lec9.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from cs771 import genSyntheticData as gsd\n",
    "from cs771 import plotData as pd\n",
    "from matplotlib import pyplot as plt\n",
    "import time as tm\n",
    "import random\n",
    "\n",
    "d = 2 \n",
    "n = 60\n",
    "\n",
    "muPos1 = np.array( [-5,5] )\n",
    "muPos2 = np.array( [1,-5] )\n",
    "muNeg = np.array( [-5,-5] )\n",
    "r = 3\n",
    "\n",
    "nOutlier = n//10\n",
    "tmp1 = gsd.genSphericalData( d, n, muPos1, r)\n",
    "tmp2 = gsd.genSphericalData( d, nOutlier, muPos2, r//3 )\n",
    "XPos = np.vstack( (tmp1, tmp2) )\n",
    "XNeg = gsd.genSphericalData( d, n, muNeg, r )\n",
    "yPos = np.ones( (n + nOutlier,) )\n",
    "yNeg = -np.ones( (n,) )\n",
    "X = np.vstack( (XPos, XNeg) )\n",
    "y = np.concatenate( (yPos, yNeg) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nSV =  26  out of  126 data points\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9PljAVVoAZkIoAkCVGmpIpZZPv281BF4YhCIAVJBaCadSIRQBoIgyjb0RdOWDUASAIShEgBGC5YtQBFDzCCkkRR6KZnalpKWSYpJWuPs/pN3eKOn7ki6S9HtJ17r73qjrBaC6EXQYjkhD0cxikr4j6UOS9kvabGbt7v6rlGKfkfSGu59nZtdJ+oaka6OsF4DyQXihnETdUpwmaY+7/1qSzOwBSbMlpYbibEmLg8trJS0zM3N3j7huACJC0KFSRR2KZ0h6JeX6fknvyVbG3XvM7KCkP5L0esR1AzAEBB1qQdShaBmOpbcAw5SRmc2XNF+Sxowbk3/NgCpFeAHDF3Uo7pd0Zsr1sZIOZCmz38zqJZ0k6Q/pD+TuyyUtl6SW1ha6VlFTCDqgOKIOxc2SJpjZOZJ+I+k6SZ9IK9Mu6UZJ/yVpjqQnGE9ELSDogPITaSgGY4QLJP1UiSUZK919p5ndJmmLu7dLulvSKjPbo0QL8boo6wQMBwEG1IbI1ym6+3pJ69OOLUq5fFTSNVHXA0hH0AFIx442qGjp+0gSdADyQSiiJDKFWaYTlCZvG+yxAKAQCEUU1FACqlbP1wagfBGKGBRhBaBWEIo1grE3ABgcoVjmChleBCEA5EYolgDhBADliVAsEIIOACpfzYUi4QUAyKYqQpGgAwAUQkWG4glHCUIAQOHVlboCAACUC0IRAIAAoQgAQIBQBAAgQCgCABAgFAEACBCKAAAECEUAAAKEIgAAAUIRAIAAoQgAQIBQBAAgQCgCABAgFAEACBCKAAAECEUAAAKEIgAAgfpSVwDlo6Nzn+7YvVL37W3XoZ7Daq5v0g1nz9Itk+Zp/Khxed8OAOXO3L3UdRiy1pYW37JuXamrUfFSQ6yz5y1JksnkOv6eaLB6NdQ16K8n/5W+sWuFunu71e09Q7597fSlahtzafGeHICaYhMnbnX31rwfh1CsTRsObNScTQsHhFhUmmIj9VxbOy1GAJEoVCjSfVqlkq3A7+99SG/1HO47fmJspD469oP60SuP6mhvV9Hq093brW89f4+WtS7qV8evb/+2frhvQ18wN1i9rhl3pW6bspAABVB0tBSrULIV2BU/prjipa5On9ENzTo4Z6ukRB2v/sUCdfUey1i2sW6EHrxkGV2uAEIpVEuR2adVpqNzn+ZsWqjD8SNlFYiSdKg7MW7Z0blPH9t0c9ZAlKSu3mP6i1/crI7OfcWqHgAQitXmjt0r1d3bXepqZNTccKKkRB2PxrMHYlJX7zF96/l7Iq4VABzHmGIFy7QE4mi8qygTZ4aqweo19+zZkqT79rb3m+Gajcu1au9D/cYhASBKhGKFyjR7NLmsohw11DXoyxM/JUk6lDLxZzDJLlcAKAa6TytQ6rhh1K3CBqtXU2yklrTcrKbYSDVY/bBuXzt9ad9s0ub6ptC/P9nlCgDFQChWoEKOG5os43WTaXRDs+afd62ea2vXoikL9Fxbu+afd61GNzSrboi3p84iveHsWQN+b7a6JbtcAaAYIlmSYWbflPTnko5J6pD0aXf/nwzl9krqlBSX1BN2Om2tL8kYvWZqQbpKR8Ya9bGxH1b7gSd0qPstNTecqLlnz9aXJ34q0jWCHZ37NGXDVToSz71O8oS6Ru2Y+XDGurClHIBU5b54/zFJX3P3HjP7hqSvSfrrLGUvc/fXI6pHRcv2wT+UMblMYqpTY6yxZFuvjR81Tj+afueg6xTXXXJnxoDLNp763T2r9d09q/WR0y/V0ov+hnAEMGSRdJ+6+6PufYNdT0kaG8XvqWYbDmzUuzfM0oqONerseUsuV2fPW1rRsSbUzE1JGlHXMGD8rrm+SZ+bcP2ALs1iaxtzqXbOfESfPGuWRtQ19B1vsHrdcNYs7Zz5SMb6hRlPfeTVjZr4yJVa2bE2svoDqE7FmH06T9IPstzmkh41M5f0PXdfnu1BzGy+pPmSNG7MmIJXspykfvCnCzuxpsHq9b/Gf7yslzOMHzVO973vm7pP3wx9n7DjqXGP6zNP3yrJNW/8NXnUEkAtGXZL0cx+ZmY7MvzMTilzq6QeSfdneZj3u/tUSW2SvmBmf5bt97n7cndvdffWd5xyynCrXREKMZEmdQlENblvb/uQZtzOf/rr7IoDILRhh6K7f9DdWzL8PCRJZnajpKskfdKzzOZx9wPBv7+T9KCkacOtTzUZygd/mCUQ1WSo46lxxdkVB0BokYwpmtmVSkysmeXuGT/FzOxEMxuVvCzpCkk7oqhPpQn7wW9SqCUQ1WQoaxyTvvPi/Rq9Zqpu2ryYViOAnKJakrFHUqOk3weHnnL3z5nZGEkr3H2mmZ2rROtQSoxt/pu7/32Yx6/2JRlhl1yknnWiVty0ebFWdKwZ9qYFMcW0fNoSxhmBKlPWSzLc/bwsxw9Imhlc/rWkP47i91eKbEsuZp1xeb9zDGaSupdoLbll0jzd+9KP1R0fXijGFddnnv4bSaZ54+cUtnIAKh472pTIyo41mvjwlfruntX9llz8654f6kevPKo6y/3SVOtEmsGMHzVOa6cv1Ql1jXk9zmc3L6IrFcAAhGIJrOxYq888/TcZz3fYo7iO9iZ2ehkZa6y5iTRhtI25VDtmPqzLTn3PsB+jx+P6+vY7C1grANWAUCyyjs59+uzmwdcOxnvj+tjYD9fcRJqwxo8apyc+8H3dPe3vFFNsWI9x/8vtWtmxpsA1A1DJOHVUkd2xe6V6fGALMV2P4mo/8IQOztla1gvwS23e+Gt06anv0beev0er9j6kN7sPDen+jC8CSEVLscju29seuiznEgxn/KhxWta6SAfnbNXnz7t+yPdnfBFAEqFYZENZfM65BIfulknzhtyd2uMs8AeQQCgW2VAWn9fikot8jR81TsunLRny/VbtfSiC2gCoNIRikd1w9izV2+AtmZhiNbnkohDmjb9Gd08LtQ9EH7qqAUiEYtHdMmmeRtSNGLTc8mlLanbJRSHMGz9HnzjrqtDl6aoGIBGKRZdcfN4UG5mxxVhvMd097e/ZhqwAbpuyMNT4Yr3F6KoGIIklGZF74rdP6Ytbb9fON/f0Hbtg9Hn63p8u0VO/f1ar9j6kQ91vqbnhRM09e7a+PPFTtBALJDm+mFh2kd2IuhF0VQOQRChG6rbty/T1HQN3Tdn55h7Nfer/aEnLzTW3oXexJVrcps9uXjRgfWjMYjJJ7r2a8PAVfXvP3jJpHl9MgBpF92lEnvjtUxkDMdXXd9ypJ377VJFqVLvmjZ+j3R/5ib4w4ZN9uwM1xU6QXJJLR3q7+vaeXdGxRu/eMEsbDmwsdbUBlAChGJEvbr09VLmFzwxtliSGJ3WB/wtXPSrJFFdcPWn7z3Z7jw7Hj2jOpoUs6AdqEKEYgY7Off3GEHPZcfCFiGuDdHfsXqnu3u6cZbp7u1nQD9QgQrHANhzYqMmPtJW6Gsjhvr3tg56kuNt7dO9LD+YsA6D6EIoF1NG5Tx/9+ReGfVZ4FEfYrfYO9RxmbBGoMYRiAS3avlTHPHe3XLqWk86PqDbIZihb7TG2CNQWQrGAfvjyhiHfZ+nUWyOoCXK54exZA07enE3Vji3OnZv4KVQ5oEoQigWUPpNxMEtabtblp10cUW2QzS2T5qmhriFU2W7vYbPwJAISNYBQLJGm2AlaNGVBqatRk5Jb7YXFZuFA7SAUS+TT536s1FWoaW1jLtWJsZGhyrJZOFA72OatgOqtXj0hZ56y12bp/eU5H9WKjjU5Zws3WH11bBae3u359NOZj6dLLbdr1/HLq1YVtn5AmaClWEDXjgu3PnHGqe9hb80yEGZssaGuoXa/wCRDMHm5szPxs2vX8fFFxhhRZWgpFtCSKV/U2ld+qq7eY1nLjLAGrZj2d0WsFbJJji3O2bRQ3b3d/VqMDVavhroGrZ2+tDq+wKS37JJhlqvFl9o6nDz5eKtx8uTC1w8oE4RiAY0fNU4PXrJMH9t0s47Gj8nlfbeZTCfERuhH0++sjg/ZKtE25lI919aubz1/D6fxSrdqVf/wDBOkQIUjFAuko3Of7ti9UvftbdfR+LG+Ewj3eI9GNTTzIVvGkpuFL2tdVOqqACgxQrEANhzYOKALrtt71GD1GhkbqQfe989qG3NpiWsJABgMoZinjs59mrNpoQ7Hjwy4rdt71B3v0ZxNC/VcWzutxAqR2uo/1HO4Ok8+HLYLlK5S1Bhmn+aJ0xBVlw0HNqpl/VW6a88D6ux5q+/kw3fteUAt66+q7Q3CV60iJFH1CMU8hT0NEVuFlb+Ozn26+hcLdLS3q98kKUlyuY72dunqXyxgg3CgihGKeersCbcFGFuFlb9F25fmXE4jSV29x7R4+51FqhGAYiMU8/DEb58KXZatwsrfmn0/CVVu9csPR1wTAKVCKObhi1tvD122KrYKq3JhTw4dVy9dqECVIhTzsPPNPaHL1uxWYVWKiVNAdSIUi6RqpvJXsbAnHpbExCmgShGKQODjITd0l5g4BVQrQjEPF4w+L1S5lpPOj7gmKIQlU74YuiwTp4DqRCjm4dsX/W2ockun3hpxTVAI40eN04xTp4Uq++djLo+4NgBKIbJQNLPFZvYbM9sW/MzMUu5KM3vezPaY2Vejqk8ULj/tYi1puTlnmSUtN+vy0y4uUo2Qr9H1zaHKddJ9ClSlqFuK33L3C4Of9ek3mllM0ncktUl6l6TrzexdEdepoBZNWaDHL7t3QBdpy0nn6/HL7tWiKQtKVDMMx4ZXfx6q3E9+G64cgMpS6g3Bp0na4+6/liQze0DSbEm/Kmmthujy0y7W9pn/XupqoADCrlU8Nsh+twAqU9QtxQVm9pyZrTSzUzLcfoakV1Ku7w+ODWBm881si5lt+e833oiirgCAGpdXKJrZz8xsR4af2ZK+K2m8pAslvSrpjkwPkeGYZzgmd1/u7q3u3vqOUzLla+l0dO7TTZsXa/SaqapbPUmj10zVTZsXs+sJAFSYvLpP3f2DYcqZ2b9KyrRh5H5JZ6ZcHyvpQD51KrZMJxju7HlLKzrW6N6Xfqy105dygmHUjrlzE/9yiilUqChnn56ecvVqSTsyFNssaYKZnWNmIyRdJ6k9qjoVWuoJhtPHorq9R4fjRzRn00JajBVkZF1jqHJNsRMirgmAUohyTPEfzWy7mT0n6TJJX5YkMxtjZuslyd17JC2Q9FNJuyT90N13Rlingrpj90p1xbtyljka72KfzApybvOZgxeSdG4z2/YB1Siy2afuPjfL8QOSZqZcXy9pwHKNSvD9l36suHpzlulVr1Z0rNGy1kVFqhXysfdwuN77vW/tj7gmQ0S3JVAQpV6SUdHeih8JVa6r95g6OvexKXgFONwT7jUNW67qzU377vv005mPE9aoEGzzViR0oVaGBouFKleWe5/u2jUwjAAMCS3FIlm19yG6UMvcE799SsdCLN6PqY6TRieltwDpxkWFIxTzcGJ9k97qORyqLKcaKn9f3Hp7qHJx9Zb+pNHZui3TW4uEEzAkdJ/m4S+H0Fo4IRZuqj9KZ+ebe0KXZXwYqE6EYh5umTRP9SHHoI7Gj7FeEYWT3gIcNSrxb2dn/+OMMQJDQijmYfyocfren94WqmyverV4+50R1wgosVWr6LJFRTP3jFuNlrXWlhbfsm5dqavRJ7Z6knozb9naT4PV69h1FbM3Qc1peeQjobpQW046v/zOijJ3bmI8cfJkQgk1ySZO3Orurfk+Di3FAggTiFL40xKhNL590d+GKrd06q0R1wRAqRCKQODy0y7Wkpabc5ZZ0nKzLj/t4iLVaAhWrUq0EgHkhVAsgAYLt7JlRF1DxDVBvhZNWaDHL7tXLSed3+94y0nn6/HL7tWiKQtKVDMAxcA6xQL4+Lg23f/y4GNM15zZVoTaIF+Xn3Zx+Y0ZhsFYIpA3WooFsGTKF9VYNyJnmca6EVoyJXfXHACgtAjFAhg/apwevGSZRsYaZbJ+t5lMI2ONevCSZSz4BoAyRygWSNuYS7W97WHdNOETGt3QrDqZmuubdMHo81RnMX1k42c1es1U3bR5MYv4AaBMsU4xIhsObNScTQvV3dvdbylGg9Wroa5Ba6cvVduYS0tYQwCoHqxTLGMdnfs0Z9NCHY4fGbA2sdt7dDiRwnyhAAAN3UlEQVR+RHM2LaTFCABlhlCMwB27V6q7tztnme7ebs6xCABlhlCMwH172wfdvabbe7Rq70NFqhEAIAxCMQKHOMciAFQkQjECzfVNocr1ypmNCgBlhFCMwA1nzwq99duKjjV694ZZ2nBgY8S1AgAMhlCMwC2T5qkh5D6nzEYFgPJBKEZg