9/Logistic_Regression_From_Scratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing Some Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy.matlib\n",
    "import matplotlib.pyplot as plt\n",
    "numpy.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = [2,3]# Cluster center for class 1 data\n",
    "c2 = [10,11]# Cluster center for class 2 data\n",
    "no = 50 # No of samples in a class\n",
    "class1 = np.matlib.repmat(c1,no,1) + np.random.randn(no,len(c1))\n",
    "class2 = np.matlib.repmat(c2, no,1)+ np.random.randn(no,len(c2))\n",
    "D = np.append(class1,class2,axis =0)\n",
    "Data = np.concatenate((D, np.ones((2*no,1))),axis = 1)\n",
    "c1_label = np.ones((no,1))\n",
    "c2_label = -1*np.ones((no,1))\n",
    "label = np.concatenate((c1_label,c2_label),axis = 0)\n",
    "Data = Data.T\n",
    "y = label.T# True label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (8,8))\n",
    "plt.plot(class1[:,0],class1[:,1],'ro',class2[:,0],class2[:,1],'bo')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "v1 = [5,4]# Cluster center for class1 data of validation data set\n",
    "v2 = [7,12]# Cluster center for class 2 data of validation data set\n",
    "v_no = 30# No of samples in a class\n",
    "v_class1 = np.matlib.repmat(v1,v_no,1) + np.random.randn(v_no,len(v1))\n",
    "v_class2 = np.matlib.repmat(v2, v_no,1)+ np.random.randn(v_no,len(v2))\n",
    "v_D = np.append(v_class1,v_class2,axis =0)\n",
    "v_Data = np.concatenate((v_D, np.ones((2*v_no,1))),axis = 1)\n",
    "v_c1_label = np.ones((v_no,1))\n",
    "v_c2_label = -1*np.ones((v_no,1))\n",
    "v_label = np.concatenate((v_c1_label,v_c2_label),axis = 0)\n",
    "v_Data = v_Data.T\n",
    "v_y = v_label.T# Test label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting validation data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(v_class1[:,0],v_class1[:,1],'ro',class2[:,0],class2[:,1],'bo')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The activation function: sigmoid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    a  = 1/(1+np.exp(-x))\n",
