IE406_Lab3.ipynb

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  "metadata": {
    "colab": {
      "name": "IE406-Lab3.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/nishi1612/Machine-Learning/blob/master/IE406_Lab3.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CRQ2cik60Rb6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!pip install -U -q PyDrive\n",
        "from pydrive.auth import GoogleAuth\n",
        "from pydrive.drive import GoogleDrive\n",
        "from google.colab import auth\n",
        "from oauth2client.client import GoogleCredentials\n",
        "auth.authenticate_user()\n",
        "gauth = GoogleAuth()\n",
        "gauth.credentials = GoogleCredentials.get_application_default()\n",
        "drive = GoogleDrive(gauth)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zi9eVp1H11j9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import random"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hiqeb8tO1Ha3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "id = \"1cO2syVjhONiY4ezuqQ-zWAKH4-9WstMy\"\n",
        "downloaded = drive.CreateFile({'id':id}) \n",
        "downloaded.GetContentFile('ex2data1-logistic.csv')  \n",
        "df1 = pd.read_csv('ex2data1-logistic.csv')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lgAn7HeL14SA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "id = \"1Ksk651w-gt7D553Ie2UL9cTccRJW4fzk\"\n",
        "downloaded = drive.CreateFile({'id':id}) \n",
        "downloaded.GetContentFile('ex2data2-logistic.csv')  \n",
        "df2 = pd.read_csv('ex2data2-logistic.csv')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ak1bKEEB2guh",
        "colab_type": "code",
        "outputId": "ac36cccf-99c5-4728-a2fb-3f210cdf5208",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "df1.head(5)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x1</th>\n",
              "      <th>x2</th>\n",
              "      <th>y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>34.623660</td>\n",
              "      <td>78.024693</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>30.286711</td>\n",
              "      <td>43.894998</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>35.847409</td>\n",
              "      <td>72.902198</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>60.182599</td>\n",
              "      <td>86.308552</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>79.032736</td>\n",
              "      <td>75.344376</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          x1         x2  y\n",
              "0  34.623660  78.024693  0\n",
              "1  30.286711  43.894998  0\n",
              "2  35.847409  72.902198  0\n",
              "3  60.182599  86.308552  1\n",
              "4  79.032736  75.344376  1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q5EOYJPI23sM",