/KhxWjt9qZpiI0O3GJmNCgClRyhGpG3MpXqurV3zz7s2VHlmowJA6RGKERo/apyWtS4asB9qNm92H6ILFQBKiFAsgrCzUSUx6QYASohQLIKhzEZl0g0AlA6hWARDmY0qMekGAEqFUCyC1NmoYTDpJj8dnft00+bFGr1mqupWT+KUXQBCIxSLJDkbNSy2gBueDQc26t0bZmlFxxp19rwll6uz5y02SQAQCqFYRONHjdOo+hNDlW1uCFcOx3HKLgD5IhSLLMykm3rFNG7k6XT/DRGn7AKQL0KxyMJMuulRXLs7f0333xBxyi4A+SIUiyzXFnD1ivVd7vF4v9vo/hscp+wCkC9CsQRSt4Ab3dCsOplGNzRr0uhzVW+xnPel+y+7sJskMF4LIBtCsUSSW8AdnLNV8et36+CcrXr58IEBLcR0dP9lF2a8tsHqNffs2UWqEYBKQyiWkbDdf292H6rJSTiDrT8MM17bUNegL0/8VBFqC6ASRRKKZvYDM9sW/Ow1s21Zyu01s+1BuS1R1KWSDGWP1FqbhBNm/WGu8doGq1dTbKTWTl+q8aPGlehZACh3kYSiu1/r7he6+4WSfiRpXY7ilwVlW6OoSyUZyh6pqap5Ek5H5z7d8J9f0cyN80OtP8w2Xjv/vGv1XFu72sZcWqJnAqASmLtH9+BmJmmfpMvd/cUMt++V1Orurw/lcVtbWnzLulw5W5k6Ovfp3Rtm6XD8yLDubzLVW0w9HldzfZNuOHuWbpk0r2JbRhsObNScTQt1JH5Urtzv0war1/zzrtWy1kVFqh2AcmITJ24tROMq6jHFSyS9likQAy7pUTPbambzcz2Qmc03sy1mtuW/33ij4BUtB7m6/8Jwubq9p69r8bt7Vuu8hz+kq56cX3EtyNTdaQYLRIkJSAAKY9ihaGY/M7MdGX5Sp/ZdL2l1jod5v7tPldQm6Qtm9mfZCrr7cndvdffWd5xyynCrXfaydf/l45FXN2rKhqsqaswxzO406Vh/CCBfkXWfmlm9pN9Iusjd94cov1jSIXf/p8HKVmv3aS6j10xVZ09+H/pNsZF6rq29IrpTh/N8Rzc06+CcrRHVCEA5q4Tu0w9K2p0tEM3sRDMblbws6QpJOyKsT0Ub7iScVKVY+J+cKDPigQtkqyfKVk/UiAcu0Cf/85acXbphl6cksf4QQCFEGYrXKa3r1MzGmNn64Oo7JW0ys2clPS3pEXf/SYT1qWhDPVFxJrnG3fI9B2FH5z598j9v6Rd+9asn6/yHP6z7X/73frNGu71H//byw7pg/UeydukOZXmKxPpDAIUR6ezTqNRi96l0fDZmd2/3oBtfZ1MnU/z63aEet8Hq1VDXoLXTl+r8Uefojt0rdd/edh3qOdxvdusLnS/p6l8sUFfvsSHX54S6Ru2Y+fCALt2bNi/Wio41gz5Pk2lk7AStnb6U5RZADStU9ymhWGE6OvfpW8/fo1V7H9Kh7rcUC5ZghJmhKQ0cdwuzDKSxboRMprjHB4RmzGLq9V4d86FNikkymW6a8IkBSynCLk+54axZWjzl5ooYJwUQnUoYU0QE0vdM3fWRDRoZOyHUfTONu4WZ5dnVe0xHe7syLpw/2ts17ECUEstIMnXphtmdZv2ly7Xqfd8kEAEUDKFY4ZLhcUJd46BlM427hTkHYdSyLaVgdxoAxUb3aZXo6NynLz3z93r4wJMDbksdG0wPkrrVk0J3vUaFpRQA8kX3KfoZP2qc/v3S72nPVY/pCxM+GbplNdRZnoVmMpZSACgb+S18Q9lJjjmG3QP0hrNnhZrlGZXGuhEspQBQNmgp1rhCrH8crsa6EVp3yZ1MlAFQNgjFGjfYLM+RsUY11o3I+RiNdSM0oi57p0NdcPaO1Me94axZ2jnzESbLACgrdJ+ib5Zn6vrH5oYTNffs2fryxE/phc6XQi3uX7z9Tv1g3/q+MiPqGnTNmW1awjpCABWC2acIJX3TgNTQJPAAlBo72hCKAIAASzIAACgwQhEAgAChCABAgFAEACBAKAIAECAUAQAIEIoAAAQIRQAAAoQiAAABQhEAgAChCABAgFAEACBAKAIAECAUAQAIEIoAAAQIRQAAAoQiAAABQhEAgAChCABAgFAEACBAKAIAECAUAQAIEIoAAAQIRQAAAoQiAAABQhEAgAChCABAgFAEACCQVyia2TVmttPMes2sNe22r5nZHjN73sw+nOX+55jZL83sRTP7gZmNyKc+AADkI9+W4g5JfyHp56kHzexdkq6TdIGkKyX9i5nFMtz/G5K+5e4TJL0h6TN51gcAgGHLKxTdfZe7P5/hptmSHnD3Lnd/SdIeSdNSC5iZSbpc0trg0L2SPppPfQAAyEd9RI97hqSnUq7vD46l+iNJ/+PuPTnK9DGz+ZLmB1e7bOLEHQWqa6m8XdLrpa5EHiq9/hLPoVzwHEqv0usvSRML8SCDhqKZ/UzSaRluutXdH8p2twzHfBhljt/gvlzS8qBOW9y9NVvZSlDpz6HS6y/xHMoFz6H0Kr3+UuI5FOJxBg1Fd//gMB53v6QzU66PlXQgrczrkk42s/qgtZipDAAARRPVkox2SdeZWaOZnSNpgqSnUwu4u0v6D0lzgkM3SsrW8gQAIHL5Lsm42sz2S3qvpEfM7KeS5O47Jf1Q0q8k/UTSF9w9HtxnvZmNCR7iryX9bzPbo8QY490hf/XyfOpdJir9OVR6/SWeQ7ngOZRepddfKtBzsESDDQAAsKMNAAABQhEAgEDZhmI1bSEX/P5twc9eM9uWpdxeM9selCvI9OJCMbPFZvablOcxM0u5K4PXZY+ZfbXY9czFzL5pZrvN7Dkze9DMTs5Sruxeh8H+rsGkth8Et//SzM4ufi2zM7Mzzew/zGxX8P96YYYyM8zsYMp7bFEp6prLYO8NS/h28Do8Z2ZTS1HPTMxsYsrfdpuZvWlmX0orU3avgZmtNLPfmdmOlGNvM7PHgs/3x8zslCz3vTEo86KZ3RjqF7p7Wf5ImqzEYswnJbWmHH+XpGclNUo6R1KHpFiG+/9Q0nXB5bskfb7Uzymoyx2SFmW5ba+kt5e6jlnqtljSVwYpEwtej3MljQhep3eVuu4p9btCUn1w+RuSvlEJr0OYv6ukmyTdFVy+TtIPSl3vtPqdLmlqcHmUpBcyPIcZkh4udV0HeR453xuSZkraoMQ67Isl/bLUdc7xnvqtpLPK/TWQ9GeSpkrakXLsHyV9Nbj81Uz/lyW9TdKvg39PCS6fMtjvK9uWolfhFnJBvT4uaXWp6xKRaZL2uPuv3f2YpAeUeL3Kgrs/6sd3UHpKibWxlSDM33W2Eu9zKfG+/0DwfisL7v6quz8TXO6UtEs5drCqYLMlfd8TnlJiLfbppa5UBh+Q1OHuL5e6IoNx959L+kPa4dT3e7bP9w9Leszd/+Dub0h6TIm9uHMq21DM4QxJr6Rcz3sLuSK6RNJr7v5ilttd0qNmtjXY1q7cLAi6hFZm6a4I89qUi3lKfKPPpNxehzB/174ywfv+oBL/D8pO0LX7J5J+meHm95rZs2a2wcwuKGrFwhnsvVEp/weuU/Yv5+X+GkjSO939VSnxhUvSqRnKDOu1iGrv01CsTLaQK4SQz+V65W4lvt/dD5jZqZIeM7Pdwbekosj1HCR9V9LtSvwdb1eiG3he+kNkuG9R1/yEeR3M7FZJPZLuz/IwJX0dMijL9/xwmFmzpB9J+pK7v5l28zNKdOcdCsasf6zExh/lZLD3Rtm/DsH8ilmSvpbh5kp4DcIa1mtR0lD0KtpCbrDnYmb1Spxm66Icj3Eg+Pd3ZvagEt1mRfswDvt6mNm/Sno4w01hXptIhXgdbpR0laQPeDDwkOExSvo6ZBDm75ossz94r52kgV1OJWVmDUoE4v3uvi799tSQdPf1ZvYvZvZ2dy+bjapDvDdK/n8ghDZJz7j7a+k3VMJrEHjNzE5391eD7unfZSizX4kx0qSxSsxRyakSu08rdQu5D0ra7e77M91oZiea2ajkZSUmhZTNmUDSxkWuVua6bZY0wRIzf0co0UXTXoz6hWFmVyqxi9Isdz+cpUw5vg5h/q7tSrzPpcT7/olsoV8Kwfjm3ZJ2ufs/ZylzWnIc1MymKfH59Pvi1TK3kO+Ndkl/GcxCvVjSwWQ3XxnJ2mNV7q9BitT3e7bP959KusLMTgmGe64IjuVW6plFOWYcXa1E0ndJek3ST1Nuu1WJ2XjPS2pLOb5e0pjg8rlKhOUeSWskNZb4+dwj6XNpx8ZIWp9S32eDn51KdPeV/HVIqesqSdslPRe8IU9Pfw7B9ZlKzCzsKMPnsEeJMYZtwU9ytmbZvw6Z/q6SblMi4CXphOB9vid4359b6jqn1X+6El1Xz6X8/WdK+lzy/4WkBcHf/FklJkK9r9T1TnsOGd8bac/BJH0neJ22K2XmfDn8SGpSIuROSjlW1q+BEgH+qqTuIBM+o8R4+eOSXgz+fVtQtlXSipT7zgv+T+yR9Okwv49t3gAACFRi9ykAAJEgFAEACBCKAAAECEUAAAKEIgAAAUIRAIAAoQgAQOD/A8aA/bA66Oh6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def getCyclicCoord( currentCoord ):\n",
    "    if currentCoord >= n-1 or currentCoord < 0:\n",
    "        return 0\n",
    "    else:\n",
    "        return currentCoord + 1\n",
    "\n",
    "def getRandCoord( currentCoord ):\n",
