test_kernels.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cvxpy as cp\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from data import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 50)\n"
     ]
    }
   ],
   "source": [
    "X = np.random.multivariate_normal([0,0], [[1,0],[0,1]], 100)\n",
    "# print(np.argpartition(X[:, 0]**2+X[:, 1]**2, 99))\n",
    "X = X[np.argsort(X[:, 0]**2+X[:, 1]**2), :]\n",
    "Y = X[50:, :].T\n",
    "X = X[:50, :].T\n",
    "Pos = X\n",
    "Neg = Y\n",
    "\n",
    "plt.plot(Pos[0,:], Pos[1,:], 'r.')\n",
    "plt.plot(Neg[0,:], Neg[1,:], 'b.')\n",
    "plt.show()\n",
    "\n",
    "print(Pos.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100,)\n"
     ]
    }
   ],
   "source": [
    "labels = np.concatenate([np.ones(50,), -1*np.ones(50,)])\n",
    "print(labels.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 100)\n"
     ]
    }
   ],
   "source": [
    "points = np.concatenate([X, Y],axis = 1)\n",
    "print(points.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 100)\n",
      "[1.         0.11706804 0.16052871 0.0132885  0.00685246 0.01288473]\n",
      "0.1170680423009838\n"
     ]
    }
   ],
   "source": [
    "def polynomial_kernel(M):\n",
    "    return np.array([1, 2**0.5*M[0], 2**0.5*M[1], 2**0.5*np.multiply(M[0],M[1]),M[0]**2, M[1]**2])\n",
    "\n",
    "points_in_6d = np.apply_along_axis(polynomial_kernel, 0, points)\n",
    "print(points_in_6d.shape)\n",
    "print(points_in_6d[:,0])\n",
    "#for checking\n",
    "print(2**0.5*points[0,0])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7, 100)\n",
      "[ 1.          1.69186484  0.45015256  0.5385306   1.43120331  0.10131866\n",
      " -1.        ]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "dataset = np.vstack([points_in_6d, labels])\n",
    "print(dataset.shape)\n",
    "print(dataset[:,51])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 100)\n",
      "[-1.         -1.69186484 -0.45015256 -0.5385306  -1.43120331 -0.10131866]\n"
     ]
    }
   ],
   "source": [
    "YiXi = np.multiply(points_in_6d,labels.T)\n",
    "print(YiXi.shape)\n",
    "print(YiXi[:,51])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "D = YiXi.T @YiXi + np.eye(YiXi.shape[1])*1e-5\n",
    "print(np.all(np.linalg.eigvals(D) >= 0))\n",
    "lambd = cp.Variable(shape=(100,))\n",
    "gamma = cp.Variable(shape=(100,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.737097458751094"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 2\n",
    "C = 0.1\n",
    "objective = cp.Minimize( -cp.sum(lambd) + 0.5*cp.quad_form(lambd, D))\n",
    "\n",
    "constraints= [lambd >= 0, lambd.T @ labels == 0, lambd <= C*np.ones(100,), lambd+gamma==C*np.ones(100)]\n",
    "problem = cp.Problem(objective, constraints)\n",
    "problem.solve(solver=cp.ECOS, verbose=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-6.408762409648716e-14\n",
      "[-1.79621015e-12 -4.30635002e-12 -6.49434536e-12 -1.00795845e-11\n",
      " -3.44107239e-13 -4.61704719e-12 -9.97427985e-12]\n"
     ]
    }
   ],
   "source": [
    "print(lambd.value.T @labels)\n",
    "print(lambd.value[np.where(lambd.value <=0)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 100)\n",
      "(6,)\n",
      "[-6.36371671e-14 -1.51733581e-01  7.67055176e-02  2.00003262e-01\n",
      " -9.79967252e-01 -8.80513906e-01]\n"
     ]
    }
   ],
   "source": [
    "j = np.multiply(YiXi, lambd.value.T)\n",
    "print(j.shape)\n",
    "w = np.sum(j,axis = 1)\n",
    "print(w.shape)\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([22, 62, 63, 73, 79, 81]),)\n",
      "[ 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      "  0.     0.     0.     0.     0.     0.     0.     0.     0.     0.\n",
      "  0.     0.     0.02   0.     0.     0.1    0.     0.     0.     0.1\n",
      "  0.     0.     0.     0.1    0.     0.1    0.1    0.1    0.1    0.1\n",
      "  0.1    0.1    0.1    0.1    0.1    0.1    0.1    0.1    0.1    0.1\n",
      "  0.1    0.1    0.1    0.1    0.1    0.1    0.1    0.1    0.1    0.1\n",
      "  0.1    0.1    0.057  0.021  0.1    0.1    0.     0.     0.     0.1\n",
      "  0.     0.     0.     0.039  0.     0.     0.     0.     0.1    0.047\n",
      "  0.     0.057  0.     0.     0.     0.     0.     0.     0.    -0.\n",
      "  0.     0.    -0.    -0.     0.    -0.    -0.    -0.     0.    -0.   ]\n"
     ]
    }
   ],
   "source": [
    "lamb2 = np.round(lambd.value,3)\n",
    "k = np.where((lamb2 < C - 1e-5) & (lamb2 > 0))\n",
    "print(k)\n",
    "print(np.round(lambd.value,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.72169335 1.72168679 1.72167274 1.72167988 1.72168355 1.72168372]\n",
      "1.7216933513769068\n"
     ]
    }
   ],
   "source": [
    "for i in k:\n",
    "    print(labels[i] - w.T @ points_in_6d[:,i])\n",
    "b = labels[k[0][0]] - w.T @ points_in_6d[:,k[0][0]]\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
      "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,\n",
      "       34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51,\n",
      "       52, 53, 56, 60]),)\n"
     ]
    }
   ],
   "source": [
    "print(np.where(w.T @ points_in_6d + b >=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,\n",
      "       72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88,\n",
      "       89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]),)\n"
     ]
    }
   ],
   "source": [
    "print(np.where(w.T @ points_in_6d + b <=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.038261285745942 3.6954560327909878\n",
      "-3.056209168987136 4.147529935555744\n",
      "(361, 337)\n"
     ]
    }
   ],
   "source": [
    "h = 0.02\n",
    "x_min, x_max = points[0, :].min() - 1, points[0, :].max() + 1\n",
    "y_min, y_max = points[1, :].min() - 1, points[1, :].max() + 1\n",
    "print(x_min, x_max)\n",
    "print(y_min,y_max)\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                     np.arange(y_min, y_max, h))\n",
    "print(xx.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def polynomial_hyperplane(x,y,w,b):\n",
    "    m = np.array([1, 2**0.5*x, 2**0.5*y, 2**0.5*x*y ,x**2, y**2])\n",
    "    return (w.T @ m + b)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = np.ones((xx.shape))\n",
    "for i in range(xx.shape[0]):\n",
    "    for j in range(xx.shape[1]):\n",
    "        Z[i][j] = polynomial_hyperplane(xx[i][j],yy[i][j],w,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Pos[0,:], Pos[1,:], 'r.')\n",
    "plt.plot(Neg[0,:], Neg[1,:], 'b.')\n",
    "plt.contour(xx, yy, Z,[0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"
  },
  "kernelspec": {
   "display_name": "Python 3.8.10 64-bit",
   "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": "3.8.10"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}