Morten Hjorth-Jensen
2015 lines
433 KiB
Plaintext
2015 lines
433 KiB
Plaintext
{
|
||
"cells": [
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Support Vector Machines, overarching aims\n",
|
||
"\n",
|
||
"A Support Vector Machine (SVM) is a very powerful and versatile\n",
|
||
"Machine Learning method, capable of performing linear or nonlinear\n",
|
||
"classification, regression, and even outlier detection. It is one of\n",
|
||
"the most popular models in Machine Learning, and anyone interested in\n",
|
||
"Machine Learning should have it in their toolbox. SVMs are\n",
|
||
"particularly well suited for classification of complex but small-sized or\n",
|
||
"medium-sized datasets. \n",
|
||
"\n",
|
||
"The case with two well-separated classes only can be understood in an\n",
|
||
"intuitive way in terms of lines in a two-dimensional space separating\n",
|
||
"the two classes (see figure below).\n",
|
||
"\n",
|
||
"The basic mathematics behind the SVM is however less familiar to most of us. \n",
|
||
"It relies on the definition of hyperplanes and the\n",
|
||
"definition of a **margin** which separates classes (in case of\n",
|
||
"classification problems) of variables. It is also used for regression\n",
|
||
"problems.\n",
|
||
"\n",
|
||
"With SVMs we distinguish between hard margin and soft margins. The\n",
|
||
"latter introduces a so-called softening parameter to be discussed\n",
|
||
"below. We distinguish also between linear and non-linear\n",
|
||
"approaches. The latter are the most frequent ones since it is rather\n",
|
||
"unlikely that we can separate classes easily by say straight lines.\n",
|
||
"\n",
|
||
"\n",
|
||
"## Hyperplanes and all that\n",
|
||
"\n",
|
||
"The theory behind support vector machines (SVM hereafter) is based on\n",
|
||
"the mathematical description of so-called hyperplanes. Let us start\n",
|
||
"with a two-dimensional case. This will also allow us to introduce our\n",
|
||
"first SVM examples. These will be tailored to the case of two specific\n",
|
||
"classes, as displayed in the figure here based on the usage of the petal data.\n",
|
||
"\n",
|
||
"We assume here that our data set can be well separated into two\n",
|
||
"domains, where a straight line does the job in the separating the two\n",
|
||
"classes. Here the two classes are represented by either squares or\n",
|
||
"circles."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 1,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"LinearSVC: [0.28475098] [[1.05364854 1.09903804]]\n",
|
||
"SVC: [0.31896852] [[1.1203284 1.02625193]]\n",
|
||
"SGDClassifier(alpha=0.00200): [0.117] [[0.77714169 0.72981762]]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": "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\n",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_1_1.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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\n",
|
||
"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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\n",
|
||
"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/_base.py:1206: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
|
||
" warnings.warn(\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": "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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_2.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": "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\n",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_3.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": "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\n",
|
||
"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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\n",
|
||
"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 Input \u001b[0;32mIn [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": "3.9.10"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
} |