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@tgjeon
Created July 15, 2019 04:13
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Project02-dga
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Project02-dga",
"version": "0.3.2",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
},
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/tgjeon/16a89fdd87cc24ee23813cb5bd4bdbf0/project02-dga.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"id": "ggmu4ODVrJht",
"colab_type": "code",
"colab": {}
},
"source": [
"### First imports and default parameters\n",
"\n",
"%matplotlib inline\n",
"\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"\n",
"import numpy as np\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Overwritting matplotlib default linestyle of negative contours\n",
"matplotlib.rcParams['contour.negative_linestyle'] = 'solid'\n",
"\n",
"SEED = 42"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "T-COHgYnrXi4",
"colab_type": "code",
"colab": {}
},
"source": [
"from scipy.stats import multivariate_normal\n",
"\n",
"\n",
"class GaussianMixture(object):\n",
" \"\"\" Gaussian mixture.\n",
" Parameters\n",
" ----------\n",
" weights : array, shape (n_components, )\n",
" Weights of the Gaussian mixture components.\n",
" means : array, shape (n_components, n_features)\n",
" Means of the Gaussian mixture components.\n",
" covars : array, shape (n_components, n_features, n_features)\n",
" Covariances of the Gaussian mixture components.\n",
" random_state : int\n",
" Seed used by the random number generator.\n",
" \"\"\"\n",
" def __init__(self, weights, means, covars, random_state=42):\n",
"\n",
" self.weights = weights\n",
" self.means = means\n",
" self.covars = covars\n",
" self.random_state = random_state\n",
"\n",
" def sample(self, n_samples):\n",
" \"\"\" Generating samples from the Gaussian Mixture. \"\"\"\n",
"\n",
" weights = self.weights\n",
" means = self.means\n",
" covars = self.covars\n",
" random_state = self.random_state\n",
"\n",
" rng = np.random.RandomState(random_state)\n",
" n_samples_comp = rng.multinomial(n_samples, weights)\n",
"\n",
" X = np.vstack([\n",
" rng.multivariate_normal(mean, cov, int(sample))\n",
" for (mean, cov, sample) in zip(\n",
" means, covars, n_samples_comp)])\n",
"\n",
" return X\n",
"\n",
" def density(self, X):\n",
" \"\"\" Gaussian Mixture density of the samples X. \"\"\"\n",
"\n",
" weights = self.weights\n",
" means = self.means\n",
" covars = self.covars\n",
"\n",
" n_samples, _ = X.shape\n",
" density = np.zeros(n_samples)\n",
"\n",
" for (weight, mean, cov) in zip(weights, means, covars):\n",
" density += weight * multivariate_normal.pdf(X, mean, cov)\n",
"\n",
" return density"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "545WWDn2rJh-",
"colab_type": "text"
},
"source": [
"# 1. First steps with unsupervised anomaly detection algorithms"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "R_3u0W9FrJiC",
"colab_type": "text"
},
"source": [
"The goal of this section is to get familiar with different unsupervised anomaly detection approaches and algorithms. In order to visualise the output of the different algorithms we consider a toy data set consisting in a two-dimensional Gaussian mixture."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4ddRH58VrJiG",
"colab_type": "text"
},
"source": [
"### Generating the data set"
]
},
{
"cell_type": "code",
"metadata": {
"id": "RuoPa6oirJiJ",
"colab_type": "code",
"colab": {}
},
"source": [
"n_samples = 500\n",
"n_features = 2\n",
"weight_1 = 0.5\n",
"weight_2 = 0.5\n",
"mean_1 = np.zeros(n_features)\n",
"mean_2 = -1 * np.ones(n_features)\n",
"cov_1 = np.array([[2., 2.,], [2., 4.]])\n",
"cov_2 = 2 * np.identity(n_features)\n",
"weights = np.array([weight_1, weight_2])\n",
"means = np.array([mean_1, mean_2])\n",
"covars = np.array([cov_1, cov_2])\n",
"\n",
"gm = GaussianMixture(weights, means, covars, random_state=SEED)\n",
"X = gm.sample(n_samples)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "tCuK1qrxrJiW",
"colab_type": "text"
},
"source": [
"### Plot the samples and levels set of the density"
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": true,
"id": "QoKPtWZIrJia",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 269
},
"outputId": "5d9918dd-72ba-472f-c891-41394660fb01"
},
"source": [
"X_range = np.zeros((n_features, 2))\n",
"X_range[:, 0] = np.min(X, axis=0)\n",
"X_range[:, 1] = np.max(X, axis=0)\n",
"\n",
"h = 0.1 # step size of the mesh\n",
"x_min, x_max = X_range[0, 0] - 0.1, X_range[0, 1] + 0.1\n",
"y_min, y_max = X_range[1, 0] - 0.1, X_range[1, 1] + 0.1\n",
"xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
" np.arange(y_min, y_max, h))\n",
"\n",
"grid = np.c_[xx.ravel(), yy.ravel()]\n",
"Z = gm.density(grid)\n",
"Z = Z.reshape(xx.shape)\n",
"\n",
"plt.figure()\n",
"plt.contour(xx, yy, Z, 10, cmap=plt.cm.Blues_r)\n",
"plt.scatter(X[:, 0], X[:, 1], s=1.)\n",
"plt.show()"
],
"execution_count": 7,
"outputs": [
{
"output_type": "display_data",
"data": {
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Ye7Y1ufS0lBBeemwGq6bHYfDuWzagNhOK2eZAp1H1KvA/X54KZF36eeXoacB5dPFIXlh/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\nRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "aaov89T7rJix",
"colab_type": "text"
},
"source": [
"The goal is to estimate a Minimum volume set with mass at least 0.95. We know that under regularity assumption of the underlying distribution a Minimum volume set is a density level set of the density $f$.\n",
"$$\n",
"\\{x, f(x) \\geq F_f^{-1}(1-\\alpha) \\}\n",
"$$\n",
"where $F_f^{-1}(1-\\alpha)$ is the quantile of order $1-\\alpha$ of the distribution of the random variable $f(X)$.\n",
"\n",
"1. Draw a sample $\\mathcal{S}$ from the previous Gaussian mixture of size $n = 1,000,000$.\n",
"\n",
"2. Using the sample $\\mathcal{S}$ and the true density $f$ given by `gm.density` compute the empirical quantile of order $1-\\alpha$ for $\\alpha = 0.95$ and $\\alpha = 0.99$. You can use for instance the `scipy.stats.mstats.mquantiles` function.\n",
"\n",
"3. Plot the corresponding Minimum Volume set in a figure like the previous one, using `plt.contour` and replacing the number of levels (10) by the threshold you computed: `levels=threshold`.\n",
"\n",
"4. Emphasize the outliers (for instance use a different color) in the previous plot where an outlier is a sample outside the Minimum Volume set."
