Morten Hjorth-Jensen
2025 lines
433 KiB
Plaintext
2025 lines
433 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": {
|
||
"image/png": 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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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},
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"metadata": {
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"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_2.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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",
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"<Figure size 1100x400 with 2 Axes>"
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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": "3.9.18"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
} |