From 9f96be84fc0c16b4327288263dff814d9717d4c0 Mon Sep 17 00:00:00 2001
From: jtsauer <jtsauer@zedat.fu-berlin.de>
Date: Thu, 13 Jul 2017 23:33:39 +0200
Subject: [PATCH] basic implementation of svm classifier with toy example
---
.../SVM_Predictor-checkpoint.ipynb | 124 ++++++++++++++++++
SVM_Predictor.ipynb | 124 ++++++++++++++++++
2 files changed, 248 insertions(+)
diff --git a/.ipynb_checkpoints/SVM_Predictor-checkpoint.ipynb b/.ipynb_checkpoints/SVM_Predictor-checkpoint.ipynb
index cbe8341..53e8b35 100644
--- a/.ipynb_checkpoints/SVM_Predictor-checkpoint.ipynb
+++ b/.ipynb_checkpoints/SVM_Predictor-checkpoint.ipynb
@@ -536,6 +536,130 @@
" tol=0.001, verbose=False)"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "from sklearn.metrics.pairwise import linear_kernel, polynomial_kernel, rbf_kernel # there are some more..\n",
+ "import numpy as np\n",
+ "import cvxopt\n",
+ "\n",
+ "class SVM_Predictor(object):\n",
+ " \n",
+ " def __init__(self, kernel):\n",
+ " self.kernel = kernel\n",
+ " \n",
+ " def train(self, X, Y):\n",
+ " n_samples, dim = X.shape\n",
+ " K = self.kernel(X)\n",
+ " P = cvxopt.matrix(np.outer(y, y) * K)\n",
+ " q = cvxopt.matrix(-1 * np.ones(n_samples))\n",
+ " G = cvxopt.matrix(-np.eye(n_samples))\n",
+ " h = cvxopt.matrix(np.zeros(n_samples))\n",
+ " A = cvxopt.matrix(y, (1, n_samples))\n",
+ " b = cvxopt.matrix(0.0)\n",
+ " #solvers.options['show_progress'] = False\n",
+ " sol = cvxopt.solvers.qp(P, q, G, h, A, b)\n",
+ " self.alphas = np.array(sol['x'])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " pcost dcost gap pres dres\n",
+ " 0: -1.1154e+01 -2.0912e+01 3e+02 2e+01 2e+00\n",
+ " 1: -1.7080e+01 -8.7902e+00 6e+01 3e+00 4e-01\n",
+ " 2: -1.1243e+01 -5.9376e+00 4e+01 2e+00 2e-01\n",
+ " 3: -3.7199e+00 -4.0980e+00 2e+00 8e-02 8e-03\n",
+ " 4: -3.6777e+00 -3.7750e+00 2e-01 5e-03 6e-04\n",
+ " 5: -3.7366e+00 -3.7654e+00 3e-02 2e-04 3e-05\n",
+ " 6: -3.7626e+00 -3.7629e+00 4e-04 3e-06 3e-07\n",
+ " 7: -3.7629e+00 -3.7629e+00 4e-06 3e-08 3e-09\n",
+ "Optimal solution found.\n",
+ "x (100, 2) y (100,)\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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FTxiClTcPEVEhTsL9DQCNIjJLRKoA3AFgV+YBIjI94+kqAMe8a2K4hCFYo3Dz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\nf7clxzX6+Kk6AAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fe285ddec50>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "dim = 2\n",
+ "colours = ['red', 'blue']\n",
+ "\n",
+ "# 2-D mean of ones\n",
+ "M1 = np.ones((dim,))\n",
+ "# 2-D mean of threes\n",
+ "M2 = 3 * np.ones((dim,))\n",
+ "# 2-D covariance of 0.3\n",
+ "C1 = np.diag(0.3 * np.ones((dim,)))\n",
