Datacenter anomaly detection.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Datacenter anomaly detection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.patches import Ellipse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Log file with VM usage statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_filename = \"system-load.csv\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Number of Gaussians."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_gaussians = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convergence threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "convergence_eps = 0.0001"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random seed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "random_seed = 42"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_load = pd.read_csv(input_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df_load.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalizing the data to the range [0..1]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = (X - np.min(X, axis=0)) / (np.max(X, axis=0) - np.min(X, axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "m, n = X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(X.T[0], X.T[1], \"o\", c=\"#144C59\", alpha=0.5, markersize=3)\n",
    "\n",
    "plt.xlabel(\"CPU usage\")\n",
    "plt.ylabel(\"RAM usage\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training misture of Gaussians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(random_seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initializing Gaussians at random data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "means = X[np.random.choice(m, size=num_gaussians, replace=False)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "covariances = np.ones((num_gaussians, n, n)) * np.identity(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initializing source probability for every Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "phis = np.ones(num_gaussians) / num_gaussians"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initializing correspondence probability matrix for every point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 936)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W = np.zeros((num_gaussians, m))\n",
    "W.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement multivariate Gaussian PDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def multivariate_gaussian_pdf(X, mu, sigma):    \n",
    "    # formula:\n",
    "    # https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.multivariate_normal.html\n",
    "    \n",
    "    two_pi_to_pow_k = np.power(2 * np.pi, X.shape[1])\n",
    "    const_multiplier = 1 / np.sqrt(two_pi_to_pow_k * np.linalg.det(sigma))\n",
    "    sigma_inverse = np.linalg.inv(sigma)\n",
    "    x_minus_mu = (X - mu).T\n",
    "    \n",
    "    res = np.zeros(X.shape[0])\n",
    "    \n",
    "    for i in range(X.shape[0]):\n",
    "        res[i] = const_multiplier * np.exp(-1/2*((x_minus_mu[:,i].T)).dot(sigma_inverse).dot(x_minus_mu[:,i]))\n",
    "    \n",
    "    return res \n",
    "    \n",
    "#     from scipy.stats import multivariate_normal\n",
    "#     return multivariate_normal(mu, sigma).pdf(X)\n",
    "    \n",
    "    # ===================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement E step of EM algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def e_step(X, means, covariances, phis):\n",
    "    num_gaussians = len(means)\n",
    "    W = np.zeros((num_gaussians, len(X)))\n",
    "    \n",
    "    for i, mu in enumerate(means):\n",
    "        W[i] = phis[i] * multivariate_gaussian_pdf(X, mu, covariances[i])\n",
    "    W /= W.sum(0)\n",
    "    # ====================================================\n",
    "        \n",
    "    return W"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement M step of EM algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def m_step(X, W):\n",
    "    num_gaussians = len(W)\n",
    "    m, n = X.shape\n",
    "    \n",
    "    phis = np.zeros(num_gaussians)\n",
    "    means = np.zeros((num_gaussians, n))\n",
    "    covariances = np.zeros((num_gaussians, n, n))\n",
    "    \n",
    "    for i in range(num_gaussians):\n",
    "        for j, xj in enumerate(X):\n",
    "            phis[i] += W[i,j]\n",
    "            means[i] += W[i,j] * xj\n",
    "        means[i] /= W[i,:].sum()         \n",
    "    phis /= m\n",
    "    \n",
    "    for i in range(num_gaussians):\n",
    "        for j, xj in enumerate(X):\n",
    "            covariances[i] += W[i,j] * np.dot((xj - means[i]).reshape(2,1)\n",
    "                                              ,(xj - means[i]).reshape(2,1).T)\n",
    "        covariances[i] /= W[i,:].sum()  \n",
    "    # ====================================================\n",
    "    \n",
    "    return phis, means, covariances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Run EM until convergence**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gmm_log_likelihood(x, phis, means, covariances, num_gaussians):\n",