    "    return random.randint( 0, n-1 )\n",
    "\n",
    "def getRandpermCoord( currentCoord ):\n",
    "    global randperm, randpermInner\n",
    "    if randpermInner >= n-1 or randpermInner < 0 or currentCoord < 0:\n",
    "        randpermInner = 0\n",
    "        randperm = np.random.permutation( y.size )\n",
    "        return randperm[randpermInner]\n",
    "    else:\n",
    "        randpermInner = randpermInner + 1\n",
    "        return randperm[randpermInner]\n",
    "\n",
    "# Get the CSVM objective value in order to plot convergence curves\n",
    "def getCSVMObjVal( theta ):\n",
    "    w = theta[0:-1]\n",
    "    b = theta[-1]\n",
    "    hingeLoss = np.maximum( 1 - np.multiply( (X.dot( w ) + b), y ), 0 )\n",
    "    return 0.5 * w.dot( w ) + C * np.sum(hingeLoss)\n",
    "\n",
    "def getCSVMObjValDual( alpha, w, b ):\n",
    "    # Recall that b is supposed to be treated as the last coordinate of w\n",
    "    return np.sum(alpha) - 0.5 * np.square( np.linalg.norm( w ) ) - 0.5 * b * b\n",
    "\n",
    "def doSDCM( getCoordFunc, init, horizon = 10 ):\n",
    "    primalObjValSeries = np.zeros( (horizon,) )\n",
    "    dualObjValSeries = np.zeros( (horizon,) )\n",
    "    timeSeries = np.zeros( (horizon,) )\n",
    "    totTime = 0\n",
    "    \n",
    "    # Initialize model as well as some bookkeeping variables\n",
    "    alpha = init\n",
    "    alphay = np.multiply( alpha, y )\n",
    "    # Initialize the model vector using the equations relating primal and dual variables\n",
    "    w = X.T.dot( alphay )\n",
    "    # Recall that we are imagining here that the data points have one extra dimension of ones\n",
    "    # This extra dimension plays the role of the bias in this case\n",
    "    b = alpha.dot( y )\n",
    "    # Calculate squared norms taking care that we are appending an extra dimension of ones\n",
    "    normSq = np.square( np.linalg.norm( X, axis = 1 ) ) + 1\n",
    "    # We have not made any choice of coordinate yet\n",
    "    i = -1\n",
    "    \n",
    "    for t in range( horizon ):\n",
    "        tic = tm.perf_counter()\n",
    "        \n",
    "        i = getCoordFunc( i )\n",
    "        x = X[i,:]\n",
    "        \n",
    "        # Find the unconstrained new optimal value of alpha_i\n",
    "        newAlphai =  alpha[i] + (1 - y[i] * (x.dot(w) + b)) / normSq[i]\n",