+ "# 2-D covariance of 0.2\n",
+ "C2 = np.diag(0.2 * np.ones((dim,)))\n",
+ "\n",
+ "def generate_gaussian(m, c, n_samples):\n",
+ " return np.random.multivariate_normal(m, c, n_samples)\n",
+ "\n",
+ "def plot_data_with_labels(x, y, ax):\n",
+ " unique = np.unique(y)\n",
+ " for li in range(len(unique)):\n",
+ " x_sub = x[y == unique[li]]\n",
+ " ax.scatter(x_sub[:, 0], x_sub[:, 1], c = colours[li])\n",
+ "\n",
+ "def plot_separator(w, b, ax):\n",
+ " slope = -w[0] / w[1]\n",
+ " intercept = -b / w[1]\n",
+ " x = np.arange(0, 6)\n",
+ " ax.plot(x, x * slope + intercept, 'k-')\n",
+ " \n",
+ "n_samples = 50\n",
+ "\n",
+ "# generate 50 points from gaussian 1\n",
+ "x1 = generate_gaussian(M1, C1, n_samples)\n",
+ "# labels\n",
+ "y1 = np.ones((x1.shape[0],))\n",
+ "# generate 50 points from gaussian 2\n",
+ "x2 = generate_gaussian(M2, C2, n_samples)\n",
+ "y2 = -np.ones((x2.shape[0],))\n",
+ "# join\n",
+ "x = np.concatenate((x1, x2), axis = 0)\n",
+ "y = np.concatenate((y1, y2), axis = 0)\n",
+ "\n",
+ "lin_clf = SVM_Predictor(linear_kernel)\n",
+ "lin_clf.train(x, y)\n",
+ "\n",
+ "# get weights\n",
+ "w = np.sum(lin_clf.alphas * y[:, None] * x, axis = 0)\n",
+ "# get bias\n",
+ "cond = (lin_clf.alphas > 1e-4).reshape(-1)\n",
+ "b = y[cond] - np.dot(x[cond], w)\n",
+ "bias = b[0]\n",
+ "\n",
+ "print('x {} y {}'.format(x.shape, y.shape))\n",
+ "fig, ax = plt.subplots()\n",
+ "plot_separator(w, bias, ax)\n",
+ "plot_data_with_labels(x, y, ax)\n",
+ "plt.show()"
+ ]
+ },
{
"cell_type": "markdown",
"metadata": {},
diff --git a/SVM_Predictor.ipynb b/SVM_Predictor.ipynb
index cbe8341..53e8b35 100644
--- a/SVM_Predictor.ipynb
+++ b/SVM_Predictor.ipynb
@@ -536,6 +536,130 @@
" tol=0.001, verbose=False)"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "from sklearn.metrics.pairwise import linear_kernel, polynomial_kernel, rbf_kernel # there are some more..\n",
+ "import numpy as np\n",
+ "import cvxopt\n",
+ "\n",
+ "class SVM_Predictor(object):\n",
+ " \n",
+ " def __init__(self, kernel):\n",
+ " self.kernel = kernel\n",
+ " \n",
+ " def train(self, X, Y):\n",
+ " n_samples, dim = X.shape\n",
+ " K = self.kernel(X)\n",
+ " P = cvxopt.matrix(np.outer(y, y) * K)\n",
+ " q = cvxopt.matrix(-1 * np.ones(n_samples))\n",
+ " G = cvxopt.matrix(-np.eye(n_samples))\n",
+ " h = cvxopt.matrix(np.zeros(n_samples))\n",
+ " A = cvxopt.matrix(y, (1, n_samples))\n",
+ " b = cvxopt.matrix(0.0)\n",
+ " #solvers.options['show_progress'] = False\n",
+ " sol = cvxopt.solvers.qp(P, q, G, h, A, b)\n",
+ " self.alphas = np.array(sol['x'])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " pcost dcost gap pres dres\n",