]
},
{
"cell_type": "code",
"metadata": {
"id": "MAysHbITrJi1",
"colab_type": "code",
"colab": {}
},
"source": [
"alpha_set = 0.95\n",
"\n",
"from scipy.stats.mstats import mquantiles\n",
"\n",
"n_quantile = 1000000\n",
"Xq = gm.sample(n_quantile)\n",
"density_q = gm.density(Xq)\n",
"tau = mquantiles(density_q, 1 - alpha_set)\n",
"\n",
"X_outliers = X[gm.density(X) < tau]"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "iztZXKY8rJjB",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 269
},
"outputId": "bca6bc1e-a2c1-4169-aac1-c8cfce75d1ac"
},
"source": [
"plt.figure()\n",
"c_0 = plt.contour(xx, yy, Z, levels=tau, colors='green', linewidths=3)\n",
"plt.clabel(c_0, inline=1, fontsize=15, fmt={tau[0]: str(alpha_set)})\n",
"plt.scatter(X[:, 0], X[:, 1], s=1.)\n",
"plt.scatter(X_outliers[:, 0], X_outliers[:, 1], color='red', s=4.)\n",
"plt.show()"
],
"execution_count": 42,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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Bi13Hz/Pr/rwqk5VGpDZh46F8jxanNqHWIKW9vxN3QkCm6zhteFu3n8LUZMXh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\niSTE+H+tff4LwSe+BwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "NmjmK67drJjR",
"colab_type": "text"
},
"source": [
"## 1.1. Density estimation"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "yAkrp992rJjV",
"colab_type": "text"
},
"source": [
"We are going to use the plug-in approach to estimate the Minimum Volume set with mass at least 0.95. The plug-in approach means that we replace the density $f$ by an estimate $\\hat f$.\n",
"\n",
"1. Equation of the corresponding Minimum Volume set estimate.\n",
"\n",
"2. Using a Gaussian kernel, compute a kernel density estimator of $f$. To stick with `sklearn` you can use `sklearn.neighbors.kde.KernelDensity` with the default bandwidth.\n",
"\n",
"3. Compute the empirical quantile $\\widehat F_{\\hat f}^{-1}(1-\\alpha)$ from the original sample for $\\alpha = 0.95$ (still using the function `mquantiles`).\n",
"\n",
"4. Add the corresponding Minimum Volume set estimate to the previous plot to visualize the difference between the true MV set and the estimated one."
]
},
{
"cell_type": "code",
"metadata": {
"id": "O6-ji71drJjZ",
"colab_type": "code",
"colab": {}
},
"source": [
"from sklearn.neighbors.kde import KernelDensity\n",
"\n",
"# Estimate density with a Gaussian kernel density estimator\n",
"kde = KernelDensity(kernel='gaussian')\n",
"kde = kde.fit(X)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "cMO-ufdxrJjl",
"colab_type": "code",
"colab": {}
},
"source": [
"kde_X = kde.score_samples(X)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "qHSU3KW5rJjz",
"colab_type": "code",
"colab": {}
},
"source": [
"tau_kde = mquantiles(kde_X, 1 - alpha_set)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"scrolled": true,
"id": "5qic6w1brJkB",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 269
},
"outputId": "2f3b05cc-43cf-4fbf-b36b-fbecc2bc8618"
},
"source": [
"Z_kde = kde.score_samples(grid)\n",
"Z_kde = Z_kde.reshape(xx.shape)\n",
"\n",
"plt.figure()\n",
"c_0 = plt.contour(xx, yy, Z_kde, levels=tau_kde, colors='red', linewidths=3)\n",
"plt.clabel(c_0, inline=1, fontsize=15, fmt={tau_kde[0]: str(alpha_set)})\n",
"c_1 = plt.contour(xx, yy, Z, levels=tau, colors='green', linewidths=2, label='True')\n",
"plt.clabel(c_1, inline=1, fontsize=15, fmt={tau[0]: 'True'})\n",
"plt.scatter(X[:, 0], X[:, 1], s=1.)\n",
"plt.legend()\n",
"plt.show()"
],
"execution_count": 13,
"outputs": [
{
"output_type": "display_data",
"data": {
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dfN8Krhjy6FK7S6leKckWJS8FoiSzbx+88w7MnWuqrGjk5ptlGYBhw9iTfYRp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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "88E4m4vUrJkR",
"colab_type": "text"
},
"source": [
"### Bandwidth selection with cross validation"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "X2LeJ4hprJkU",
"colab_type": "text"
},
"source": [
"We used the default bandwidth.\n",
"\n",
"1. Use cross validation to learn the bandwidth from the data. You may use `sklearn.model_selection.GridSearchCV` to perform a 3-fold cross validation.\n",
"\n",
"2. Plot the Minimum Volume set estimate obtained with the learnt bandwidth."
]
},
{
"cell_type": "code",
"metadata": {
"id": "aYv6Fj7GrJkY",
"colab_type": "code",
"colab": {}
},
"source": [
"from sklearn.model_selection import GridSearchCV"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "GLJc8QSIrJkk",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 89
},
"outputId": "19f68ee1-5d88-4d67-eaeb-f1567c4d9d16"
},
"source": [
"grid_cv = GridSearchCV(KernelDensity(kernel='gaussian'), {'bandwidth': np.linspace(0.1, 2.0, 30)}, cv=3)\n",
"grid_cv.fit(X)\n",
"grid_cv.best_params_"
],
"execution_count": 15,
"outputs": [
{
"output_type": "stream",
"text": [
"/usr/local/lib/python2.7/dist-packages/sklearn/model_selection/_search.py:841: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
" DeprecationWarning)\n"
],
"name": "stderr"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"{'bandwidth': 0.7551724137931034}"
]
},
"metadata": {
"tags": []
},
"execution_count": 15
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "BrE258AjrJky",
"colab_type": "code",
"colab": {}
},
"source": [
"kde_best = grid_cv.best_estimator_\n",
"\n",
"kde_best_X = kde_best.score_samples(X)\n",
"tau_kde_best = mquantiles(kde_best_X, 1 - alpha_set)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "FQIuz4kirJk9",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 269
},
"outputId": "d98a0e71-8d22-48d5-9173-a4a1e7a52eb1"
},
"source": [
"Z_kde_best = kde_best.score_samples(grid)\n",
"Z_kde_best = Z_kde_best.reshape(xx.shape)\n",
"\n",
"plt.figure()\n",
"c_0 = plt.contour(xx, yy, Z_kde_best, levels=tau_kde_best, colors='red', linewidths=3)\n",
"plt.clabel(c_0, inline=1, fontsize=15, fmt={tau_kde_best[0]: str(alpha_set)})\n",
"c_1 = plt.contour(xx, yy, Z, levels=tau, colors='green', linewidths=2, label='True')\n",
"plt.clabel(c_1, inline=1, fontsize=15, fmt={tau[0]: 'True'})\n",
"plt.scatter(X[:, 0], X[:, 1], s=1.)\n",
"plt.legend()\n",
"plt.show()"
],
"execution_count": 17,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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IC7tJs+hm3N34buXq9yNUYXcXWq3cK//8czlU0RwdOnB8TH8+r32R/6X8TNZF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\nRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "TtYILzMwrJlM",
"colab_type": "text"
},
"source": [
"## 1.2. One-Class SVM"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "c5jwVFtXrJlQ",
"colab_type": "text"
},
"source": [
"The One-Class SVM separates the data from the origin by solving the following optimization problem.\n",
"\n",
"\\begin{equation}\n",
"\\min_{\\boldsymbol{w},\\boldsymbol{\\xi},\\rho} \\quad \\frac{1}{2}\\Vert \\boldsymbol{w} \\Vert^2 - \\rho + \\frac{1}{\\nu n}\\sum_{i=1}^n\\xi_i\\\\\n",
"\\text{s.t.} \\quad \\langle \\boldsymbol{w}, \\Phi(x_i) \\rangle \\geqslant \\rho - \\xi_i, \\quad \\xi_i \\geqslant 0 \\quad \\quad 1 \\leqslant i \\leqslant n \n",
"\\end{equation}\n",
"\n",
"where the parameter $\\nu \\in (0,1)$ has to be set by the user and controls the proportion of outliers.\n",
"\n",
"\n",
"It is in general solved via the dual given by\n",
"\\begin{equation}\n",
"\\min_{\\boldsymbol{\\alpha}} \\quad \\frac{1}{2}\\sum_{i,j} k(x_i, x_j)\\\\\n",
"\\text{s.t.} \\quad 0 \\leqslant \\alpha_i \\leqslant \\frac{1}{\\nu n},\\quad \\sum_{i}\\alpha_i = 1 \\quad \\quad 1 \\leqslant i \\leqslant n \n",
"\\end{equation}\n",
"\n",
"1. Show that when using a Gaussian kernel, all data in the feature space lies on the same hypersphere. Show that data are always linearly separable from the origin. Hint: what's the formula of $k(x, x')$ in terms of the feature map $\\Phi$."
