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‎soft_margin_svm/Qp-cvxopt.pdf‎

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‎soft_margin_svm/soft_margin_svm.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy\n",
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"from cvxopt import matrix\n",
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"from cvxopt import solvers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 定义二次规划参数\n",
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"P = matrix([[1.0,0.0],[0.0,0.0]])\n",
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"q = matrix([3.0,4.0])\n",
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"G = matrix([[-1.0,0.0,-1.0,2.0,3.0],[0.0,-1.0,-3.0,5.0,4.0]])\n",
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"h = matrix([0.0,0.0,-15.0,100.0,80.0])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" pcost dcost gap pres dres\n",
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" 0: 1.0780e+02 -7.6366e+02 9e+02 4e-17 4e+01\n",
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" 1: 9.3245e+01 9.7637e+00 8e+01 8e-17 3e+00\n",
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" 2: 6.7311e+01 3.2553e+01 3e+01 8e-17 1e+00\n",
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" 3: 2.6071e+01 1.5068e+01 1e+01 7e-17 7e-01\n",
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" 4: 3.7092e+01 2.3152e+01 1e+01 1e-16 4e-01\n",
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" 5: 2.5352e+01 1.8652e+01 7e+00 9e-17 4e-16\n",
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" 6: 2.0062e+01 1.9974e+01 9e-02 7e-17 2e-16\n",
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" 7: 2.0001e+01 2.0000e+01 9e-04 8e-17 2e-16\n",
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" 8: 2.0000e+01 2.0000e+01 9e-06 1e-16 2e-16\n",
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"Optimal solution found.\n"
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]
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}
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],
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"source": [
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"# 构建求解\n",
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"sol = solvers.qp(P,q,G,h)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[ 7.13e-07]\n",
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"[ 5.00e+00]\n",
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" 20.00000617311241\n"
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]
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}
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],
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"source": [
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"# 获取最优值\n",
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"print(sol['x'],sol['primal objective'])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"from numpy import linalg\n",
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"import cvxopt\n",
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"import cvxopt.solvers\n",
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"import pylab as pl"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 定义一个线性核\n",
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"def linear_kernel(x1, x2):\n",
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" return np.dot(x1, x2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [],
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"source": [
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"def gen_non_lin_separable_data():\n",
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" mean1 = [-1, 2]\n",
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" mean2 = [1, -1]\n",
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" mean3 = [4, -4]\n",
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" mean4 = [-4, 4]\n",
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" cov = [[1.0, 0.8], [0.8, 1.0]]\n",
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" X1 = np.random.multivariate_normal(mean1, cov, 50)\n",
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" X1 = np.vstack((X1, np.random.multivariate_normal(mean3, cov, 50)))\n",
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" y1 = np.ones(len(X1))\n",
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" X2 = np.random.multivariate_normal(mean2, cov, 50)\n",
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" X2 = np.vstack((X2, np.random.multivariate_normal(mean4, cov, 50)))\n",
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" y2 = np.ones(len(X2)) * -1\n",
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" return X1, y1, X2, y2\n",
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"\n",
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"X1, y1, X2, y2 = gen_non_lin_separable_data()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(180, 2) (180,) (20, 2) (20,)\n"
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]
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}
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],
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"source": [
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"def split_train(X1, y1, X2, y2):\n",
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" X1_train = X1[:90]\n",
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" y1_train = y1[:90]\n",
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" X2_train = X2[:90]\n",
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" y2_train = y2[:90]\n",
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" X_train = np.vstack((X1_train, X2_train))\n",
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" y_train = np.hstack((y1_train, y2_train))\n",
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" return X_train, y_train\n",
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"\n",
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"\n",
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"def split_test(X1, y1, X2, y2):\n",
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" X1_test = X1[90:]\n",
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" y1_test = y1[90:]\n",
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" X2_test = X2[90:]\n",
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" y2_test = y2[90:]\n",
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" X_test = np.vstack((X1_test, X2_test))\n",
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" y_test = np.hstack((y1_test, y2_test))\n",
