}\\boldsymbol{\\lambda},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"subject to $\\boldsymbol{y}^T\\boldsymbol{\\lambda}=0$. Here we defined the vectors $\\boldsymbol{\\lambda} =[\\lambda_1,\\lambda_2,\\dots,\\lambda_n]$ and \n",
|
||
"$\\boldsymbol{y}=[y_1,y_2,\\dots,y_n]$. \n",
|
||
"With the slack constants this leads to the additional constraint $0\\leq \\lambda_i \\leq C$.\n",
|
||
"\n",
|
||
"**code will be added**"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.15"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
} |