Assignment_5_ML_SVM_linear_kernelized.ipynb

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  "metadata": {
    "colab": {
      "name": "Assignment_5_ML_SVM_linear_kernelized.ipynb",
      "provenance": [],
      "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/sp1999/SHALA2020/blob/master/Assignment_5_ML_SVM_linear_kernelized.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "arLDVfoh4rOg",
        "colab_type": "text"
      },
      "source": [
        "#**SVM**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MEEp0sf04pIP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "from numpy import linalg as LA"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vJ2o5DL4478w",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "**Generating Random linearly separable data**\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UbaJAhdL5BLA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = [[np.random.rand(), np.random.rand()] for i in range(10)]\n",
        "\n",
        "for i, point in enumerate(data):\n",
        "  x, y = point\n",
        "  if 0.5*x - y + 0.25 > 0:\n",
        "    data[i].append(-1)\n",
        "  else:\n",
        "    data[i].append(1)\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S3afrVhJ5FSS",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "**Visualizing the above data**\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6x0FkJik5LPi",
        "colab_type": "code",
        "outputId": "fad4d4d6-3aca-4e3e-8835-8023d9efa726",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "for x, y, l in data:\n",
        "  if l == 1: \n",
        "    clr = 'red'\n",
        "  else: \n",
        "    clr = 'blue'\n",
        "  plt.scatter(x, y, c=clr)\n",
        "  plt.xlim(0,1)\n",
        "  plt.ylim(0,1)"
      ],
      "execution_count": 381,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yXabL9FB5Qe1",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "**Train a SVM classifier using gradient descent and return a Weight Matrix which is a numpy array of length (N + 1) where N is dimension of training samples. You can refer to Fig. 1 in [this](https://www.cs.huji.ac.il/~shais/papers/ShalevSiSrCo10.pdf) paper for implementation. You can add arguments to svm_function according to your implementation.**\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LpSHX3lT5VDt",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def svm_function(x, y, epoch, l_rate):\n",
        "    ###################################\n",
        "    ######## write your code here #####\n",
        "    ###################################\n",
        "    w=np.zeros(len(x[0])+1)\n",
        "    x=np.insert(x,2,1,axis=1)\n",
        "    for t in range(1,epoch+1):\n",
        "      i=np.random.randint(0,len(x),1)\n",
        "      if ((y[i[0]])*(x[i[0]]@w)<1):\n",
        "        w=((1-(1/t))*w)+((l_rate)*(y[i[0]]))*(x[i[0]])\n",
        "      else:\n",
        "        w=(1-(1/t))*w\n",
        "    return w"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-GMSHqOB5Y7n",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "**Run SVM Classifier**\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MY2AcFkZ5d2a",
        "colab_type": "code",
        "outputId": "21e8f290-7b97-4e75-fed1-1046e6ccd4ac",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "data = np.asarray(data)\n",
        "X = data[:,:2]\n",
        "Y = data[:,2]\n",
        "w = svm_function(X, Y, 10000, 0.01)\n",
        "print(w)"
      ],
      "execution_count": 383,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[-0.06544226  4.36605696 -1.845562  ]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4t6lPISE5h4e",
        "colab_type": "text"
      },
      "source": [
        "# **Visualize the classifier**\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "Write a code to draw a lines corrosponding to 'w' vector you got as output from svm_function and for a line from which actual data was generated (0.5*x - y + 0.25). \n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wrCLTSVx5mBF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "b5fa18c1-e902-4f34-908a-d3c002b1e2b6"
      },
      "source": [
        "###################################\n",
        "###### write your code here########\n",
        "###################################\n",
        "x = np.linspace(-5,5,100)\n",