        "colab_type": "code",
        "outputId": "55edb6f2-91b9-4cb3-c07e-7a18d048160b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "df2.head(5)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x1</th>\n",
              "      <th>x2</th>\n",
              "      <th>y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.051267</td>\n",
              "      <td>0.69956</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-0.092742</td>\n",
              "      <td>0.68494</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-0.213710</td>\n",
              "      <td>0.69225</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.375000</td>\n",
              "      <td>0.50219</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.513250</td>\n",
              "      <td>0.46564</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         x1       x2  y\n",
              "0  0.051267  0.69956  1\n",
              "1 -0.092742  0.68494  1\n",
              "2 -0.213710  0.69225  1\n",
              "3 -0.375000  0.50219  1\n",
              "4 -0.513250  0.46564  1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_-ArUX5O25_L",
        "colab_type": "code",
        "outputId": "e52e8dd7-ecd5-4490-f4e6-aee51b29a795",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "df1.index"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "RangeIndex(start=0, stop=100, step=1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TgPLXYpx28EA",
        "colab_type": "code",
        "outputId": "69739dba-6dba-43f8-a668-b32170bc57be",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "df2.index"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "RangeIndex(start=0, stop=118, step=1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GJruSB5U29qj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot(df):\n",
        "  x1_1 = df['x1']\n",
        "  x2_1 = df['x2']\n",
        "  y_1 = df['y']\n",
        "  for i in range(len(x1_1)):\n",
        "    if(y_1[i]==0):\n",
        "      plt.scatter(x1_1[i],x2_1[i],color='red')\n",
        "    else:\n",
        "      plt.scatter(x1_1[i],x2_1[i],color='blue')\n",
        "  plt.xlabel('$x1$')\n",
        "  plt.ylabel('$x2$')\n",
        "  plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WE1C0jII3kWD",
        "colab_type": "code",
        "outputId": "020eb546-7c83-414b-ebee-6c523ed71260",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 553
        }
      },
      "source": [
        "plot(df1)\n",
        "plot(df2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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DPyI7iF/Pn08Tb6wOfMXM9pjZ9nzbWnc/kj9+EVgbJrQzXAQsAvflTXqfNbPz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\nQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3f31h3+fd/bh2lnzbBuAB4A3u/uPCumeBVcAu4HF3v3ZUmjRWmDSm6XHPUh/Q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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Yt1nHkgC34RI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sigmoid(z):\n",