]
},
{
"cell_type": "code",
"metadata": {
"id": "kPHH9vRKrJlT",
"colab_type": "code",
"colab": {}
},
"source": [
"from sklearn.svm import OneClassSVM"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "tqblHRM4rJle",
"colab_type": "text"
},
"source": [
"Under mild assumptions the following inequality holds true for all sample size $n$:\n",
"\n",
"$$ \\frac{\\text{Outliers}}{n} \\leq \\nu \\leq \\frac{\\text{Support Vectors}}{n} $$.\n",
"\n",
"Futhermore the two fractions on the left-hand side and right-hand converge almost surely towards $\\nu$.\n",
"\n",
"1. If we want to estimate a Minimum Volume set with mass at least $\\alpha$, how can we set $\\nu$?\n",
"\n",
"2. Use `sklearn.svm.OneClassSVM` with the default parameters (except the parameter $\\nu$ set according to the previous question) to learn a Minimum Volume set with mass at least $0.95$.\n",
"\n",
"3. Plot the Minimum Volume set estimate."
]
},
{
"cell_type": "code",
"metadata": {
"id": "sHXjWnWNrJll",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 69
},
"outputId": "5ef908b3-74c5-4ae3-f912-a023ce1e871b"
},
"source": [
"nu = 0.05\n",
"ocsvm = OneClassSVM(kernel='rbf', gamma=0.05, nu=nu)\n",
"#ocsvm = OneClassSVM(kernel='rbf', gamma=50., nu=nu)\n",
"#ocsvm = OneClassSVM(kernel='rbf', nu=nu)\n",
"ocsvm.fit(X)"
],
"execution_count": 19,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"OneClassSVM(cache_size=200, coef0=0.0, degree=3, gamma=0.05, kernel='rbf',\n",
" max_iter=-1, nu=0.05, random_state=None, shrinking=True, tol=0.001,\n",
" verbose=False)"
]
},
"metadata": {
"tags": []
},
"execution_count": 19
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "AfsbO1GhrJl6",
"colab_type": "code",
"colab": {}
},
"source": [
"X_outliers = X[ocsvm.predict(X) == -1]"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"scrolled": false,
"id": "IQdeD4_IrJmG",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 269
},
"outputId": "88d2dd46-c08c-4e5c-f188-0edf31b80c2a"
},
"source": [
"Z_ocsvm = ocsvm.decision_function(grid)\n",
"Z_ocsvm = Z_ocsvm.reshape(xx.shape)\n",
"\n",
"plt.figure()\n",
"c_0 = plt.contour(xx, yy, Z_ocsvm, levels=[0], colors='red', linewidths=3)\n",
"plt.clabel(c_0, inline=1, fontsize=15, fmt={0: str(alpha_set)})\n",
"c_1 = plt.contour(xx, yy, Z, levels=tau, colors='green', linewidths=2, label='True')\n",
"plt.clabel(c_1, inline=1, fontsize=15, fmt={tau[0]: 'True'})\n",
"plt.scatter(X[:, 0], X[:, 1], s=1.)\n",
"plt.scatter(X_outliers[:, 0], X_outliers[:, 1], s=4., color='red')\n",
"plt.legend()\n",
"plt.show()"
],
"execution_count": 21,
"outputs": [
{
"output_type": "display_data",
"data": {
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GR//0k+o7v3o156OsAPg5Gj5pD7uqqO+FBYXyVMtRvNTuJaJKR/nI6MKNQ375AQPUpGFf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\nRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "OwLD1qocrJmY",
"colab_type": "text"
},
"source": [
"1. What do you notice? The kernel used by the One-Class SVM is given by $$ k(x, x') = \\exp(-\\gamma\\Vert x - x' \\Vert^2). $$\n",
"\n",
"2. What is the default gamma used when we trained the One-Class SVM? Do we need to increase or decrease its value?"
]
},
{
"cell_type": "code",
"metadata": {
"id": "z8ZMvdARrJmc",
"colab_type": "code",
"colab": {}
},
"source": [
"ocsvm?"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "CpoNAdVBrJmp",
"colab_type": "text"
},
"source": [
"### Support vectors - Outliers"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "f41LkQtvrJms",
"colab_type": "text"
},
"source": [
"1. Check that we indeed have $$ \\frac{\\text{Outliers}}{n} \\leq \\nu \\leq \\frac{\\text{Support Vectors}}{n} $$.\n",
"\n",
"2. Use `gamma=10`. Is the inequality always satisfied? Can you guess why?"
]
},
{
"cell_type": "code",
"metadata": {
"id": "fhBbTcY1rJmw",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "7d3beec3-bed8-4bb9-dcef-8157ee8589a1"
},
"source": [
"X_SV = X[ocsvm.support_]\n",
"n_SV = len(X_SV)\n",
"n_outliers = len(X_outliers)\n",
"\n",
"print('{0:.2f} <= {1:.2f} <= {2:.2f}?'.format(1./n_samples*n_outliers, nu, 1./n_samples*n_SV))"
],
"execution_count": 23,
"outputs": [
{
"output_type": "stream",
"text": [
"0.05 <= 0.05 <= 0.06?\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "wAsN3iWirJnC",
"colab_type": "text"
},
"source": [
"Only the support vectors are involved in the decision function of the One-Class SVM.\n",
"\n",
"1. Plot the level sets of the One-Class SVM decision function as we dit for the true density.\n",
"2. Emphasize the Support vectors."