    "    return a\n",
    "\n",
    "def prediction(w, Data):\n",
    "    pred = []\n",
    "    z = np.dot(w,Data)\n",
    "    a = sigmoid(z)\n",
    "    for i in range(0,len(a[0])):\n",
    "        if (a[0][i] > 0.5): \n",
    "            pred.append(1)\n",
    "        elif (a[0][i] <= 0.5):\n",
    "            pred.append(-1)\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "learning_rate = 0.01\n",
    "w = np.random.randn(1,3)\n",
    "for i in range(1,1500):\n",
    "    \n",
    "    z = np.dot(w,Data)\n",
    "    y_pred = prediction(w, Data)\n",
    "    val = -np.multiply(y,z)\n",
    "    J = np.sum(np.log(1+np.exp(val)))\n",
    "    num = -np.multiply(y,np.exp(val))\n",
    "    den = 1+np.exp(val)\n",
    "    f = num/den\n",
    "    gradJ = np.dot(Data,f.T)\n",
    "    w = w - learning_rate*gradJ.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classifier\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S3PTV+12Lf852VzzxuXth1ib3y9lzgSk6CzJ7ZmpaI/ly5dLffsqpnAs/M3smrD/vITOj+dT+Ksup/+6Sc8iN6Rqg+kUhvxmolHy/ErA5o20o5POe7Jyan5Gjp067oRO/dVHDp7v2L3zjVuw+GriN56C8HoLpTSf5My0VqO9iJPekF/IBO07ezKoD051zDZMfH3fOlU7x/DHn3CVTNmbWH+gPUK1atRa7MzrwV4LO15sP8uSUtRw4+Qv3ta7BHzrVISK8kNdlpWvCBN9Ux549vumrC9M0eUFqrRtSk9bJUmmdMGYGSeownSflyslQWQ35lHQyVMF16vQ5npu5ifeX7KZKmaI826sxbWuX97qsfCu1DyHw74MprRPGdGJV3uVVyG8GfuecO2BmlYBvnHN109uGQl6W7TzK8Mlr2Hn4J26LrsKTXetTqmjebXgWjPxt4iZ5h1dnvE4D+ibf7wtMzcF9SZBoWaMsMwe346HYK5i88js6xM1j1vrvvS6rQEl5dJC/R/lI3hWoQyg/BBYDdc1sn5ndDzwLdDCzrUCH5MciGSoSFsrjXa5k6sA2lC9emAffX8HACSs59OPptF+kY/4C6sLZvklJvp8K+PxLDcokTzt7PonX43cweu5WioaH8nS3+vRqXvm3Dc80vyAFnLpQSr637eAphk9ew4rdx4itE8m/ejWicumivif1TaEUcOpCKflerQrF+fjBa/jrjfVZvusoHePm8f7iXb6GZ2mdgqoWjCIKeck/QkOM+9rUYNaQGJpHleEvU9fT+/Ul7GiQ6gAma/0XRIKMQl7ynaplI3ivX0uev6Uxm74/SeduT/Nq2zs4Zyn+OWfUgEakgFDIS75kZtwaXZW5j8VyXf1KPNemDz0feIn1FWvqmD+RFPTFqwSFmWsP8Jep6zmWeIaHYmvy6HW1KRKWzpVBRIKIvniVoNelUSXmDouhZ9PKvPz1drqOmc+K3Ue9LkvEcwp5CRqlI8J54bYmjOvXkl/OJnHL2MX8bdp6fjp9zuvSRDyjkJf0BepM0tw4IzV5H7FXVmT2mwPoW/Y04xbvouPIeOK3HMr9mnQWruQFafUg9uKmfvJ5TFYbp48f/9sLoRYv7lxY2G+3Ex7uWye7jeov3tdFtS5/7UN37X+/dlHDp7vHPl7ljr074deG6RdfYSOQTeFT+92ZOTdgQGC2L5ICusarZElWrh4xfvylgZ4TFxxNL9wvqvXnM+fc819scjWHf+ZaPDLezajTOt31M1VDWldUSet3Z5Z3ri4iQUMhXxAF4pJOWbmStz/Bm92AzcyVslPUuq5JG9e17ygXNXy6e7DnE+6HYmUy994yqiHlB1V61+HTJZYkwBTyBU2grk+X2ZH8gAFZD/jMBGxWr29n5s5aiHvl6ptd7cemuEaDJ7qPGrV3SVkJ4Ix+N+nV6O/7FPFTeiGvL16D0ZNPXnrtt8RE3/K0pPYl4YgRvjNHUzKDG25I/fWvvpq9uv1tQ5CZnjQpz3qtVo1CLokBSycz851HqXtoN3+6YQj33PYP9paskLmzZDPqlzNihO93lRq1W5DclFb6e3HTSD5AMjvNkt7If8AA/76gzM40TVrbTGvKyd+RfLly6b7P85h7r1lXV3/Ix67esMnunUHPufNR1f2b4vLnrxx/f3ci2YSmawqYzE6zpBeaoaH+bSur0zNpBer48b4jcFKuHx7uW+7PnHxaYZrKB8feoz+5u//5iYsaPt316vMft7VclYwD2d8psUB8NyKSAYV8QZPZOfn0viT0d145vXWLF099+cUj7ZTS+svgwmsuDs8BA7IVpklRUW5Sg+tck0EfuNqPfeJevOY2dyYkNOMjiRTgkgco5AuizARQZr7ITGskn1YoFyuWtaN00tt3oN+/c/9f48GI0u7hHsNd1PDprvO9Y9zay2r5tz8RD6UX8vriNVhl5iKdqX3Bmp7UvqAcPRrCwn67LCwMXnst7S8ac+oLyAuXA9y92/exsHu373F6Z5wm1xKZeJyXpz7H2CkjOFysND3ufoFnZ27il7PnA1ebzoKV3JRW+ntx00jeQxdGvunNzWc0Kk5r9JyVQzozmq5JT1ZP4rqoxuNlIt0fn53sooZPd9c+/7VbuuNIxvtOT6AObRW5CJquEb/lVBBldvoktTNnw8L8qyMr00Pp1Dh/yyHX9rkvXdTw6e6pT9a6kz+f8eMNpyIrHz4ifkgv5NVPXi41YYLvmPo9e3zTGCNGeHMBjqzWkQMX9k48c47/ztrCO4t2UqlkEUb0asS1dStkbiMhIb5Yv5iZb1pNJIvS6yevkJfgc2FOPuUJYRERAbla1Mo9xxg+aQ1bD57ipmaVebpbfcoUC/fvxTnw4SMCumiIFDR9+vgCPSrKN0oO4OUAm1crw/RBbRl0XS0+W72f9nHzmL5mP34NllL7glvXopUcppG8SBZtPHCS4ZPXsGbfCTrUr8gzPRtSsWSR9F+UV6bCJKh4Ol1jZp2B0UAo8KZz7tm01lXIS35z7nwSby3YSdycLYQXCuGprvW4LboqllbfGpEc4Nl0jZmFAi8DXYD6wB1mVj8n9ymSmwqFhvBg7BV8MSSGepVKMnzyWu56ayl7jiRm/GKRXJDTc/ItgW3OuR3OuTPARKBHDu9TJNfVKF+Mib9vxTM9G7J67wk6jYrnrQU7OZ+Ud6ZDpWDK6ZCvDOxN8Xhf8jKRoBMSYtzVKorZQ2NoVbMs/5y+gVvGLmLrDz96XZoUYDkd8qlNTP5maGNm/c0swcwSDh1K5WLLIvnM5aWL8va9VzG6d1N2Hf6JrmMWMObLrZw5p2PhJffldMjvA6qmeFwF2J9yBefc6865aOdcdGRkZA6XI5I7zIweTSszd1gsnRpeRtycLXR/aQGr9x73ujQpYHI65JcDtc2shpmFA72BaTm8T5E8o1zxwrx4RzPeuCeaY4lnuOmVhfx7xkZ+PhOghmciGcjRkHfOnQMeAWYBG4GPnXPrc3KfInlRh/oVmTMsltuvqspr8TvoMjqeJTuOeF2WFAA6GUokly3adpjHp6xlz9FE+lxdjce7XEmJImEZv1AkDWprIJKHtK5VnllDYnigbQ0+XLaHjiPj+