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" return X_test, y_test\n",
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"\n",
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"X_train, y_train = split_train(X1, y1, X2, y2)\n",
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"X_test, y_test = split_test(X1, y1, X2, y2)\n",
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"print(X_train.shape, y_train.shape, X_test.shape, y_test.shape)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [],
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"source": [
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"def fit(X, y, C):\n",
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" n_samples, n_features = X.shape\n",
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"\n",
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" # Gram matrix\n",
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" K = np.zeros((n_samples, n_samples))\n",
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" for i in range(n_samples):\n",
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" for j in range(n_samples):\n",
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" K[i, j] = linear_kernel(X[i], X[j])\n",
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"\n",
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" P = cvxopt.matrix(np.outer(y, y) * K)\n",
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" q = cvxopt.matrix(np.ones(n_samples) * -1)\n",
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" A = cvxopt.matrix(y, (1, n_samples))\n",
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" b = cvxopt.matrix(0.0)\n",
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"\n",
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" if C is None:\n",
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" G = cvxopt.matrix(np.diag(np.ones(n_samples) * -1))\n",
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" h = cvxopt.matrix(np.zeros(n_samples))\n",
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" else:\n",
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" tmp1 = np.diag(np.ones(n_samples) * -1)\n",
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" tmp2 = np.identity(n_samples)\n",
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" G = cvxopt.matrix(np.vstack((tmp1, tmp2)))\n",
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" tmp1 = np.zeros(n_samples)\n",
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" tmp2 = np.ones(n_samples) * C\n",
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" h = cvxopt.matrix(np.hstack((tmp1, tmp2)))\n",
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"\n",
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" # solve QP problem\n",
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" solution = cvxopt.solvers.qp(P, q, G, h, A, b)\n",
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"\n",
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" # Lagrange multipliers\n",
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" a = np.ravel(solution['x'])\n",
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" # Support vectors have non zero lagrange multipliers\n",
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" sv = a > 1e-5\n",
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" ind = np.arange(len(a))[sv]\n",
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" a = a[sv]\n",
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" sv_x = X[sv]\n",
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" sv_y = y[sv]\n",
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" print(\"%d support vectors out of %d points\" % (len(a), n_samples))\n",
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"\n",
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" # Intercept\n",
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" b = 0\n",
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" for n in range(len(a)):\n",
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" b += sv_y[n]\n",
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" b -= np.sum(a * sv_y * K[ind[n], sv])\n",
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" b /= len(a)\n",
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"\n",
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" # Weight vector\n",
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" w = np.zeros(n_features)\n",
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" for n in range(len(a)):\n",
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" w += a[n] * sv_y[n] * sv[n]\n",
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" else:\n",
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" w = None"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" pcost dcost gap pres dres\n",
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" 0: -5.5569e+04 -7.4952e+07 8e+07 1e-02 5e-11\n",
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" 1: -7.3687e+04 -9.6455e+05 9e+05 1e-04 5e-11\n",
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" 2: -8.2531e+04 -1.6849e+05 9e+04 1e-05 6e-11\n",
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" 3: -1.2558e+05 -1.4468e+05 2e+04 1e-06 8e-11\n",
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" 4: -1.2939e+05 -1.3440e+05 5e+03 3e-07 8e-11\n",
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" 5: -1.3084e+05 -1.3145e+05 6e+02 2e-08 9e-11\n",
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" 6: -1.3103e+05 -1.3115e+05 1e+02 4e-09 9e-11\n",
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" 7: -1.3107e+05 -1.3109e+05 2e+01 6e-10 1e-10\n",
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" 8: -1.3108e+05 -1.3108e+05 2e+00 4e-11 1e-10\n",
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" 9: -1.3108e+05 -1.3108e+05 2e-01 3e-11 1e-10\n",
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"10: -1.3108e+05 -1.3108e+05 2e-03 4e-11 1e-10\n",
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"Optimal solution found.\n",
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"158 support vectors out of 180 points\n"
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]
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}
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],
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"source": [
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"w, b = fit(X_train, y_train, C=1000.1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"toc": {
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"base_numbering": 1,
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