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": true,
"id": "BLla-ISPrJnG",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 269
},
"outputId": "a5863a14-c971-4f70-bd0b-449ead772ab2"
},
"source": [
"plt.figure()\n",
"plt.contourf(xx, yy, Z_ocsvm, 10, cmap=plt.cm.Blues_r)\n",
"plt.scatter(X[:, 0], X[:, 1], s=1.)\n",
"plt.scatter(X_SV[:, 0], X_SV[:, 1], s=20., color='orange')\n",
"plt.show()"
],
"execution_count": 24,
"outputs": [
{
"output_type": "display_data",
"data": {
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rVi6LdVy/+nzdfYG8qNzC0Ubr+rFiLwF55eW9cvVrSuU9f5DAvRUf3td4ZRZn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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "t7J06fgDrJnT",
"colab_type": "text"
},
"source": [
"1. Concerning the support vectors, what is the main difference between the OneClass SVM and a Kernel Density estimator when using a Gaussian Kernel?\n",
"\n",
"2. When is it particularly advantageous to use the OneClass SVM?"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "yGe1EC_srJnW",
"colab_type": "text"
},
"source": [
"### What if we change the value of $\\nu$?"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "1JGcjNCXrJnY",
"colab_type": "text"
},
"source": [
"1. Set $\\nu = 0.4$. How can we estimate a Minimum Volume set with mass at least $0.95$. Hint: Use the `decision_function`."
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": true,
"id": "c-PC7_H2rJna",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 69
},
"outputId": "20c4cfe5-846c-4034-b5f2-286084caeecb"
},
"source": [
"nu = 0.4\n",
"ocsvm = OneClassSVM(kernel='rbf', gamma=0.5, nu=nu)\n",
"ocsvm.fit(X)"
],
"execution_count": 25,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"OneClassSVM(cache_size=200, coef0=0.0, degree=3, gamma=0.5, kernel='rbf',\n",
" max_iter=-1, nu=0.4, random_state=None, shrinking=True, tol=0.001,\n",
" verbose=False)"
]
},
"metadata": {
"tags": []
},
"execution_count": 25
}
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": true,
"id": "YsqpgCU8rJnj",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 269
},
"outputId": "d2a1bb74-4e42-4855-bcf1-f23a97cb3de6"
},
"source": [
"Z_ocsvm = ocsvm.decision_function(grid)\n",
"Z_ocsvm = Z_ocsvm.reshape(xx.shape)\n",
"\n",
"ocsvm_X = ocsvm.decision_function(X)\n",
"tau_ocsvm = mquantiles(ocsvm_X, 1 - alpha_set)\n",
"\n",
"\n",
"plt.figure()\n",
"c_0 = plt.contour(xx, yy, Z_ocsvm, levels=tau_ocsvm, colors='red', linewidths=3)\n",
"plt.clabel(c_0, inline=1, fontsize=15, fmt={tau_ocsvm[0]: str(alpha_set)})\n",
"c_1 = plt.contour(xx, yy, Z, levels=tau, colors='green', linewidths=2, label='True')\n",
"plt.clabel(c_1, inline=1, fontsize=15, fmt={tau[0]: 'True'})\n",
"plt.scatter(X[:, 0], X[:, 1], s=1.)\n",
"plt.legend()\n",
"plt.show()"
],
"execution_count": 26,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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D8uUWdynVymmM/SV/pUz2KlRhV/Etiorgzz/h999h1SpIS6uw+UoYzO8K/+sOGWUd8eiA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\npo9stQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "cqZ8uYpZrJnq",
"colab_type": "text"
},
"source": [
"### Equivalence with SVDD"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4zzj6T4xrJnr",
"colab_type": "text"
},
"source": [
"Support Vector Data Description consists in finding the ball of minimum volume containing an arbitrary proportion of data. This is obtained by minimizing the following optimization problem."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "pTWYCHXzrJnu",
"colab_type": "text"
},
"source": [
"\\begin{equation}\n",
"\\min_{R, \\boldsymbol{\\xi},\\boldsymbol{c}} \\quad R^2 + \\frac{1}{\\nu n}\\sum_{i=1}^{n}\\xi_i\\\\\n",
" \\text{s.t.} \\quad \\Vert \\boldsymbol{x}_i - \\boldsymbol{c}\\Vert^2 \\leqslant R^2 + \\xi_i, \\quad \\xi_i \\geqslant 0 \\quad \\quad 1\\leqslant i \\leqslant n\\\\\n",
"\\end{equation}\n",
"\n",
"It is in general solved via the dual given by\n",
"\\begin{equation}\n",
"\\min_{\\boldsymbol{\\alpha}} \\quad \\sum_{i,j} k(x_i, x_j) + \\sum_{i}\\alpha_i k(x_i,x_i)\\\\\n",
"\\text{s.t.} \\quad 0 \\leqslant \\alpha_i \\leqslant \\frac{1}{\\nu n},\\quad \\sum_{i}\\alpha_i = 1 \\quad \\quad 1 \\leqslant i \\leqslant n \n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "KdL4_PQqrJnv",
"colab_type": "text"
},
"source": [
"1. When are SVDD and the One-Class SVM equivalent?"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "2mGXpfSHrJnw",
"colab_type": "text"
},
"source": [
"## 1.3. Isolation Forest"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "6nJ71HjcrJnx",
"colab_type": "text"
},
"source": [
"1. Run Isolation with `n_estimators=1` , i.e., only one tree will be built.\n",
"\n",
"2. Plot the contour of the set with the $95\\%$ most normal observations. Hint: use the `decision_function` and the `contamination` parameter. Compare it with the true Minimum Volume set with mass at least $0.95$.\n",
"\n",
"3. Increase `n_estimators` to 50, 100 and then 500.\n",
"\n",
"4. What does the `max_sample` parameter change?"