    "        # Make sure that the constraints are satisfied\n",
    "        if newAlphai > C:\n",
    "            newAlphai = C\n",
    "        if newAlphai < 0:\n",
    "            newAlphai = 0\n",
    "        \n",
    "        # Update the model vector and bias values\n",
    "        # Takes only O(d) time to do so :)\n",
    "        w = w + (newAlphai - alpha[i]) * y[i] * x\n",
    "        b = b + (newAlphai - alpha[i]) * y[i]\n",
    "        \n",
    "        alpha[i] = newAlphai\n",
    "\n",
    "        toc = tm.perf_counter()\n",
    "        totTime = totTime + (toc - tic)\n",
    "        \n",
    "        primalObjValSeries[t] = getCSVMObjVal( np.append( w, b ) )\n",
    "        dualObjValSeries[t] = getCSVMObjValDual( alpha, w, b )\n",
    "        timeSeries[t] = totTime\n",
    "        \n",
    "    print( \"nSV = \", np.sum( alpha > C/100 ), \" out of \", y.size, \"data points\" )    \n",
    "    return (np.append( w, b ), primalObjValSeries, dualObjValSeries, timeSeries)\n",
    "\n",
    "# Get a stochastic gradient for the CSVM objective\n",
    "# Choose a random data point per iteration\n",
    "def getCSVMSGrad( theta ):\n",
    "    w = theta[0:-1]\n",
    "    b = theta[-1]\n",
    "    n = y.size\n",
    "    i = random.randint( 0, n-1 )\n",
    "    x = X[i,:]\n",
    "    discriminant = (x.dot( w ) + b) * y[i]\n",
    "    g = 0\n",
    "    if discriminant < 1:\n",
    "        g = -1\n",
    "    delb = C * n * g * y[i]\n",
    "    delw = w + C * n * (x * g) * y[i]\n",
    "    return np.append( delw, delb )\n",
    "\n",
    "# Quite standard for strongly convex but non-smooth objectives like CSVM\n",
    "def getStepLength( grad, t ):\n",
    "    return eta/(t+1)\n",
    "\n",
    "# Given a gradient oracle, a step length oracle, an initialization,\n",
    "# perform GD for a specified number of steps (horizon)\n",
    "def doGD( gradFunc, stepFunc, init, horizon = 10 ):\n",
    "    objValSeries = np.zeros( (horizon,) )\n",
    "    timeSeries = np.zeros( (horizon,) )\n",
    "    totTime = 0\n",
    "    theta = init\n",
    "    cumulative = init\n",
    "    for t in range( horizon ):\n",
    "        tic = tm.perf_counter()\n",
    "        delta = gradFunc( theta )\n",
    "        theta = theta - stepFunc( delta, t+1 ) * delta\n",
    "        cumulative = cumulative + theta\n",
    "        toc = tm.perf_counter()\n",
    "        totTime = totTime + (toc - tic)\n",