WrTD16XJUFKIS/igaLhoTzVrT6TB7SmRJFC9Hs3gcETv+XIqdNelyZBRiEv4qFm1cow/dF2DL6+NjPWHqDDyHimrvrOv4ZnIn5QyIt4LLxQCEM71GH6o+2oWjaCwRNX8fv3Ejhw4mevS5MgoJAXySPqXlaCKQNa81TXeizYdpiOcfF8sHQPSWqNINmgkBfJQ0JDjAfa1WTWkBgaVSnFnz9Zy51vLmH3kZ+8Lk3yKYW8SB4UVa4YEx64mmd7NWL9dyfpNCqeN+fvUMMzyTSFvEgeZWb0blmNOcNiaVurPM98vpFery5i8/dqeCb+U8iL5HGXlSrCG/dE8+Idzdh3NJFuL85n5JwtangmflHIi+QDZsaNTS5nzrBYbmhUidFfbqXbi/NZpYZnkgGFvEg+UrZYOKN7N+Pte6P58Zdz9HplIc9M36CGZ5ImhbxIPnTdlRWZPTSGO1pW480FO+k0Kp5F2w97XZbkQQp5kXyqRJEwRtzUiIn9WxFicOcbS3liyhpO/HzW69IkD1HIi+RzrWqW44shMTwYU5OPlu+l48h5zNmghmfio5AXCQJFwkJ54oZ6fDqwDWUiwvn9ewk88sFKDqvhWYGnkBcJIo2rlGbaI215rEMdZq//gQ5x8/j0WzU8K8gU8iJBJrxQCI9eX5vPB7WlevliDPloFf3eXc7+42p4VhAp5EWCVO2KJZj0UGue7lafJTuO0nFkPO8v2a2GZwWMQl4kiIWGGP3a1mD20BiaVC3FXz5dR+83lrDj0CmvS5NcopAXKQCqlo1g/P1X89zNjdh44CRdRs9n7LztnDuv1gjBTiEvUkCYGbdfVY25w2KJrRPJszM3cdMri9iw/6TXpUkOUsiLFDAVSxbhtbtb8PKdzTlw4me6v7SAF2Zv5vQ5tUYIRgp5kQLIzOjauBJzhsbSvcnlvPjVNrqOWcCK3ce8Lk0CTCEvUoCVKRZO3O1Nefe+q0g8fY5bxi7i75+tJ/HMOa9LkwBRyIsIv6tbgdnDYrm7VRTvLNxFx5HxLNiqhmfBQCEvIgAUL1yIf/RoyMcPXkN4aAh3vbWUP01azYlENTzLz7IV8mZ2q5mtN7MkM4u+6LknzGybmW02s07ZK1NEckvLGmWZMbgdA353BZNXfkf7kfP4Yt33XpclWZTdkfw6oBcQn3KhmdUHegMNgM7AK2YWms19iUguKRIWyvDOVzJ1YBsiixfmofEreHjCCg7++IvXpUkmZSvknXMbnXObU3mqBzDROXfaObcT2Aa0zM6+RCT3NaxciqmPtOGPneoyd+NBOsTFM2nFPjU8y0dyak6+MrA3xeN9ycsuYWb9zSzBzBIOHTqUQ+WISFaFhYYw8NpazBjUjloVivOH/62m7zvL2Xcs0evSxA8ZhryZzTWzdanceqT3slSWpfrR75x73TkX7ZyLjoyM9LduEclltSoU538PXsPfuzcgYZev4dm4RbvU8CyPK5TRCs659lnY7j6gaorHVYD9WdiOiOQhISFG39bVub5eBZ6Yspa/TlvP9DX7efbmxlwRWdzr8iQVOTVdMw3obWaFzawGUBtYlkP7EpFcVqVMBO/1a8l/b23Clh9O0WX0fF75Zhtn1fAsz8nuIZQ3mdk+4BrgczObBeCcWw98DGwAvgAGOufUGEMkiJgZt7SowpxhMVx/ZQX+88Vmer68kHXfnfC6NEnB8tK35NHR0S4hIcHrMkQkC2auPcBfpq7nWOIZHoqtyaPX1aZImI6czg1mtsI5F53aczrjVUQCokujSnw5LJabmlXm5a+3c8OY+STsOup1WQWeQl5EAqZURBj/vbUJ7/VryemzSdz62mL+OnUdp06r4ZlXFPIiEnAxdSKZPTSGvtdU570lu+k0Mp55W3QejBcU8iKSI4oVLsTfujdg0kPXUCQshL5vL+Oxj1dzPPGM16UVKAp5EclRLaLK8vmgdjxybS2mrvqO9nHzmLH2gNdlFRgKeRHJcUXCQvlDp7pMfaQNl5UqwsMTVvLg+wkcPKmGZzlNIS8iuabB5aX49OE2DO98JV9vPkT