        "  return 1/(1+np.exp(-z))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ywvd33uq4grI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def logistic_cost(y_actual,y_predicted):\n",
        "  return np.sum(((-y_actual*np.log(y_predicted)) - ((1-y_actual)*np.log(1-y_predicted))))/y_predicted.shape[0]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8YKm1omL4ivB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def logistic_output(X,theta):\n",
        "  t = sigmoid(np.dot(X,theta))\n",
        "  for i in range(t.shape[0]):\n",
        "    if(t[i]<0.5):\n",
        "      t[i]=0\n",
        "    else:\n",
        "      t[i]=1\n",
        "  return t"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3QV91pjp4q__",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def logistic_gradient_descent(X,Y,rate):\n",
        "  epochs = 100000\n",
        "  alphas = [rate]\n",
        "  for alpha in alphas:\n",
        "    theta = np.zeros((3,1))\n",
        "    x0 = X[:,0]*theta[0]\n",
        "    x1 = X[:,1]*theta[1]\n",
        "    x2 = X[:,2]*theta[2]\n",
        "    h = sigmoid(x0+x1+x2)\n",
        "    cost = np.zeros((epochs,1))\n",
        "    for i in range(epochs):\n",
        "      theta[0] = theta[0] - alpha*np.sum(h-Y)/X.shape[0]\n",
        "      for j in range(1,X.shape[1]):\n",
        "        theta[j] = theta[j] - alpha/X.shape[0] * np.sum((h-Y)*X[:,j])\n",
        "        x0 = X[:,0]*theta[0]\n",
        "        x1 = X[:,1]*theta[1]\n",
        "        x2 = X[:,2]*theta[2]\n",
        "        h = sigmoid(x0+x1+x2)\n",
        "      cost[i] = logistic_cost(Y,h)\n",
        "      if(i>0 and cost[i]>cost[i-1]):\n",
        "        epochs = i\n",
        "        break\n",
        "      if(i%10000==0):\n",
        "        print(\"Epoch : \" , i , \" Cost : \" , cost[i])\n",
        "    plt.plot(np.arange(epochs),cost[:epochs])\n",
        "    plt.xlabel('Epochs')\n",
        "    plt.ylabel('Cost')\n",
        "    plt.title('Cost v/s Epoch for gradient descent')\n",
        "    plt.show()\n",
        "    if(alpha==rate):\n",
        "      return theta"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PhcieNxC4uCw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def perform_descent(df1,rate):\n",
        "  msk = random.sample(range(0,100),int(len(df1)*90/100))\n",
        "  vals = np.full((100,1),True)\n",
        "  for i in msk:\n",
        "    vals[i] = False\n",
        "  train_df1 = df1[~vals]\n",
        "  test_df1 = df1[vals]\n",
        "\n",
        "  X = np.zeros((len(train_df1['x1']),3))\n",
        "  X[:,0] = np.ones(len(train_df1['x1']))\n",
        "  X[:,1] = train_df1['x1']\n",
        "  X[:,2] = train_df1['x2']\n",
        "  Y = train_df1['y']\n",
        "  \n",
        "  theta = logistic_gradient_descent(X,Y,rate)\n",
        "  print(theta)\n",
        "  \n",
        "  X = np.zeros((len(test_df1['x1']),3))\n",
        "  X[:,0] = np.ones(len(test_df1['x1']))\n",
        "  X[:,1] = test_df1['x1']\n",
        "  X[:,2] = test_df1['x2']\n",
        "  Y = test_df1['y'].values\n",
        "\n",
        "  x0 = X[:,0]*theta[0]\n",
        "  x1 = X[:,1]*theta[1]\n",
        "  x2 = X[:,2]*theta[2]\n",
        "  h = sigmoid(x0+x1+x2)\n",
        "  count=0\n",
        "  for i in range(len(h)):\n",
        "    if(h[i]<0.5 and Y[i]==0):\n",
        "      count+=1\n",
        "    elif(h[i]>=0.5 and Y[i]==1):\n",
        "      count+=1\n",
        "  acc = count/len(h)\n",
        "  print(acc)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nCassvib66mp",
        "colab_type": "code",
        "outputId": "d76c0eae-0d13-44a1-da9a-87cd99048768",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 533
        }
      },
      "source": [
        "perform_descent(df1,0.001)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch :  0  Cost :  [0.62644682]\n",
            "Epoch :  10000  Cost :  [0.57982922]\n",
            "Epoch :  20000  Cost :  [0.54070193]\n",
            "Epoch :  30000  Cost :  [0.50771031]\n",
            "Epoch :  40000  Cost :  [0.47973115]\n",
            "Epoch :  50000  Cost :  [0.4558354]\n",
            "Epoch :  60000  Cost :  [0.43527093]\n",
            "Epoch :  70000  Cost :  [0.41743565]\n",
            "Epoch :  80000  Cost :  [0.40184968]\n",
            "Epoch :  90000  Cost :  [0.38813035]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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WCbeeTJf02vzhzflc9PgXzFuzPezSREKnwBA5jJYp1XluRB/+fVk31mzdw6BH\npnDPOwvYtT8v7NJEQqPAECmEmTG4Wxof33Yqw3o34z9TV3DmA5P5YN56KspdnkWOhAJDpBi1qyXy\nlws78+qN/ahTLYkbnpvNyHGZrN6yJ+zSREqVAkMkSj2a1eXtm/rzu3PaM215Nmf+azL//miJviku\nlYYCQ+QIJMTHcf3JrfjotlM4vX0q//roW87812Q+nK/DVFLxKTBEjkKTOlV59PIevDCyD1UT4/nx\ns7MZ/tQslm3aFXZpIjGjwBA5Bv3apPDuzSfxh/M68NWqrQx88DPufX+hrqaSCkmBIXKMEuPjGHFi\nSz755alc0C2NUZOXc/o/P+XNOWt0mEoqFAWGSAlpULMK913aldd+2o+GNZO5Zfwcho6azjdZ+tKf\nVAwKDJES1qNZXd74WX/uvagzyzbtYtCjU7j9pbms3657U0n5psAQiYH4OGNY72ZM+tWp/PjkVrw9\ndy0/uv9THvzoW/bk6PyGlE8xDQwzG2hmi81sqZndUcRwF5uZM7MM393CzPaa2Rz/eCKWdYrESq3k\nRO48uz0f334Kpx3fkAc/WsJp90/m1dlZHNBNDaWciVlgmFk88ChwNtABGGZmHQ4zXE3gFmBGgV7L\nnHPd/OOGWNUpUhrS61Xj0St68MoNJ5Baqwq3vzyXwY9OZYZ+6U/KkVjuYfQGljrnljvncoDxwODD\nDHcP8HdAB3ilwstoUY/Xf9qfB4d2Y/Ou/QwdPZ0bnp3Nys27wy5NpFixDIw0YHVEd5Zv+56Z9QDS\nnXPvHmb8lmb2lZlNNrOTDjcDM/uxmWWaWeamTZtKrHCRWIqLMy7onsYnt5/K7We247Mlmzjjgcn8\n8c15bNq5