+ " 0: -1.1154e+01 -2.0912e+01 3e+02 2e+01 2e+00\n",
+ " 1: -1.7080e+01 -8.7902e+00 6e+01 3e+00 4e-01\n",
+ " 2: -1.1243e+01 -5.9376e+00 4e+01 2e+00 2e-01\n",
+ " 3: -3.7199e+00 -4.0980e+00 2e+00 8e-02 8e-03\n",
+ " 4: -3.6777e+00 -3.7750e+00 2e-01 5e-03 6e-04\n",
+ " 5: -3.7366e+00 -3.7654e+00 3e-02 2e-04 3e-05\n",
+ " 6: -3.7626e+00 -3.7629e+00 4e-04 3e-06 3e-07\n",
+ " 7: -3.7629e+00 -3.7629e+00 4e-06 3e-08 3e-09\n",
+ "Optimal solution found.\n",
+ "x (100, 2) y (100,)\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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FTxiClTcPEVEhTsL9DQCNIjJLRKoA3AFgV+YBIjI94+kqAMe8a2K4hCFYo3Dz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\nf7clxzX6+Kk6AAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fe285ddec50>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "dim = 2\n",
+ "colours = ['red', 'blue']\n",
+ "\n",
+ "# 2-D mean of ones\n",
+ "M1 = np.ones((dim,))\n",
+ "# 2-D mean of threes\n",
+ "M2 = 3 * np.ones((dim,))\n",
+ "# 2-D covariance of 0.3\n",
+ "C1 = np.diag(0.3 * np.ones((dim,)))\n",
+ "# 2-D covariance of 0.2\n",
+ "C2 = np.diag(0.2 * np.ones((dim,)))\n",
+ "\n",
+ "def generate_gaussian(m, c, n_samples):\n",
+ " return np.random.multivariate_normal(m, c, n_samples)\n",
+ "\n",
+ "def plot_data_with_labels(x, y, ax):\n",
+ " unique = np.unique(y)\n",
+ " for li in range(len(unique)):\n",
+ " x_sub = x[y == unique[li]]\n",
+ " ax.scatter(x_sub[:, 0], x_sub[:, 1], c = colours[li])\n",
+ "\n",
+ "def plot_separator(w, b, ax):\n",
+ " slope = -w[0] / w[1]\n",
+ " intercept = -b / w[1]\n",
+ " x = np.arange(0, 6)\n",
+ " ax.plot(x, x * slope + intercept, 'k-')\n",
+ " \n",
+ "n_samples = 50\n",
+ "\n",
+ "# generate 50 points from gaussian 1\n",
+ "x1 = generate_gaussian(M1, C1, n_samples)\n",
+ "# labels\n",
+ "y1 = np.ones((x1.shape[0],))\n",
+ "# generate 50 points from gaussian 2\n",
+ "x2 = generate_gaussian(M2, C2, n_samples)\n",
+ "y2 = -np.ones((x2.shape[0],))\n",
+ "# join\n",
+ "x = np.concatenate((x1, x2), axis = 0)\n",
+ "y = np.concatenate((y1, y2), axis = 0)\n",
+ "\n",
+ "lin_clf = SVM_Predictor(linear_kernel)\n",
+ "lin_clf.train(x, y)\n",
+ "\n",
+ "# get weights\n",
+ "w = np.sum(lin_clf.alphas * y[:, None] * x, axis = 0)\n",
+ "# get bias\n",
+ "cond = (lin_clf.alphas > 1e-4).reshape(-1)\n",
+ "b = y[cond] - np.dot(x[cond], w)\n",
+ "bias = b[0]\n",
+ "\n",
+ "print('x {} y {}'.format(x.shape, y.shape))\n",
+ "fig, ax = plt.subplots()\n",
+ "plot_separator(w, bias, ax)\n",
+ "plot_data_with_labels(x, y, ax)\n",
+ "plt.show()"
+ ]
+ },
{
"cell_type": "markdown",
"metadata": {},
--
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