        "y1 = (((-w[0])*(x))-w[2])/w[1]\n",
        "y2 = 0.5*x+0.25\n",
        "plt.plot(x, y1, '-g', label='y1=w*x+w0')\n",
        "plt.plot(x, y2, '-y', label='y2=0.5*x+0.25')\n",
        "for x, y, l in data:\n",
        "  if l == 1: \n",
        "    clr = 'red'\n",
        "  else: \n",
        "    clr = 'blue'\n",
        "  plt.scatter(x, y, c=clr)\n",
        "  plt.xlim(0,1)\n",
        "  plt.ylim(0,1)\n",
        "plt.title('Visualizing the Classifier')\n",
        "plt.xlabel('x', color='#1C2833')\n",
        "plt.ylabel('y', color='#1C2833')\n",
        "plt.legend(loc='lower right',prop={'size':8})\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 384,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zSQ2B6IK7pRq",
        "colab_type": "text"
      },
      "source": [
        "#**Linearly Non-separable Data**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kZ5Mt_3Z73WS",
        "colab_type": "code",
        "outputId": "2d7ccd59-f874-4e84-c0e9-2770bf10b028",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        }
      },
      "source": [
        "from sklearn.datasets import make_circles\n",
        "from matplotlib import pyplot\n",
        "from pandas import DataFrame\n",
        "\n",
        "# generate 2d classification dataset\n",
        "X, y = make_circles(n_samples=100, noise=0.05)\n",
        "# scatter plot, dots colored by class value\n",
        "df = DataFrame(dict(x=X[:,0], y=X[:,1], label=y))\n",
        "colors = {0:'red', 1:'blue'}\n",
        "fig, ax = pyplot.subplots()\n",
        "grouped = df.groupby('label')\n",
        "for key, group in grouped:\n",
        "    group.plot(ax=ax, kind='scatter', x='x', y='y', label=key, color=colors[key])\n",
        "pyplot.show()\n"
      ],
      "execution_count": 385,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SDtuOIuy6xPL",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "**Train a SVM classifier on the linearly non-separable data by appropriate features crafted from input data For linearly non-separable data, you need to transform the data in a space where it can be linearly seprable.\n",
        "These features can be exponential, polynomial, trignometric or any other function of actual input features.\n",
        "For example, if your input data is (x1, x2) you can have hand-crafted features as (sin(x1), cos(x1), cos(x2), x1-x2).\n",
        "Here you need to think of which hand-crafted features can be best suited for data given to you.\n",
        "Write a function to convert input features to hand-crafted features. Use these features to train a SVM using svm_function.\n",
        "Note that, if you choose to have L hand-crafted features, SVM will return L+1 dimensional 'w'.**\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rZF4nHvz6-2I",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#####################################\n",
        "######## write your code here########\n",
        "#####################################\n",
        "phi1 = np.exp(-(X[:,0])*(X[:,0]))\n",
        "phi2 = np.exp(-(X[:,1])*(X[:,1]))\n",
        "\n",
        "x = np.transpose(np.array([phi1,phi2]))\n",
        "w = svm_function(x, y, 10000, 1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k9RC8lVS81F8",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "**Visualize the data points in the new feature space \"if possible\" to see whether they got separated or not.**\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T_M3rNKF7g-W",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "861b1173-6e9f-479c-e98b-4f347b3a56df"
      },
      "source": [
        "#####################################\n",
        "####### write your code here ########\n",
        "#####################################\n",
        "x = np.linspace(-5,5,100)\n",
        "y1 = (((-w[0])*(x))-w[2])/w[1]\n",
        "for i in range(len(X)):\n",
        "  if y[i] == 1: \n",
        "    clr = 'red'\n",
        "  else: \n",
        "    clr = 'blue' \n",
        "  plt.scatter(phi1[i], phi2[i], c=clr)\n",
        "  plt.xlim(0.2,1.2)\n",
        "  plt.ylim(0.2,1.2)\n",
        "plt.title('Visualizing the Non-linear data')\n",
        "plt.xlabel('x1', color='#1C2833')\n",
        "plt.ylabel('x2', color='#1C2833')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 387,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}