7uHn8L2GvGp7lIIW8iOSqQqEhDPjdFXwxuB1XXlaSP05awz1vL2PvUTU8ywkKeRHxRM3I4kzs34p/9mjAyt3H6DQqnncW7uS8Gp4FlEJeRDwTEmLcfU11Zg+L5arqZfn7Zxu47bXFbDv4o9elBQ2FvIh4rnLporx731XE3daE7YdOccPoBbz01VY1PAsAhbyI5AlmRq/mVZgzNJYODSry39lb6P6SGp5ll0JeRPKUyBKFefnO5rx2dwuOnDpNj5cX8uzMTfxyVo1ss0IhLyJ5UqcGlzFnaCy3NK/C2HnbuWH0fJbtVMOzzFLIi0ieVSoijOduacyEB67mbFISt722mL98uo4ffznrdWn5hkJeRPK8NrXKM2tIDP3a1GD8Ul/Ds683H/S6rHxBIS8i+UJEeCGevrE+kwe0pljhQtz3znKGfbSKYz+p4Vl6FPIikq80r1aG6YPaMuj62kxbvZ/2cfOYvma/WiOkQSEvIvlO4UKhDOtQh88ebUvlMkV55INv6f/+Cn5Qw7NLKORFJN+qV6kkUwa05skb6hG/xdfw7KPlezSqT0EhLyL5WqHQEH4fU5NZQ2JocHlJhk9eS583l7LniBqegUJeRIJE9fLF+OCBVoy4qSFr9p2g46h5vDl/R4FveKaQF5GgERJi9Lk6ijnDYmh9RXme+XwjN7+6iC0/FNyGZwp5EQk6lUoV5a2+0Yzu3ZTdR36i65j5jPlyK2fOFbyGZwp5EQlKZkaPppWZOyyWzg0rETdnC91fWsDqvce9Li1XKeRFJKiVK16YF+9oxhv3RHMs8Qw3vbKQf83YyM9nCkbDs2yFvJk9b2abzGyNmX1iZqVTPPeEmW0zs81m1in7pYqIZF2H+hWZMyyW26+qyuvxO+gyOp7F2494XVaOy+5Ifg7Q0DnXGNgCPAFgZvWB3kADoDPwipmFZnNfIiLZUrJIGP/u1ZgPfn81DrjjjSX8+dF0BkQAAAfKSURBVJO1nAzihmfZCnnn3Gzn3Lnkh0uAKsn3ewATnXOnnXM7gW1Ay+zsS0QkUFpfUZ4vBsfw+3Y1mLhsDx3j4vlq0w9el5UjAjkn3w+YmXy/MrA3xXP7kpddwsz6m1mCmSUcOnQogOWIiKStaHgoT3atz5SH21CqaBj93k1g8MRvOXLqtNelBVSGIW9mc81sXSq3HinWeRI4B0y4sCiVTaV6RoJz7nXnXLRzLjoyMjIr70FEJMuaVi3NZ4+2ZUj72sxYe4AOI+OZuuq7oGmNUCijFZxz7dN73sz6At2A692vv5V9QNUUq1UB9me1SBGRnBReKIQh7evQpWEl/jR5DYMnrmLaqv08c1NDKpUq6nV52ZLdo2s6A8OB7s65lI0ipgG9zaywmdUAagPLsrMvEZGcVveyEkwZ0JqnutZj4fbDdIiLZ8LS3STl49YI2Z2TfwkoAcwxs1VmNhbAObce+BjYAHwBDHTOFYyDUkUkXwsNMR5o52t41rhKKZ78ZB13vrmEXYd/8rq0LLG8NO8UHR3tEhISvC5DRAQA5xwfLd/LiM83cuZ8Eo91rEO/NjUoFJq3ziM1sxXOuejUnstblYqI5CFmRu+W1ZgzLJZ2tSP514xN3PzqIjZ9f9Lr0vymkBcRycBlpYrwxj0tGHNHM/Yd+5luYxYQN2cLp8/l/VlohbyIiB/MjO5NLmfOsFi6Na7EmC+3cuOLC/h2zzGvS0uXQl5EJBPKFgtnVO9mvHPvVfz4yzl6vbqIf07fQOKZcxm/2AMKeRGRLLj2ygrMHhpDn6ur8daCnXQeNZ9F2w57XdYlFPIiIllUokgYz/RsxEf9WxEaYtz55lIen7yGEz/nnYZnCnkRkWy6umY5Zg5ux4OxNfk4YS8d4uYxe/33XpcFKORFRAKiSFgoT3Spx6cD21C2WDj931/BIx+s5LDHDc8U8iIiAdS4iq/h2WMd6jB7/Q+0j5vHJ9/u86zhmUJeRCTAwkJDePT62nw+qC01yhdj6Eer6ffucvYf/znXa1HIi4jkkNoVSzDpodY83a0+S3YcpePIeN5fkrsNzxTyIiI5KDTE6Ne2BrOHxtC0amn+8uk6er+xhB2HTuXK/hXyIiK5oGrZCN6/vyX/ubkxGw+cpMvo+Yydt51z55NydL8KeRGRXGJm3HZVVeYOiyW2TiTPztxEz1cWsmF/zjU8U8iLiOSyiiWL8NrdLXilT3O+P/EL3V9awFsLdubIvjK8/J+IiASemXFDo0pcU7Mcz3y+kaiyETmyH4W8iIiHyhQL54XbmuTY9jVdIyISxBTyIiJBTCEvIhLEFPIiIkFMIS8iEsQU8iIiQUwhLyISxBTyIiJBzLxqZJ8aMzsE7M7iy8sDee8quv5R7d5Q7d7Ir7Xn5bqjnHORqT2Rp0I+O8wswTkX7XUdWaHavaHavZFfa8+vdWu6RkQkiCnkRUSCWDCF/OteF5ANqt0bqt0b+bX2fFl30MzJi4jIpYJpJC8iIhdRyIuIBLGgCHkz62xmm81sm5k97nU9/jKzqmb2tZltNLP1ZjbY65oyw8xCzexbM5vudS2ZYWalzWySmW1K/t1f43VN/jKzocn/VtaZ2YdmVsTrmtJiZm+b2UEzW5diWVkzm2NmW5N/lvGyxrSkUfvzyf9m1pjZJ2ZW2ssa/ZXvQ97MQoGXgS5AfeAOM6vvbVV+Owc85pyrB7QCBuaj2gEGAxu9LiILRgNfOOeuBJqQT96DmVUGBgHRzrmGQCjQ29uq0vUu0PmiZY8DXzrnagNfJj/Oi97l0trnAA2dc42BLcATuV1UVuT7kAdaAtucczucc2eAiUAPj2vyi3PugHNuZfL9H/GFTWVvq/KPmVUBugJvel1LZphZSSAGeAvAOXfGOXfc26oypRBQ1MwKARHAfo/rSZNzLh44etHiHsC45PvjgJ65WpSfUqvdOTfbOXcu+eESoEquF5YFwRDylYG9KR7vI58EZUpmVh1oBiz1thK/jQL+BCR5XUgm1QQOAe8kTzW9aWbFvC7KH86574D/AnuAA8AJ59xsb6vKtIrOuQPgG+QAFTyuJ6v6ATO9LsIfwRDylsqyfHVcqJkVByYDQ5xzJ72uJyNm1g046Jxb4XUtWVAIaA686pxrBvxE3p0y+I3k+eseQA3gcqCYmd3lbVUFj5k9iW+qdYLXtfgjGEJ+H1A1xeMq5OE/YS9mZmH4An6Cc26K1/X4qQ3Q3cx24Zseu87Mxntbkt/2Afuccxf+YpqEL/Tzg/bATufcIefcWWAK0NrjmjLrBzOrBJD886DH9WSKmfUFugF9XD45ySgYQn45UNvMaphZOL4voqZ5XJNfzMzwzQ1vdM7FeV2Pv5xzTzjnqjjnquP7fX/lnMsXI0rn3PfAXjOrm7zoemCDhyVlxh6glZlFJP/buZ588qVxCtOAvsn3+wJTPawlU8ysMzAc6O6cS/S6Hn/l+5BP/iLkEWAWvn/wHzvn1ntbld/aAHfjGwmvSr7d4HVRBcCjwAQzWwM0Bf7lcT1+Sf7rYxKwEliL7//fPHuqvZl9CCwG6prZPjO7H3gW6GBmW4EOyY/znDRqfwkoAcxJ/n91rKdF+kltDUREgli+H8mLiEjaFPIiIkFMIS8iEsQU8iIiQUwhLyISxBTyIiJBTCEvIhLE/g9jGGNY8m7yBQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "domain =  np.linspace(0,13,100)\n",
    "h_x = -(w[0,0]/w[0,1])*domain - (w[0,2]/w[0,1])\n",
    "\n",
    "plt.plot(v_class1[:,0],v_class1[:,1],'ro',v_class2[:,0],v_class2[:,1],'bo')\n",
    "plt.plot(domain,h_x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Logistic Regression has successfully learnt to categorize the given dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}