    "\n",
    "    cluster_likelihood = np.log(sum([phi * multivariate_gaussian_pdf(X, means[i], covariances[i]) \n",
    "                                     for i, phi in enumerate(phis)]))\n",
    "    return sum(cluster_likelihood)\n",
    "    # ===================================================="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_likelihoods = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:   0    Log-likelihood: -1792.4863\n",
      "Iteration:   1    Log-likelihood:  1126.1728\n",
      "Iteration:   2    Log-likelihood:  1147.6845\n",
      "Iteration:   3    Log-likelihood:  1196.3866\n",
      "Iteration:   4    Log-likelihood:  1239.3713\n",
      "Iteration:   5    Log-likelihood:  1263.4331\n",
      "Iteration:   6    Log-likelihood:  1274.2707\n",
      "Iteration:   7    Log-likelihood:  1278.8859\n",
      "Iteration:   8    Log-likelihood:  1280.9282\n",
      "Iteration:   9    Log-likelihood:  1281.8832\n",
      "Iteration:  10    Log-likelihood:  1282.3662\n",
      "Iteration:  11    Log-likelihood:  1282.6470\n",
      "Iteration:  12    Log-likelihood:  1282.8473\n",
      "Iteration:  13    Log-likelihood:  1283.0233\n",
      "Iteration:  14    Log-likelihood:  1283.2026\n",
      "Iteration:  15    Log-likelihood:  1283.4005\n",
      "Iteration:  16    Log-likelihood:  1283.6280\n",
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      "Iteration:  18    Log-likelihood:  1284.2206\n",
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      "Iteration:  20    Log-likelihood:  1285.1417\n",
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      "Iteration:  27    Log-likelihood:  1300.1455\n",
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      "Iteration: 174    Log-likelihood:  1367.6365\n",
      "Iteration: 175    Log-likelihood:  1367.6369\n",
      "Iteration: 176    Log-likelihood:  1367.6373\n",
      "Iteration: 177    Log-likelihood:  1367.6376\n",
      "Iteration: 178    Log-likelihood:  1367.6379\n",
      "Iteration: 179    Log-likelihood:  1367.6381\n",
      "Iteration: 180    Log-likelihood:  1367.6384\n",
      "Iteration: 181    Log-likelihood:  1367.6386\n",
      "Iteration: 182    Log-likelihood:  1367.6388\n",
      "Iteration: 183    Log-likelihood:  1367.6389\n",
      "Iteration: 184    Log-likelihood:  1367.6391\n",
      "Iteration: 185    Log-likelihood:  1367.6392\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 186    Log-likelihood:  1367.6393\n",
      "Iteration: 187    Log-likelihood:  1367.6394\n",
      "Iteration: 188    Log-likelihood:  1367.6395\n",
      "EM has converged. Stopping early.\n"
     ]
    }
   ],
   "source": [
    "max_em_iterations = 1000\n",
    "for iteration in range(max_em_iterations):\n",
    "    # E-step.\n",
    "    W = e_step(X, means, covariances, phis)\n",
    "\n",
    "    # Compute log-likelihood.\n",
    "    log_likelihood = gmm_log_likelihood(X, phis, means, covariances, num_gaussians)\n",
    "    log_likelihoods.append(log_likelihood)\n",
    "    print(\"Iteration: {0:3d}    Log-likelihood: {1:10.4f}\".format(iteration, log_likelihood))\n",
    "\n",
    "    # M-step.\n",
    "    phis, means, covariances = m_step(X, W)\n",
    "    \n",
    "    # Check log-likelihood for convergence.\n",
    "    if len(log_likelihoods) > 2 and np.abs(log_likelihoods[-1] - log_likelihoods[-2]) < convergence_eps:\n",
    "        print(\"EM has converged. Stopping early.\")\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 6))\n",
    "plt.plot(log_likelihoods)\n",
    "\n",
    "plt.xlabel(\"# Iteration\")\n",
    "plt.ylabel(\"Log-likelihood\")\n",
    "plt.title(\"Learning Progress\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_ellipse(pos, cov, nstd=2, ax=None, **kwargs):\n",
    "    def eigsorted(cov):\n",
    "        vals, vecs = np.linalg.eigh(cov)\n",
    "        order = vals.argsort()[::-1]\n",
    "        return vals[order], vecs[:,order]\n",
    "\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "\n",
    "    vals, vecs = eigsorted(cov)\n",
    "    theta = np.degrees(np.arctan2(*vecs[:,0][::-1]))\n",
    "\n",
    "    width, height = 2 * nstd * np.sqrt(abs(vals))\n",
    "    ellip = Ellipse(xy=pos, width=width, height=height, angle=theta, **kwargs)\n",
    "\n",
    "    ax.add_artist(ellip)\n",
    "    return ellip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_gaussians(X, means, covs, ax=None):\n",
    "    n = len(means)\n",
    "    colors = [\"#1F77B4\", \"#2CA02C\", \"#FFBB78\", \"#4C529B\"]\n",
    "    \n",
    "    plt.cla()\n",
    "    plt.plot(X.T[0], X.T[1], \"o\", c=\"#144C59\", alpha=0.5, markersize=3)\n",
    "    \n",
    "    for k in range(num_gaussians):\n",
    "        plot_ellipse(means[k], covs[k], ax=ax, alpha=0.4, color=colors[k % len(colors)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 8))\n",
    "plot_gaussians(X, means, covariances)\n",
    "\n",
    "plt.xlabel(\"CPU usage\")\n",
    "plt.ylabel(\"RAM usage\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}