nicococo/WordpressTest.ipynb

## WordpressTest.ipynb
{
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Support Vector Data Description\n",
      "===================================\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The problem of *data description* or one-class classification is to make a description of a training set of objects and to detect which (new) objects resemble this training set. \n",
      "\n",
      "This has been greatly used in outlier detection, i.e. the detection of uncharacteristic objects from a data set. Furthermore, another possible application of data description is in a classification problem where one of the classes is sampled very well, while the other class is severely undersampled. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here, the method proposed by Tax and Duin in 2004. called *Support Vector Data Description* has been implemented. This method obtains a spherically shaped boundary around the complete target set. To minimize the chance of accepting outliers, the volume of this description is minimized. \n",
      "\n",
      "The error function to be minimized is defined as:\n",
      "\n",
      "$$F(R, \\mathbf{a}) = R^2$$\n",
      "\n",
      "with the constraint:\n",
      "\n",
      "$$\\|\\Phi(\\mathbf{x}_i)-\\mathbf{a}\\|^2 \\le R^2, \\hspace{3mm}\\forall i,$$\n",
      "\n",
      "where $\\Phi$ defines an implicit mapping of the data into an another (possibly highdimensional) feature space.\n",
      "\n",
      "To allow the possibility of outliers in the training set, the distance from $\\Phi(\\mathbf{x}_i)$ to the center $\\mathbf{a}$ should not be strictly smaller than $R^2$, but larger distances should be penalized. Therefore, the slack variables $\\xi_i \\ge 0$ are introduced, so the minimization problem becomes:\n",
      "\n",
      "$$F(R, \\mathbf{a}) = R^2 + C\\sum_i{\\xi_i}$$\n",
      "with the constraint which ensures that almost all objectives are within the sphere:\n",
      "\n",
      "$$\\|\\Phi(\\mathbf{x}_i)-\\mathbf{a}\\|^2 \\le R^2 + \\xi_i, \\hspace{3mm} \\xi_i \\ge 0 \\hspace{3mm} \\forall i.$$\n",
      "\n",
      "\n",
      "This optimization problem can be solved using the Lagrange multipliers, so the following expression is obtained:\n",
      "\n",
      "<!--$$L(R,\\mathbf{a}, \\alpha_i, \\gamma_i, \\xi_i) = R^2 + C\\sum_i{\\xi_i} - \\sum_i{\\alpha_i(R^2 + \\xi_i - ({\\|\\mathbf{x}_i\\|}^2 - 2\\mathbf{a}\\mathbf{x}_i + {\\|\\mathbf{a}\\|}^2))} - \\sum_i{\\gamma_i\\xi_i},$$\n",
      "\n",
      "where $L$ should be minimized with respect to $R, \\mathbf{a}, \\xi_i$ and maximized with respect to the Lagrange multipliers $\\alpha_i \\ge 0$ and $\\gamma_i \\ge 0$. -->\n",
      "\n",
      "<!--After setting the partial derivatives to zero and resubstituting the obtained equations into $L$,--> \n",
      "\n",
      "$$L = \\sum_i{\\alpha_i(\\Phi(\\mathbf{x}_i)\\cdot\\Phi(\\mathbf{x}_i))} -  \\sum_i\\sum_j{\\alpha_i \\alpha_j(\\Phi(\\mathbf{x}_i)\\cdot\\Phi(\\mathbf{x}_j))}$$\n",
      "\n",
      "subject to the constraints:\n",
      "\n",
      "$$\\sum_i{\\alpha_i} = 1,$$\n",
      "\n",
      "$$\\mathbf{a} = \\sum_i{\\alpha_i\\Phi(\\mathbf{x}_i)},$$\n",
      "\n",
      "$$0 \\le \\alpha_i \\le C.$$\n",
      "\n",
      "Only objects $\\Phi(\\mathbf{x}_i)$ with $\\alpha_i \\gt 0$ are needed in the data description and these objects are called the *support vectors* (SVs) of the description.\n",
      "\n",
      "The above used inner products $(\\Phi(\\mathbf{x}_i)\\cdot\\Phi(\\mathbf{x}_j))$ can be replaced by a *kernel* function $K(\\mathbf{x}_i, \\mathbf{x}_j) = (\\Phi(\\mathbf{x}_i)\\cdot\\Phi(\\mathbf{x}_j))$ to obtain more flexible methods, so the optimization problem above becomes:\n",
      "\n",