]
},
{
"cell_type": "code",
"metadata": {
"id": "47k-bC8lrJny",
"colab_type": "code",
"colab": {}
},
"source": [
"from sklearn.ensemble import IsolationForest"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "wSoVLNZXrJn3",
"colab_type": "code",
"colab": {}
},
"source": [
"# iforest = IsolationForest(n_estimators=1, contamination=0.05)\n",
"iforest = IsolationForest(n_estimators=100, contamination=0.05)\n",
"iforest = iforest.fit(X)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"scrolled": true,
"id": "ASDzuiLSrJn6",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 339
},
"outputId": "bcbf5f54-ba40-475f-bd1c-cce9ce6f41d4"
},
"source": [
"Z_iforest = iforest.decision_function(grid)\n",
"Z_iforest = Z_iforest.reshape(xx.shape)\n",
"\n",
"plt.figure()\n",
"c_0 = plt.contour(xx, yy, Z_iforest, levels=[iforest.threshold_], colors='red', linewidths=3)\n",
"plt.clabel(c_0, inline=1, fontsize=15, fmt={iforest.threshold_: str(alpha_set)})\n",
"c_1 = plt.contour(xx, yy, Z, levels=tau, colors='green', linewidths=2, label='True')\n",
"plt.clabel(c_1, inline=1, fontsize=15, fmt={tau[0]: 'True'})\n",
"plt.scatter(X[:, 0], X[:, 1], s=1.)\n",
"plt.legend()\n",
"plt.show()"
],
"execution_count": 29,
"outputs": [
{
"output_type": "stream",
"text": [
"/usr/local/lib/python2.7/dist-packages/sklearn/ensemble/iforest.py:417: DeprecationWarning: threshold_ attribute is deprecated in 0.20 and will be removed in 0.22.\n",
" \" be removed in 0.22.\", DeprecationWarning)\n",
"/usr/local/lib/python2.7/dist-packages/sklearn/ensemble/iforest.py:417: DeprecationWarning: threshold_ attribute is deprecated in 0.20 and will be removed in 0.22.\n",
" \" be removed in 0.22.\", DeprecationWarning)\n"
],
"name": "stderr"
},
{
"output_type": "display_data",
"data": {
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jdP3fdHnF66/LIQsUCqtQVl4GQKDko55ITqIqdhXvp7gYfvsN5s2T3eiyshyuKjsCvukM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\nRcMAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LQUtT4O7rJn-",
"colab_type": "text"
},
"source": [
"## 1.4. Local Outlier Factor"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "QpF23xn9rJoA",
"colab_type": "text"
},
"source": [
"k-NN based anomaly detection algorithm. Available on the dev version of Scikit-Learn."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "VYePkHEPrJoB",
"colab_type": "text"
},
"source": [
"## 1.5. Unsupervised as supervised using SVM"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "OK5SmFt7rJoC",
"colab_type": "text"
},
"source": [
"Let $P$ be a distribution with finite support $C$. Let $\\mu$ be the uniform distribution over the support $C$: $\\mu(A) = \\lambda(A)/\\lambda(C)$. We now consider the joint distribution $Q$ of $(X, Y) \\in \\mathbb{R}^d \\times \\{-1, +1\\}$ given by the class conditionals distributions:\n",
"\n",
"$$\n",
"X \\vert Y= +1 \\sim P \\quad \\text{and} \\quad X \\vert Y=-1 \\sim \\mu\n",
"$$\n",
"and a priori class probabilities $p = \\mathbb{P}(Y=1)$.\n",
"\n",
"We are as before interested in finding a given density level set $\\{ f \\geq \\tau \\}$ where $f$ is the density of $P$ with respect to the Lebesgue measure $\\lambda$.\n",
"\n",
"The marginal distribution of $X$, $P_X$, is given by\n",
"$$\n",
"P_X = p P + (1-p) Q.\n",
"$$\n",
"\n",
"Assuming that $P$ has a density $f$. It can be shown that\n",
"\n",
"$$\\eta(x) = P(Y=1\\vert X=x) = \\frac{pf(x)}{pf(x) + (1-p)/\\lambda(C)}$$\n",
"\n",
"The optimal classification set is given by $\\{ \\eta \\geq 1/2 \\}$\n",
"\n",
"1. Show that if $p=1/(1 + \\lambda(C)\\tau)$ then $\\lambda(\\{\\eta \\geq 1/2 \\} \\Delta \\{f \\geq \\tau \\} ) = 0$\n",
"\n",
"Thus solving a binary classification problem assigning weights $p$ and $1-p$ to the samples can lead to a density level set."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "P9ypaxZerJoC",
"colab_type": "text"
},
"source": [
"### Generate uniform data in the range of X"
]
},
{
"cell_type": "code",
"metadata": {
"id": "gv6Ikw0MrJoD",
"colab_type": "code",
"colab": {}
},
"source": [
"### Generating artificial second class \n",
"rng = np.random.RandomState(SEED)\n",
"\n",
"U = np.zeros((n_samples, n_features))\n",
"for i in range(n_features):\n",
" U [:, i] = rng.uniform(X_range[i, 0], X_range[i, 1], n_samples)\n",
" \n",
"vol = np.prod(X_range[:, 1] - X_range[:, 0])"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "ywnEd57IrJoG",
"colab_type": "code",
"colab": {}
},
"source": [
"X_bin = np.r_[X, U]\n",
"y_bin = np.r_[np.ones(n_samples), np.zeros(n_samples)].astype(int)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"scrolled": false,
"id": "Vr3qXCnfrJoI",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 269
},
"outputId": "9960b650-c5e6-4e5d-8f4e-453b799b31a2"
},
"source": [
"from sklearn.svm import SVC\n",
"# SVM parameters\n",
"\n",
"C = 1.\n",
"lambda_reg = 0.00005\n",
"gamma = 0.01\n",
"\n",
"p = 1. / (1. + vol * tau[0])\n",
"\n",
"weight_1 = p * 1. / (lambda_reg * n_samples)\n",
"weight_0 = (1 - p) * 1. / (lambda_reg * n_samples)\n",
"class_weight = {1: weight_1, 0: weight_0}\n",
"\n",
"clf = SVC(C=C, kernel='rbf', gamma=gamma, class_weight=class_weight)\n",
"clf = clf.fit(X_bin, y_bin)\n",
"\n",
"Z_svm = clf.decision_function(grid)\n",
"Z_svm = Z_svm.reshape(xx.shape)\n",
"\n",
"plt.figure()\n",
"c_0 = plt.contour(xx, yy, Z_svm, levels=[0], colors='red', linewidths=3)\n",
"plt.clabel(c_0, inline=1, fontsize=15, fmt={0: str(alpha_set)})\n",
"c_1 = plt.contour(xx, yy, Z, levels=tau, colors='green', linewidths=2, label='True')\n",
"plt.clabel(c_1, inline=1, fontsize=15, fmt={tau[0]: 'True'})\n",
"plt.scatter(X[:, 0], X[:, 1], s=1.)\n",
"plt.legend()\n",
"plt.show()"
],
"execution_count": 32,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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Lg4o+/FDOYWHMkCFyh2nLlmY3vZF/g59P/Mzio4vZcnZLicRZHWI68ECTBxiW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\nUkoFmf8HP/Xmma01MJ0AAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "-PUN5NrBrJoM",
"colab_type": "code",
"colab": {}
},
"source": [
""
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "2PzFJeSTrJoP",
"colab_type": "text"
},
"source": [
"# 2. Anomaly scoring and Mass Volume curve"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "obOOQWzPrJoP",
"colab_type": "text"
},
"source": [
"Usually unsupervised anomaly detection algorithms returns a scoring function $s$ such that the smaller $s(x)$ the more abnormal $x$ is. To assess the performance of such a scoring function we can use the Mass Volume curve. The MV curve of a scoring function $s$ is given for all $\\alpha \\in (0,1)$ by\n",
"$$\n",
"MV_s(\\alpha) = \\lambda\\{x, s(x) \\geq F_s^{-1}(1-\\alpha) \\}\n",
"$$\n",
"where $F_s^{-1}(1-\\alpha)$ is the quantile of order $1-\\alpha$ of the distribution of the random variable $s(X)$.\n",
"\n",
"Under regularity assumptions, the MV curve is also given by the parametric curve\n",
"\n",
"$$\n",
"(\\mathbb{P}(s(X) \\geq t), \\lambda(x, s(x) \\geq t))\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "yMmRZhfurJoQ",
"colab_type": "text"
},
"source": [
"Assume that the random variable $X$ with distribution $P$ has a density $f$ with respect to the Lebesgue measure. Furthermore assume that for all $\\alpha \\in (0,1)$ the Minimum Volume set optimization problem\n",
"$$\n",
"\\min_{\\Omega \\in \\mathcal{M}} \\lambda(\\Omega) \\quad \\text{ s.t } \\quad P(\\Omega) \\geq \\alpha .\n",
"$$\n",
"has a unique solution given by\n",
"$$\n",
"\\Omega^*_{\\alpha} = \\{x, f(x) \\geq F_f^{-1}(1-\\alpha) \\}.\n",
"$$\n",
"\n",
"1. Show that for all $\\alpha \\in (0,1)$, $MV_s(\\alpha) - MV_f(\\alpha) \\leq \\lambda(\\Omega^*_{\\alpha} \\Delta \\{x, s(x) \\geq F_s^{-1}(1-\\alpha) \\})$.\n",
"\n",
"2. Show that for all $\\alpha \\in (0,1)$, $MV_f(\\alpha) \\leq MV_s(\\alpha)$. Hint: use the following property: for all $\\alpha \\in (0,1)$, $\\mathbb{P}(s(X) < F_s^{-1}(1-\\alpha)) \\leq 1-\\alpha$.\n",
"\n",
"3. In what sense a scoring function minimizing the area under the Mass Volume curve is optimal?\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "xA_7jCLPrJoR",
"colab_type": "text"
},
"source": [
"## 2.1. Using Mass Volume curve for performance evaluation"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "e-IHFXvprJoS",
"colab_type": "text"
},
"source": [
"The lower $MV_s$ the better the scoring function $s$. The goal is to compare the performance of scoring functions given by the One-Class SVM for different values of $\\gamma$ using the Mass Volume curve. To easily plot the Mass Volume we are going to use the ROC curve function given by `sklearn`. The idea is to use a uniform sample as the positive class and to consider the Gaussian mixture data set as the negative class. To plot the MV curve we want to plot the volume against the mass $\\alpha$. This will be given by $1-TPR$ against $1-FPR$.\n",
"\n",
"1. Using `sklearn.model_selection.ShuffleSplit` split the data set into a training set and a test set.\n",
"\n",
"2. Generate `n_sim=100000` uniform random variables in the hypercube enclosing the data using `numpy.random.uniform`.\n",
"\n",
"3. Build a training set consisting in the concatenation of the training set of the Gaussian mixture data set (obtained in 1.) and the uniform sample.\n",
"\n",
"4. Similarly, build the test set by concatenating the test set of the Gaussian mixture data set (obtained in 1.) and the uniform sample."