P+zyRAoV2klvM4sDHgBuP0zvdUAz51x34DbgBTOrVXAg59xo51yGcy6jQYMGsS1YpIRV\nTYrn56e35dNfnsrQXuk8P+M7TrlvEv+a+K2++CdlUiwDYw2QHtHd1LcdVBPoBHxqZiuBvsBbZpbh\nnNvvnMsGcM7NBpYB7WJYq0hoGtZK5i8XdmbiL07m1OMa8O+Pl3DKPyYx7ouV5OQdCLs8ke/FMjBm\nAW3NrKWZJQGXAW8d7Omc2+6cS3HOtXDOtQCmA4Occ5lm1sCfNMfMWgFtgeUxrFUkdK0a1OCxK3ry\nxs/60za1Bne9NZ8zHpjMW3PX6ooqKRNiFhjOuTzgJmACsBB4yTk338zuNrNBxYx+MvC1mc0BXgFu\ncM5tiVWtImVJt/Q6vHh9X56+thfVkuK5+cWvOP+RKXy+ROfpJFxWUe51k5GR4TIzM8MuQ6REHTjg\neHPuGv754bdkbd3LCa3qc/sGeWLdAAAQUklEQVSAdmS0qBd2aVJBmNls51xGVMMqMETKvv15+Tw/\n/Tse+3QZm3ft55R2Dbh9QDu6NK0TdmlSzikwRCqoPTl5PDNtFaMmL2PrnlzO7JDKbWe2o33j/7mI\nUCQqCgyRCm7nvlyemrqSJz9fzs59eZzbuTG/OLMtbRrWDLs0KWcUGCKVxPY9uTz5+XKemrqCvbn5\nDO6Wxi2nt6VFSvWwS5NyQoEhUsls2Z3DqMnLGDdtJbn5jou6p/GzH7VRcEixFBgildTGHft47NNl\nvDjzO3LzDzC4WxAcbRrWCLs0KaMUGCKV3Mad+3jys+U8N/079uXlc07nxvz8tDYc30gnx+VQCgwR\nASB7137GTlnBuC9Wsjsnn7M6pvLz09rSKa122KVJGaHAEJFDbNuTw3+mruSpqSvYuS+P045vyM9P\na0P3ZnXDLk1CpsAQkcPasS+XcVNXMnbqCrbtyeWktinceEprTmhdHzMLuzwJgQJDRIq0a38ez01f\nxZjPV7B51366Nq3NDae0ZkDHRsTHKTgqEwWGiERlX24+r36ZxejPlrMqew+tUqpz/cmtuKhHGlUS\n4sMuT0qBAkNEjkj+Acf789bxxORlzFuzg4Y1q3DdiS25ok8zaiYnhl2exJACQ0SOinOOqUuzeXzy\nUqYuzaZmcgJX9m3Otf1b0LBmctjlSQwoMETkmH2TtZ0nJi/jvXnrSIyP4+IeaVzXvyVtU3W/qopE\ngSEiJWbF5t2M/mw5r32Zxf68A5zSrgEjT2rJiW1SdGVVBaDAEJESl71rP8/P+I5npq1i8679HJda\nkxEntmRQtyYkJ+oEeXmlwBCRmNmfl89bc9YydsoKFq3fSUqNJK7s25wr+zYnpUaVsMuTI6TAEJGY\nc87xxbJsxk5ZwSeLNpKUEMeF3dIYcVJL2uk8R7lxJIGREOtiRKRiMjP6t0mhf5sUlm7cxVNTV/Dq\nl1n8N3M1J7VNYfgJLfjR8Q31RcAKRHsYIlJitu7O4YWZ3/HstFWs37GPpnWrclXf5gzJSKdu9aSw\ny5PD0CEpEQlVbv4BPlqwgXHTVjJ9+RaqJMQxuFsTrj6hhe6UW8YoMESkzFi0fgfPTFvF61+uYW9u\nPj2b1+XqE5pzdqfGJCXEhV1epafAEJEyZ/veXF6ZncWz01ayMnsPKTWqcHmfZlzRpxmptfQt8rAo\nMESkzDpwwPHZkk08M20VkxZvJN6MM9qnMqxPM05qk0KcTpKXKl0lJSJlVlyccepxDTn1uIasyt7N\nCzO+4+XZWXwwfz3p9apyWa9mXJrRVPeuKoO0hyEiodufl8+E+Rt4YcYqpi/fQkKccWaHVC7v04z+\nrbXXEUs6JCUi5dayTbsYP/M7XpmdxdY9uTSvX43LejXjkp5NaVBT3yQvaQoMESn39uXmM2H+ep6f\n8R0zV2whMd4Y0KERw3o3o1/r+trrKCEKDBGpUJZu3MkLM1bz6pdZbN+bS1qdqlzSsymX9GxKer1q\nYZdXrikwRKRC2pebz4cLNvBy5mqmLN2Mc9C/TX2GZKRzVsdGumvuUSgzgWFmA4F/A/HAGOfc3woZ\n7mLgFaCXcy7Tt90JjADygZudcxOKmpcCQ6Ryydq6h1dnr+Hl2avJ2rqXmskJDOrahCEZ6XRpWlu/\n1RGlMhEYZhYPfAucCWQBs4BhzrkFBYarCbwLJAE3OecyzawD8CLQG2gCfAS0c87lFzY/BYZI5XTg\ngGP6imxezszivW/WsT/vAMel1uTSjKZc0D1Nt1wvxpEERiy/l98bWOqcW+6cywHGA4MPM9w9wN+B\nfRFtg4Hxzrn9zrkVwFI/PRGRQ8TFGf1ap/Cvod2Y9fsz+OuFnamaFM+f311I379+zI+fyeSDeevY\nn1fo502JUiy/uJcGrI7ozgL6RA5gZj2AdOfcu2b2qwLjTi8wblrBGZjZj4EfAzRr1qyEyhaR8qpW\nciKX92nG5X2a8e2GnbycuZrXv1rLhws2ULtqIud2acxF3dPo2byuDlkdhdC+6W1mccADwDVHOw3n\n3GhgNASHpEqmMhGpCNql1uR353bgNwOPZ8rSzbz+1Rpe+zKLF2Z8R7N61bigexoXdk+jZUr1sEst\nN2IZGGuA9Ijupr7toJpAJ+BTn/SNgLfMbFAU44qIRCUhPu77W5Hs2p/HhHnref2rNTz8yRIe+ngJ\n3dLrcFGPNM7r0oR6+s2OIsXypHcCwUnv0wk29rOAy51z8wsZ/lPgl/6kd0fgBX446f0x0FYnvUWk\npKzfvo8356zh9a/WsGj9ThL8Pa4u6pHGacc3