      "$$L = \\sum_i{\\alpha_iK(\\mathbf{x}_i, \\mathbf{x}_i)} -  \\sum_i\\sum_j{\\alpha_i \\alpha_jK(\\mathbf{x}_i, \\mathbf{x}_j)}.$$\n"
     ]
    },
    {
     "cell_type": "code",
     "execution_count": null,
     "metadata": {},
     "outputs": [],
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "from tilitools.svdd_dual_qp import SvddDualQP\n",
      "from tilitools.svdd_primal_sgd import SvddPrimalSGD\n",
      "\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "execution_count": null,
     "metadata": {},
     "outputs": [],
     "input": [
      "# generate raw training data\n",
      "Dtrain = np.random.randn(2, 1000)\n",
      "Dtrain /= np.max(np.abs(Dtrain))"
     ],
     "language": "python",
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "execution_count": null,
     "metadata": {},
     "outputs": [],
     "input": [
      "nu = 0.15  # outlier fraction\n",
      "\n",
      "# train dual svdd\n",
      "svdd = SvddDualQP('linear', 0.1, nu)\n",
      "svdd.fit(Dtrain)\n",
      "\n",
      "# train primal svdd\n",
      "psvdd = SvddPrimalSGD(nu)\n",
      "psvdd.fit(Dtrain, max_iter=1000, prec=1e-4)\n",
      "\n",
      "# print solutions\n",
      "print('\\n  dual-svdd: obj={0}  T={1}.'.format(svdd.pobj, svdd.radius2))\n",
      "print('primal-svdd: obj={0}  T={1}.\\n'.format(psvdd.pobj, psvdd.radius2))"
     ],
     "language": "python",
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "execution_count": null,
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(2, 1764)\nCalculating linear kernel with size 1764x151.\nCalculating diagonal of a linear kernel with size 1764x1764.\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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frUG+21HIAthAaK3OBc61r6fYz8cikr+GrIm7UdWxKL5ISOS3Z7c/s1W+soRn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\nroeHh0cF4UXXw8PDo4Lwouvh4eFRQfx/StyVkURl3L4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f20f510>"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# generate test data grid\n",
      "delta = 0.1\n",
      "x = np.arange(-2.0-delta, 2.0+delta, delta)\n",
      "y = np.arange(-2.0-delta, 2.0+delta, delta)\n",
      "X, Y = np.meshgrid(x, y)\n",
      "(sx, sy) = X.shape\n",
      "Xf = np.reshape(X,(1, sx*sy))\n",
      "Yf = np.reshape(Y,(1, sx*sy))\n",
      "Dtest = np.append(Xf, Yf, axis=0)\n",
      "if Dtrain.shape[0] > 2:\n",
      "    Dtest = np.append(Dtest, np.random.randn(Dtrain.shape[0]-2, sx*sy), axis=0)\n",
      "print(Dtest.shape)\n",
      "\n",
      "res = svdd.predict(Dtest)\n",
      "pres = psvdd.predict(Dtest)\n",
      "\n",
      "# nice visualization\n",
      "plt.figure(1)\n",
      "plt.subplot(1, 2, 1)\n",
      "plt.title('Dual QP SVDD')\n",
      "Z = np.reshape(res,(sx, sy))\n",
      "plt.contourf(X, Y, Z)\n",
      "plt.contour(X, Y, Z, [0.0], linewidths=3.0, colors='k')\n",
      "plt.scatter(Dtrain[0, svdd.get_support_inds()], Dtrain[1, svdd.get_support_inds()], 40, c='k')\n",
      "plt.scatter(Dtrain[0, :], Dtrain[1, :],10)\n",
      "plt.xlim((-2., 2.))\n",
      "plt.ylim((-2., 2.))\n",
      "plt.yticks(range(-2, 2), [])\n",
      "plt.xticks(range(-2, 2), [])\n",
      "\n",
      "plt.subplot(1, 2, 2)\n",
      "plt.title('Primal Subgradient SVDD')\n",
      "Z = np.reshape(pres,(sx, sy))\n",
      "plt.contourf(X, Y, Z)\n",
      "plt.contour(X, Y, Z, [0.0], linewidths=3.0, colors='k')\n",
      "plt.scatter(Dtrain[0, :], Dtrain[1, :], 10)\n",
      "plt.xlim((-2., 2.))\n",
      "plt.ylim((-2., 2.))\n",
      "plt.yticks(range(-2, 2), [])\n",
      "plt.xticks(range(-2, 2), [])\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "prompt_number": 15
    }
   ]
  }
 ],
 "cells": [],
 "metadata": {
  "name": "test_svdd"
 },
 "nbformat": 3,
 "nbformat_minor": 0
}
No results found