]
},
{
"cell_type": "code",
"metadata": {
"id": "yHla0DPbrJoU",
"colab_type": "code",
"colab": {}
},
"source": [
"from sklearn.model_selection import ShuffleSplit\n",
"\n",
"X_range = np.zeros((n_features, 2))\n",
"X_range[:, 0] = np.min(X, axis=0)\n",
"X_range[:, 1] = np.max(X, axis=0)\n",
"\n",
"n_sim = 100000\n",
"U = np.zeros((n_sim, n_features))\n",
"for i in range(n_features):\n",
" U [:, i] = rng.uniform(X_range[i, 0], X_range[i, 1], n_sim)\n",
"\n",
"### Training on half the data\n",
"ss = ShuffleSplit(n_splits=1, test_size=0.5, random_state=SEED)\n",
"\n",
"ss = ss.split(X)\n",
"train, test = ss.next()\n",
"\n",
"X_train = X[train]\n",
"X_test = X[test]\n",
"X_train_all = np.r_[U, X_train]\n",
"y_train_all = np.r_[np.zeros(n_sim), np.ones(len(train))]\n",
"X_test_all = np.r_[U, X_test]\n",
"y_test_all = np.r_[np.zeros(n_sim), np.ones(len(test))]"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "7Ht7wz3PrJoa",
"colab_type": "text"
},
"source": [
"1. Compute the Mass Volume curve, estimated on the training set, of the scoring function obtained with the One-Class SVM for $\\gamma=0.05$ and $\\gamma=10$. Compute the area under the Mass Volume curve for each value of $\\gamma$.\n",
"\n",
"2. Compute the Mass Volume curve estimated on the test set for each value of $\\gamma$. Compute the area under the Mass Volume curve for each value of $\\gamma$."
]
},
{
"cell_type": "code",
"metadata": {
"id": "Oniqsp1UrJoc",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 390
},
"outputId": "fe6bf170-1714-4de0-b411-7ed6472a7c5b"
},
"source": [
"from sklearn.metrics import roc_curve, auc\n",
"\n",
"colors = ['red', 'blue']\n",
"\n",
"plt.figure(figsize=(12, 6))\n",
"\n",
"for g, gamma in enumerate([0.05, 10]):\n",
" ocsvm = OneClassSVM(gamma=gamma, nu=0.05)\n",
" ### Train algorithm (fit), compute decision function on train and test, compute ROC and AUC, draw ROC\n",
" ocsvm.fit(X_train)\n",
" ocsvm_train_all = ocsvm.decision_function(X_train_all)\n",
" ocsvm_test_all = ocsvm.decision_function(X_test_all)\n",
" fpr_train_, tpr_train_, _ = roc_curve(y_train_all, -ocsvm_train_all, pos_label=0)\n",
" ocsvm_auc_train = auc(1 - fpr_train_, 1 - tpr_train_)\n",
" fpr_test_, tpr_test_, _ = roc_curve(y_test_all, -ocsvm_test_all, pos_label=0)\n",
" ocsvm_auc_test = auc(1 - fpr_test_, 1 - tpr_test_)\n",
" \n",
" plt.subplot(1, 2, 1)\n",
" plt.title('Performance on training set')\n",
" plt.plot(1 - fpr_train_, 1 - tpr_train_, color=colors[g], label= 'Gamma: {0:.2f} - AMV: {1:.3f}'.format(gamma, ocsvm_auc_train))\n",
" \n",
" plt.subplot(1, 2, 2)\n",
" plt.title('Performance on test set')\n",
" plt.plot(1 - fpr_test_, 1 - tpr_test_, color=colors[g], label= 'Gamma: {0:.2f} - AMV: {1:.3f}'.format(gamma, ocsvm_auc_test))\n",
"\n",
"plt.subplot(1, 2, 1)\n",
"plt.legend(loc=0)\n",
"plt.xlim((-0.05, 1.05))\n",
"plt.ylim((-0.05, 1.05))\n",
"\n",
"plt.subplot(1, 2, 2)\n",
"plt.legend(loc=0)\n",
"plt.xlim((-0.05, 1.05))\n",
"plt.ylim((-0.05, 1.05))\n",
"\n",
"plt.show()"
],
"execution_count": 34,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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t2zZ27drFrl272L59e6FyU6ZMYerUqcX+0gfn1tyTTz5JdnY2PXr0KPM9Dxgw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\nAfBfJFvjmPm3QQ0AAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 864x432 with 2 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "rhtorsNFrJoi",
"colab_type": "text"
},
"source": [
"# 3. Performance evaluation on real data sets"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "OLlErgYmrJok",
"colab_type": "text"
},
"source": [
"## 3.1. DGA data set"
]
},
{
"cell_type": "code",
"metadata": {
"id": "1dW_GrkixzcE",
"colab_type": "code",
"colab": {}
},
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"from matplotlib import rcParams\n",
"import scipy.stats as st\n",
"import itertools"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "DQ_IOA6rx2Ki",
"colab_type": "code",
"colab": {}
},
"source": [
"# For Google Drive\n",
"df_dga = pd.read_csv(\"https://drive.google.com/uc?export=download&id=1jr-AKmeb6xip3815c8xASkTJQpaYpOPb\")\n",
"\n",
"# For Github\n",
"#df_re = pd.read_csv(\"https://raw.githubusercontent.com/tgjeon/kings/master/data-02-dga.csv\")\n"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "w_V0ix1vyTeQ",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 227
},
"outputId": "e93199c5-17f9-4d59-aaa9-6adbf36b2597"
},
"source": [
"print(df_dga.shape)\n",
"print(df_dga.nunique())"
],
"execution_count": 48,
"outputs": [
{
"output_type": "stream",
"text": [
"(1200, 10)\n",
"H2 94\n",
"C2H2 72\n",
"C2H4 93\n",
"C2H6 68\n",
"CH4 97\n",
"C3H8 97\n",
"TCG 100\n",
"CO 67\n",
"CO2 89\n",
"normality 2\n",
"dtype: int64\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "zsKaKqdiyq6g",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 297
},
"outputId": "6bff478c-9f19-4d4e-9729-4057266d3223"
},
"source": [
"print(df_dga.info())"
],
"execution_count": 49,
"outputs": [
{
"output_type": "stream",
"text": [
"<class 'pandas.core.frame.DataFrame'>\n",
"RangeIndex: 1200 entries, 0 to 1199\n",
"Data columns (total 10 columns):\n",
"H2 1200 non-null float64\n",
"C2H2 1200 non-null float64\n",
"C2H4 1200 non-null float64\n",
"C2H6 1200 non-null float64\n",
"CH4 1200 non-null float64\n",
"C3H8 1200 non-null float64\n",
"TCG 1200 non-null float64\n",
"CO 1200 non-null float64\n",
"CO2 1200 non-null float64\n",