rDSX6JaJmw865/LM7CZgAsFltf9xzs03s7uBTOfc\nW0WMO9/MXgIWAHnAz4oKCxGRI9WodjI/OaU1PzmlNQvW7uD1r7J4c85aPlq4gRpVEhjQMZXzuzbh\nxDYpJMbrdztAX9wTEfle/gHHF8s28/bctXwwbz079uVRp1oiZ3dqzPldG9OnZf0K9xvlZeJ7GKVN\ngSEiJWl/Xj6ff7uZt79ey8QFG9iTk0/DmlU4t0tjzu/ahO7pdSrElVYKDBGRErQ3J59PFm3krblr\nmLR4Ezl5B0irU5Xzuzbh/K6N6dC4VrkNDwWGiEiM7NiXy8T5G3j767VMWbKZvAOOVg2qc17nxgzs\n1Jj2jWuWq/BQYIiIlIItu3P4YN563p67lhkrsjngoEX9apzduTFnd2pE57Syf08rBYaISCnbvGs/\nExds4L1v1vHFsmzyDzjS6lTlnM6NGNipMd3T65TJ3/BQYIiIhGjbnhwmLtjA+/PW8/mSTeTmOxrV\nSmZgp0ac3akRGS3qlZmrrRQYIiJlxI59uXy8cAPvf7OeT78NTpin1KjCWR1TObtTY/q0qhfq9zwU\nGCIiZdCu/XlMWrSRD+at55NFG9mbm0+t5AR+dHxDBnRoxCnHNaBGldK9xZ8CQ0SkjNubk8/nSzYx\nccEGPl60kS27c0iKj+OE1vUZ0DGVM9un0rBWcszrUGCIiJQj+Qccs1dt5cP565m4cAOrsvcA0DW9\nDgM6pDKgQyptGtaIyRVXCgwRkXLKOce3G3YxccF6Ji7YwNys7UBwue6ZHVIZ0LERPZrVLbGT5goM\nEZEKYv32fUxcuIGJCzYwbdlmcvMd9aoncepxDTijfSontU2hZnLiUU9fgSEiUgHt2JfL5MWb+Gjh\nBj5dvInte3NJjDfO6tiIRy7vcVTTLBO3NxcRkZJVKznR37+qCXn5B5i9aisfL9pIQil9p0OBISJS\nDiXEx9GnVX36tKpfavPUr4KIiEhUFBgiIhIVBYaIiERFgSEiIlFRYIiISFQUGCIiEhUFhoiIREWB\nISIiUakwtwYxs03AqmOYRAqwuYTKKS8q2zJXtuUFLXNlcSzL3Nw51yCaAStMYBwrM8uM9n4qFUVl\nW+bKtrygZa4sSmuZdUhKRESiosAQEZGoKDB+MDrsAkJQ2Za5si0vaJkri1JZZp3DEBGRqGgPQ0RE\noqLAEBGRqFT6wDCzgWa22MyWmtkdYddzpMws3cwmmdkCM5tvZrf49npmNtHMlvi/dX27mdlDfnm/\nNrMeEdMa7odfYmbDI9p7mtk3fpyHzKx0ft6rCGYWb2Zfmdk7vrulmc3wNf7XzJJ8exXfvdT3bxEx\njTt9+2IzOyuivcy9J8ysjpm9YmaLzGyhmZ1QCdbxL/x7ep6ZvWhmyRVtPZvZf8xso5nNi2iL+Xot\nbB7Fcs5V2gcQDywDWgFJwFygQ9h1HeEyNAZ6+Oc1gW+BDsA/gDt8+x3A3/3zc4D3AQP6AjN8ez1g\nuf9b1z+v6/vN9MOaH/fsMrDctwEvAO/47peAy/zzJ4Ab/fOfAk/455cB//XPO/j1XQVo6d8H8WX1\nPQGMA0b650lAnYq8joE0YAVQNWL9XlPR1jNwMtADmBfRFvP1Wtg8iq037H+EkN+UJwATIrrvBO4M\nu65jXKY3gTOBxUBj39YYWOyfjwKGRQy/2PcfBoyKaB/l2xoDiyLaDxkupGVsCnwMnAa84/8ZNgMJ\nBdcrMAE4wT9P8MNZwXV9cLiy+J4AavuNpxVor8jrOA1Y7TeCCX49n1UR1zPQgkMDI+brtbB5FPeo\n7IekDr4pD8rybeWS3w3vDswAUp1z63yv9UCqf17YMhfVnnWY9jA9CPwaOOC76wPbnHN5vjuyxu+X\ny/ff7oc/0tchTC2BTcBT/jDcGDOrTgVex865NcD9wHfAOoL1NpuKvZ4PKo31Wtg8ilTZA6PCMLMa\nwKvArc65HZH9XPAxokJcP21m5wEbnXOzw66lFCUQHLZ43DnXHdhNcBjhexVpHQP4Y+qDCcKyCVAd\nGBhqUSEojfV6JPOo7IGxBkiP6G7q28oVM0skCIvnnXOv+eYNZtbY928MbPTthS1zUe1ND9Melv7A\nIDNbCYwnOCz1b6COmSX4YSJr/H65fP/aQDZH/jqEKQvIcs7N8N2vEARIRV3HAGcAK5xzm5xzucBr\nBOu+Iq/ng0pjvRY2jyJV9sCYBbT1V14kEZwseyvkmo6Iv+phLLDQOfdARK+3gINXSwwnOLdxsP1q\nf8VFX2C73zWdAAwws7r+090AgmO864AdZtbXz+vqiGmVOufcnc65ps65FgTr6xPn3BXAJOASP1jB\n5T34Olzih3e+/TJ/dU1LoC3BCcIy955wzq0HVpvZcb7pdGABFXQde98Bfc2smq/p4DJX2PUcoTTW\na2HzKFpYJ7XKyoPgyoNvCa6Y+F3Y9RxF/ScS7E5+Dczxj3MIjt9+DCwBPgLq+eENeNQv7zdARsS0\nrgOW+se1Ee0ZwDw/ziMUOPka4rKfyg9XSbUi2BAsBV4Gqvj2ZN+91PdvFTH+7/wyLSbiqqCy+J4A\nugGZfj2/QXA1TIVex8D/AYt8Xc8SXOlUodYz8CLBOZpcgj3JEaWxXgubR3EP3RpERESiUtkPSYmI\nSJQUGCIiEhUFhoiIREWBISIiUVFgiIhIVBQYIsUws3wzmxPxKLE7m5pZi8g7lYqUZQnFDyJS6e11\nznULuwiRsGkPQ+QomdlKM/uH/72BmWbWxre3MLNP/G8WfGxmzXx7qpm9bmZz/aOfn1S8mT1pwW8/\nfGhmVf3wN1vwOydfm9n4kBZT5HsKDJHiVS1wSGpoRL/tzrnOBN+ifdC3PQyMc851AZ4HHvLtDwGT\nnXNdCe4FNd+3twUedc51BLYBF/v2O4Dufjo3xGrhRKKlb3qLFMPMdjnnahymfSVwmnNuub8B5Hrn\nXH0z20zwWwO5vn2dcy7FzDYBTZ1z+yOm0QKY6Jxr67t/AyQ65/5sZh8AuwhuBfKGc25XjBdVpEja\nwxA5Nq6Q50dif8TzfH44t3guwb2DegCzIu7SKhIKBYbIsRka8Xeaf/4Fwd1PAa4APvfPPwZuhO9/\nk7x2YRM1szgg3Tk3CfgNwe26/2cvR6Q06ROLSPGqmtmciO4PnHMHL62ta2ZfE+wlDPNtPyf4dbxf\nEfxS3rW+/RZgtJmNINiTuJHgTqWHEw8850PFgIecc9tKbIlEjoLOYYgcJX8OI8M5tznsWkRKgw5J\niYhIVLSHISIiUdEehoiIREWBISIiUVFgiIhIVBQYIiISFQWGiIhE5f8BnFnx8cib3QEAAAAASUVO\nRK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "[[-4.88833494]\n",
            " [ 0.04749026]\n",
            " [ 0.03769376]]\n",
            "0.7142857142857143\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kWYJ960NOFY3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def logistic_gradient_descent(X,Y,rate):\n",
        "  epochs = 100000\n",
        "  alphas = [rate]\n",
        "  for alpha in alphas:\n",
        "    theta = np.zeros((3,1))\n",
        "    x0 = X[:,0]*theta[0]\n",
        "    # x1 = X[:,1]*theta[1]\n",
        "    # x2 = X[:,2]*theta[2]\n",
        "    x1 = X[:,1]**2 * theta[1]\n",
        "    x2 = X[:,2]**2 * theta[2]\n",
        "    # x5 = np.dot(X[:,1],X[:,2]) * theta[5]\n",
        "    h = sigmoid(x0+x1+x2)\n",
        "    cost = np.random.random((epochs,1))\n",
        "    for i in range(epochs):\n",
        "      theta[0] = theta[0] - alpha*np.sum(h-Y)/X.shape[0]\n",
        "      # theta[1] = theta[1] - alpha/X.shape[0] * np.sum((h-Y)*X[:,1])\n",
        "      # theta[2] = theta[2] - alpha/X.shape[0] * np.sum((h-Y)*X[:,2])\n",
        "      theta[1] = theta[1] - alpha/X.shape[0] * np.sum((h-Y)*X[:,1]**2)\n",
        "      theta[2] = theta[2] - alpha/X.shape[0] * np.sum((h-Y)*X[:,2]**2)\n",
        "      # theta[5] = theta[5] - alpha/X.shape[0] * np.sum((h-Y)*np.dot(X[:,1],X[:,2]))\n",
        "      x0 = X[:,0]*theta[0]\n",
        "      # x1 = X[:,1]*theta[1]\n",
        "      # x2 = X[:,2]*theta[2]\n",
        "      x1 = X[:,1]**2 * theta[1]\n",
        "      x2 = X[:,2]**2 * theta[2]\n",
        "      # x5 = np.dot(X[:,1],X[:,2]) * theta[5]\n",
        "      h = sigmoid(x0+x1+x2)\n",
        "      cost[i] = logistic_cost(Y,h)\n",
        "      if(i>0 and cost[i]>cost[i-1]):\n",
        "        epochs = i\n",
        "        break\n",
        "      if(i%10000==0):\n",
        "        print(\"Epoch : \" , i , \" Cost : \" , cost[i])\n",
        "    plt.plot(np.arange(epochs),cost[:epochs])\n",
        "    plt.xlabel('Epochs')\n",
        "    plt.ylabel('Cost')\n",
        "    plt.title('Cost v/s Epoch for gradient descent')\n",
        "    plt.show()\n",
        "    if(alpha==rate):\n",