    "        objValSeries[t] = getCSVMObjVal( cumulative/(t+2) )\n",
    "        timeSeries[t] = totTime\n",
    "    return (cumulative/(horizon+1), objValSeries, timeSeries)\n",
    "\n",
    "def mySVM( X ):\n",
    "    return X.dot(w) + b\n",
    "\n",
    "randperm = np.random.permutation( y.size )\n",
    "randpermInner = -1\n",
    "C = 1\n",
    "eta = 2\n",
    "\n",
    "# SDCA outperforms SGD handily when dealing with more challenging problems e.g. those with large\n",
    "# values of C. SGD can get very sluggish with difficult problems and stop making progress\n",
    "\n",
    "# SCDA performs very well with the getRandpermCoord method of choosing coordinates as compared to\n",
    "# getRandCoord or getCyclicCoord. Random Permutations are the default method in liblinear as well\n",
    "(theta_SDCM, primal_SDCM, dual_SDCM, time_SDCM) = doSDCM( getRandpermCoord, C * np.ones( (y.size,) ), horizon = 500 )\n",
    "(theta_SGD, obj_SGD, time_SGD) = doGD( getCSVMSGrad, getStepLength, np.zeros( (d+1,) ), horizon = 500 )\n",
    "\n",
    "w = theta_SDCM[0:-1]\n",
    "b = theta_SDCM[-1]\n",
    "\n",
    "fig = pd.getFigure( 7, 7 )\n",
    "pd.shade2D( mySVM, fig, mode = 'batch', xlim = 10, ylim = 10 )\n",
    "pd.plot2D( XPos, fig, color = 'r', marker = '+' )\n",
    "pd.plot2D( XNeg, fig, color = 'g', marker = 'o' )\n",
    "plt.show()\n",
    "\n",
    "w = theta_SGD[0:-1]\n",
    "b = theta_SGD[-1]\n",
    "\n",
    "fig = pd.getFigure( 7, 7 )\n",
    "pd.shade2D( mySVM, fig, mode = 'batch', xlim = 10, ylim = 10 )\n",
    "pd.plot2D( XPos, fig, color = 'r', marker = '+' )\n",
    "pd.plot2D( XNeg, fig, color = 'g', marker = 'o' )\n",
    "plt.show()\n",
    "\n",
    "fig4 = pd.getFigure( 7, 7 )\n",
    "plt.figure( fig4.number )\n",
    "plt.plot( time_SDCM, primal_SDCM, color = 'b', linestyle = '-', label = \"SDCM Primal Obj Val\" )\n",
    "plt.plot( time_SDCM, dual_SDCM, color = 'b', linestyle = ':', label = \"SDCM Dual Obj Val\" )\n",
    "plt.plot( time_SGD, obj_SGD, color = 'r', linestyle = '-', label = \"SGD\" )\n",
    "plt.legend()\n",
    "plt.xlabel( \"Elapsed time (sec)\" )\n",
    "plt.ylabel( \"C-SVM Objective value\" )\n",
    "plt.ylim( -10000, 10000 )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "email": "purushot@cse.iitk.ac.in",
   "institution": "IIT Kanpur",
   "name": "Puru"
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