"normality 1200 non-null int64\n",
"dtypes: float64(9), int64(1)\n",
"memory usage: 93.8 KB\n",
"None\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "MqCqbSwgyuTh",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 204
},
"outputId": "3502f9dd-1aad-4261-9974-d72fb4cad17e"
},
"source": [
"df_dga.head()"
],
"execution_count": 50,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>H2</th>\n",
" <th>C2H2</th>\n",
" <th>C2H4</th>\n",
" <th>C2H6</th>\n",
" <th>CH4</th>\n",
" <th>C3H8</th>\n",
" <th>TCG</th>\n",
" <th>CO</th>\n",
" <th>CO2</th>\n",
" <th>normality</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>0.48</td>\n",
" <td>0.48</td>\n",
" <td>0.30</td>\n",
" <td>0.65</td>\n",
" <td>0.41</td>\n",
" <td>0.00</td>\n",
" <td>0.15</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>0.47</td>\n",
" <td>0.53</td>\n",
" <td>0.41</td>\n",
" <td>0.66</td>\n",
" <td>0.46</td>\n",
" <td>0.00</td>\n",
" <td>0.01</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>0.47</td>\n",
" <td>0.58</td>\n",
" <td>0.45</td>\n",
" <td>0.67</td>\n",
" <td>0.49</td>\n",
" <td>0.00</td>\n",
" <td>0.03</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>0.12</td>\n",
" <td>0.75</td>\n",
" <td>0.58</td>\n",
" <td>0.71</td>\n",
" <td>0.59</td>\n",
" <td>0.00</td>\n",
" <td>0.00</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>0.05</td>\n",
" <td>0.76</td>\n",
" <td>0.55</td>\n",
" <td>0.79</td>\n",
" <td>0.60</td>\n",
" <td>0.02</td>\n",
" <td>0.02</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" H2 C2H2 C2H4 C2H6 CH4 C3H8 TCG CO CO2 normality\n",
"0 0.0 0.0 0.48 0.48 0.30 0.65 0.41 0.00 0.15 0\n",
"1 0.0 0.0 0.47 0.53 0.41 0.66 0.46 0.00 0.01 0\n",
"2 0.0 0.0 0.47 0.58 0.45 0.67 0.49 0.00 0.03 0\n",
"3 0.0 0.0 0.12 0.75 0.58 0.71 0.59 0.00 0.00 0\n",
"4 0.0 0.0 0.05 0.76 0.55 0.79 0.60 0.02 0.02 0"
]
},
"metadata": {
"tags": []
},
"execution_count": 50
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "7uXt0qvTzA5S",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 504
},
"outputId": "1cbbb7e4-2536-4c7f-cee5-2381bc977929"
},
"source": [
"corr = df_dga[['H2', 'C2H2', 'C2H4', 'C2H6', 'CH4', 'C3H8', 'TCG', 'CO', 'CO2', 'normality']]\n",
"\n",
"plt.figure(figsize=(10,8))\n",
"plt.title('Correlation of variables')\n",
"sns.heatmap(corr.astype(float).corr(),vmax=1.0, annot=True)\n",
"plt.show()"
],
"execution_count": 51,
"outputs": [
{
"output_type": "display_data",
"data": {
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A/vnfuOw3+JrovmACYd1aU5ZTwJZxr1F8NLN8v3+zSC765UX2vfA5B95cSlDb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3ftjLeoERdFURRFUZoRNeKiKIqiKM3ctTTHpcl0XPyGdaP9qxMRWg3nlm/i7OIfbNYLRx2dlzyG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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 720x576 with 2 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "1gSHfWkBzhpM",
"colab_type": "code",
"colab": {}
},
"source": [
"X = df_dga.drop(\"normality\" ,axis=1).values\n",
"y = df_dga[\"normality\"].values"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "W6Z7n_IhrJoq",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "32d9fb22-6bdb-47a6-8835-58faa9382043"
},
"source": [
"n_samples, n_features = X.shape\n",
"n_samples, n_features"
],
"execution_count": 53,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(1200, 9)"
]
},
"metadata": {
"tags": []
},
"execution_count": 53
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "e-iK-3PCrJow",
"colab_type": "text"
},
"source": [
"1. What's the proportion of anomalies in the data set (label 0)?\n",
"2. Split the data set into a training a test set using `StratifiedShuffleSplit` to preserve the proportion of each class in the training and test sets.\n",
"3. Compare the performance of the OneClass SVM and Isolation Forest using the ROC curve (computed with the true labels) on the train set and the set set:\n",
" - train the algorithm on the training set (without the labels), compute the ROC curve on the training set using the labels.\n",
" - train the algorithm on the training set (without the labels), compute the ROC curve on the test set using the labels\n",
"4. Compare the performance of the OneClass SVM and Isolation Forest using the Mass Volume curve on the training and test sets"
]
},
{
"cell_type": "code",
"metadata": {
"id": "QtTCpzGxrJow",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "eda1c5a0-92cc-4428-a3e0-5ef22784f0d3"
},
"source": [
"'Percentage of anomalies: {0}'.format(1 - np.mean(y))"
],
"execution_count": 54,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"'Percentage of anomalies: 0.195833333333'"
]
},
"metadata": {
"tags": []
},
"execution_count": 54
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "TkCWu_JgrJo2",
"colab_type": "code",
"colab": {}
},
"source": [
"from sklearn.model_selection import StratifiedShuffleSplit\n",
"\n",
"sss = StratifiedShuffleSplit(n_splits=1, test_size=0.5, random_state=SEED)\n",
"\n",
"train, test = sss.split(X, y).next()\n",
"X_train, y_train = X[train], y[train]\n",
"X_test, y_test = X[test], y[test]"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"scrolled": true,
"id": "zU8Z4ymFrJo5",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 52
},
"outputId": "048f40b2-44ec-4640-bf3d-12b83434a248"
},
"source": [
"print('Percentage of anomalies in train : {0}'.format(1 - np.mean(y_train)))\n",
"print('Percentage of anomalies in test : {0}'.format(1 - np.mean(y_test)))"