        "      return theta"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w28cRZTqOJL3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def perform_descent(df1,rate):\n",
        "  msk = random.sample(range(0,100),int(len(df1)*90/100))\n",
        "  vals = np.full((100,1),True)\n",
        "  for i in msk:\n",
        "    vals[i] = False\n",
        "  train_df1 = df1[~vals]\n",
        "  test_df1 = df1[vals]\n",
        "\n",
        "  X = np.zeros((len(train_df1['x1']),3))\n",
        "  X[:,0] = np.ones(len(train_df1['x1']))\n",
        "  X[:,1] = train_df1['x1']\n",
        "  X[:,2] = train_df1['x2']\n",
        "  Y = train_df1['y']\n",
        "  \n",
        "  theta = logistic_gradient_descent(X,Y,rate)\n",
        "  print(theta)\n",
        "  \n",
        "  X = np.zeros((len(test_df1['x1']),3))\n",
        "  X[:,0] = np.ones(len(test_df1['x1']))\n",
        "  X[:,1] = test_df1['x1']\n",
        "  X[:,2] = test_df1['x2']\n",
        "  Y = test_df1['y'].values\n",
        "\n",
        "  x0 = X[:,0]*theta[0]\n",
        "  # x1 = X[:,1]*theta[1]\n",
        "  # x2 = X[:,2]*theta[2]\n",
        "  x1 = X[:,1]**2 * theta[1]\n",
        "  x2 = X[:,2]**2 * theta[2]\n",
        "  # x5 = np.dot(X[:,1],X[:,2]) * theta[5]\n",
        "  h = sigmoid(x0+x1+x2)\n",
        "  count=0\n",
        "  for i in range(len(h)):\n",
        "    if(h[i]<0.5 and Y[i]==0):\n",
        "      count+=1\n",
        "    elif(h[i]>=0.5 and Y[i]==1):\n",
        "      count+=1\n",
        "  acc = count/len(h)\n",
        "  print(acc)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BFj6TkpXHplg",
        "colab_type": "code",
        "outputId": "ddf5c359-a76f-4c7f-fe8a-5e71c2c7c496",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 533
        }
      },
      "source": [
        "perform_descent(df2,0.01)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch :  0  Cost :  [0.69311472]\n",
            "Epoch :  10000  Cost :  [0.56474625]\n",
            "Epoch :  20000  Cost :  [0.53921248]\n",
            "Epoch :  30000  Cost :  [0.53196222]\n",
            "Epoch :  40000  Cost :  [0.52950603]\n",
            "Epoch :  50000  Cost :  [0.52859268]\n",
            "Epoch :  60000  Cost :  [0.52823452]\n",
            "Epoch :  70000  Cost :  [0.52808953]\n",
            "Epoch :  80000  Cost :  [0.52802967]\n",
            "Epoch :  90000  Cost :  [0.52800465]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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R+byd3yXxEGAzsz0ULJBERDNwOdllqYXAXRExX9J1ks5OxeYAjZIWAA+QjcZqBJA0jaxH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\nxYHEzMx65f8DbI5Fn51e9M8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "[[ 2.38858087]\n",
            " [-5.60051649]\n",
            " [-3.69842856]]\n",
            "0.9166666666666666\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}