],
"execution_count": 56,
"outputs": [
{
"output_type": "stream",
"text": [
"Percentage of anomalies in train : 0.195\n",
"Percentage of anomalies in test : 0.196666666667\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "FyvXb9S8rJo9",
"colab_type": "text"
},
"source": [
"### Performance on training set and test set - ROC curve - AUC"
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": false,
"id": "h3EEvZOHrJo-",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 390
},
"outputId": "1b66a88f-75b4-4e01-9c92-40a1e63a7c33"
},
"source": [
"### !!!! This can take a few minutes. You might consider running it with Isolation Forest only at first\n",
"\n",
"algorithms = [OneClassSVM(), IsolationForest()]\n",
"name = ['Isolation Forest', 'Ocsvm']\n",
"colors = ['green', 'red']\n",
"\n",
"plt.figure(figsize=(12, 6))\n",
"\n",
"for a, algo in enumerate(algorithms):\n",
" algo.fit(X_train)\n",
" algo_train = algo.decision_function(X_train)\n",
" algo_test = algo.decision_function(X_test)\n",
" fpr_train_, tpr_train_, _ = roc_curve(y_train, -algo_train, pos_label=0)\n",
" algo_auc_train = auc(fpr_train_, tpr_train_)\n",
" fpr_test_, tpr_test_, _ = roc_curve(y_test, -algo_test, pos_label=0)\n",
" algo_auc_test = auc(fpr_test_, tpr_test_)\n",
" \n",
" plt.subplot(1, 2, 1)\n",
" plt.title('Performance on training set')\n",
" plt.plot(fpr_train_, tpr_train_, color=colors[a], label= '{0} - AUC: {1:.3f}'.format(name[a], algo_auc_train))\n",
" \n",
" plt.subplot(1, 2, 2)\n",
" plt.title('Performance on test set')\n",
" plt.plot(fpr_test_, tpr_test_, color=colors[a], label= '{0} - AUC: {1:.3f}'.format(name[a], algo_auc_test))\n",
"\n",
"plt.subplot(1, 2, 1)\n",
"plt.legend(loc=0)\n",
"plt.xlim((-0.05, 1.05))\n",
"plt.ylim((-0.05, 1.05))\n",
"\n",
"plt.subplot(1, 2, 2)\n",
"plt.legend(loc=0)\n",
"plt.xlim((-0.05, 1.05))\n",
"plt.ylim((-0.05, 1.05))\n",
"\n",
"plt.show()"
],
"execution_count": 57,
"outputs": [
{
"output_type": "display_data",
"data": {
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Nmzh9+jQAP/74I2PHjkUpRY0aNfD19eXkyZM0a9Ys17GJwuvHQz8ycHUWHTvS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\ni4iIiIgAKoxFRERERAD4/7Fpbqq7hm/zAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 864x432 with 2 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Qe74ujKZrJpB",
"colab_type": "text"
},
"source": [
"### Performance - MV curve - AMV"
]
},
{
"cell_type": "code",
"metadata": {
"id": "Xp8Bzlt1rJpC",
"colab_type": "code",
"colab": {}
},
"source": [
"X_range = np.zeros((n_features, 2))\n",
"X_range[:, 0] = np.min(X, axis=0)\n",
"X_range[:, 1] = np.max(X, axis=0)\n",
"\n",
"n_sim = 100000\n",
"U = np.zeros((n_sim, n_features))\n",
"for i in range(n_features):\n",
" U [:, i] = rng.uniform(X_range[i, 0], X_range[i, 1], n_sim)\n",
"\n",
"### We add uniform data to compute volumes\n",
"X_train_all = np.r_[U, X_train]\n",
"X_test_all = np.r_[U, X_test]\n",
"\n",
"# Assigning same label to all data (normal and anomalies): the anomalies are the uniform samples\n",
"y_train_all = np.r_[np.zeros(n_sim), np.ones(len(X_train))]\n",
"y_test_all = np.r_[np.zeros(n_sim), np.ones(len(X_test))]"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"scrolled": true,
"id": "G5zSBIoTrJpI",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 390
},
"outputId": "531e5630-a179-49ad-e0ff-49a098adcabd"
},
"source": [
"### !!!! This can take a few minutes. You might consider running it with Isolation Forest only at first\n",
"\n",
"algorithms = [OneClassSVM(), IsolationForest()]\n",
"name = ['Isolation Forest', 'Ocsvm']\n",
"colors = ['green', 'red']\n",
"# algorithms = [IsolationForest()]\n",
"# name = ['Isolation Forest']\n",
"# colors = ['green']\n",
"\n",
"plt.figure(figsize=(12, 6))\n",
"\n",
"for a, algo in enumerate(algorithms):\n",
" ### Train algorithm (fit), compute decision function on train and test, compute ROC and AUC, draw ROC\n",
" algo.fit(X_train)\n",
" algo_train_all = algo.decision_function(X_train_all)\n",
" algo_test_all = algo.decision_function(X_test_all)\n",
" fpr_train_, tpr_train_, _ = roc_curve(y_train_all, -algo_train_all, pos_label=0)\n",
" algo_auc_train = auc(1 - fpr_train_, 1 - tpr_train_)\n",
" fpr_test_, tpr_test_, _ = roc_curve(y_test_all, -algo_test_all, pos_label=0)\n",
" algo_auc_test = auc(1 - fpr_test_, 1 - tpr_test_)\n",
" \n",
" plt.subplot(1, 2, 1)\n",
" plt.title('Performance on training set')\n",
" plt.plot(1 - fpr_train_, 1 - tpr_train_, color=colors[a], label= '{0} - AMV: {1:.3f}'.format(name[a], algo_auc_train))\n",
" \n",
" plt.subplot(1, 2, 2)\n",
" plt.title('Performance on test set')\n",
" plt.plot(1 - fpr_test_, 1 - tpr_test_, color=colors[a], label= '{0} - AUC: {1:.3f}'.format(name[a], algo_auc_test))\n",
"\n",
"plt.subplot(1, 2, 1)\n",
"plt.legend(loc=0)\n",
"plt.xlim((-0.05, 1.05))\n",
"plt.ylim((-0.05, 1.05))\n",
"\n",
"plt.subplot(1, 2, 2)\n",
"plt.legend(loc=0)\n",
"plt.xlim((-0.05, 1.05))\n",
"plt.ylim((-0.05, 1.05))\n",
"\n",
"plt.show()"
],
"execution_count": 59,
"outputs": [
{
"output_type": "display_data",
"data": {
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bAq6nXdD03GbPnn1GU5zfejxZ1+kyMzMZPHgwI0aM4LzzzsszLyEhgeuuu67A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\nYII=\n",
"text/plain": [
"<Figure size 864x432 with 2 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
}
]
}
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