EM_MNIST.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "EM_MNIST.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YGNdbYLAOIM0",
        "colab_type": "text"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SoJcrSPZQQFd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import random\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import multivariate_normal\n",
        "import scipy.io\n",
        "\n",
        "%matplotlib inline"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IQCpTx_RSkmR",
        "colab_type": "text"
      },
      "source": [
        "**Load Data**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vNJLaYdMSnYP",
        "colab_type": "code",
        "outputId": "d1f337b6-5f71-459e-cb7c-59abe5c2468f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "data = scipy.io.loadmat('/content/sample_data/mnist_small.mat')\n",
        "X = data['X']\n",
        "Y = data['Y']\n",
        "\n",
        "Y.shape"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-0vHMZVcSoCm",
        "colab_type": "text"
      },
      "source": [
        "**Expectation step**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wVISxOF9k-hs",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def Expectation(mu, pk, var2, X):\n",
        "  [N, D] = X.shape\n",
        "  K=10\n",
        "  for n in range(N):\n",
        "    for k in range(K):\n",
        "      #compute the log of numerator of posterior\n",
        "      z[n][k] = np.log(pk[k]) - (np.linalg.norm(X[n] - mu[k])**2/(2*var2))\n",
        "\n",
        "    maxZ = np.max(z[n])\n",
        "    z[n] = np.exp(z[n] - maxZ - np.log(np.sum(np.exp(z[n] - maxZ)))) \n",
        "\n",
        "  return z     "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UyXPTN-5_lqY",
        "colab_type": "text"
      },
      "source": [
        "**Maximization step**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e0n_yWwn_xNZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def Maximisation(mu, pk, var2, X, z):\n",
        " [N, D] = X.shape\n",
        " K=10 \n",
        " nk = np.sum(z, axis=0)\n",
        " # re-estimate pk\n",
        " pk = nk/N\n",
        "        \n",
        " # re-estimate the variance\n",
        " mu = z.T@X \n",
        " mu = np.array([mu[k]/nk[k] for k in range(K)])\n",
        "\n",
        " # re-estimate the variance\n",
        " var2 = np.sum(z@np.square(X - mu))/(N*D)\n",
        "\n",
        " return mu, pk, z, var2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cUf2iBHBF_BR",
        "colab_type": "text"
      },
      "source": [
        "**Implementation**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H1hG6jhZGCrR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "7c4f75ee-f1b6-4cf4-a2b3-3b87511b5213"
      },
      "source": [
        "    [N, D] = X.shape\n",
        "    K = 10\n",
        "    numIter = 200 \n",
        "    \n",
        "    var2 = 1 \n",
        "    \n",
        "    pk = np.ones(K) / K \n",
        "    \n",
        "    mu = np.random.rand(K, D) \n",
        "    z = np.zeros((N, K))\n",
        "\n",
        "    for iteration in range(numIter):\n",
        "      z = Expectation(mu, pk, var2, X)\n",
        "      mu, pk, z, var2 = Maximisation(mu, pk, var2, X, z)\n",
        "      \n",
        "    nk = np.sum(z, axis=0)\n",
        "\n",
        "    for i in range(K):\n",
        "        plt.imshow(mu[i].reshape((28, 28)), cmap='gray')\n",
        "        print(nk[i])\n",
        "        plt.show()\n"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "761.4063451512259\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "761.9967532850932\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Z7Tezg2b2bBNjKGNmh81sj5ntbnp9umINvQkz2ztt2xIze8PMPiq+z7jGXkNje97Mxorn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\nOxAEYQeC+D8EgOOEfw07TwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "709.6665943653521\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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x6NUTd1d9W9KWpoME0J6pPBt/n6T/kfS2pKv72P5Q0iOS1mr8bvweSd+rnsyLvhdndqBl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\nYQcK8f+SXXatB3ZgpQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "889.6191621402455\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "1488.0964964359766\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Xr8bG03igEIQdKES/wz7c58ePNHVsTR2XxNja1ZOx9fU1O4De6feZHUCPEHagEH0Ju5k9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\nAVEp6MReiCDYAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "790.8609586216633\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "1219.6243993631056\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "1456.591517810134\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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36j6T4oxtRVmhrW+q+cqTm+3p1GvTderYOnVcEmNrVLvGxst4IAjCDgRRd9i31vz8KZ06\ntk4dl8TYGtWWsdX6NzuA9qn7yA6gTQg7EEQtYTezZ83sL2Y2YGYv1zGGMmZ21MwOmNm+utenK9bQ\nO2NmB8fd1mVmO8ysv/g84Rp7NY3tVTM7Uey7fWb2XE1j6zWzP5vZR2bWZ2Y/LG6vdd8lxtWW/db2\nv9nNbLqkQ5K+JWlQ0vuSNrn7R20dSAkzOyppvbvX/gYMM/s7SZcl/drdHy1u+zdJ5939teI/ykXu\n/i8dMrZXJV2uexnvYrWiJeOXGZf0vKR/VI37LjGuF9SG/VbHkX2DpAF3P+LuNyT9VtLGGsbR8dz9\nHUnn77h5o6RtxdfbNPbL0nYlY+sI7j7k7nuLr4cl3V5mvNZ9lxhXW9QR9h5Jx8d9P6jOWu/dJf3J\nzD4wsy11D2YC3eOW2TolqbvOwUwgu4x3O92xzHjH7LtGlj+vihN0X/W0u/+1pH+Q9IPi5WpH8rG/\nwTqpdzqpZbzbZYJlxr9Q575rdPnzquoI+wlJveO+X1bc1hHc/UTx+Yykt9R5S1Gfvr2CbvH5TM3j\n+UInLeM90TLj6oB9V+fy53WE/X1Ja8xslZnNkvRdSdtrGMdXmNn84sSJzGy+pG+r85ai3i5pc/H1\nZklv1ziWL+mUZbzLlhlXzfuu9uXP3b3tH5Ke09gZ+cOS/rWOMZSM668kfVh89NU9Nklvauxl3YjG\nzm28KOl+STsl9Uv6X0ldHTS2/9TY0t77NRasJTWN7WmNvUTfL2lf8fFc3fsuMa627DfeLgsEwQk6\nIAjCDgRB2IEgCDsQBGEHgiDsQBCEHQji/wFRzcEi6kFEUAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "997.9455312346121\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "924.1922415925895\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5af9lEXbcLJqeCGND/1JfkbR7eNCLN+5u+LaknVUHCaB9Gnk3/lFJ/yPpQ0k35iu+KGm1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\nRK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pG72QimDeSXZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        },
        "outputId": "d8dc1625-deb7-47a8-a822-735dc078bd66"
      },
      "source": [
        ""
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1684.64030286,  791.87698289, 1615.20638342,  444.05764931,\n",
              "        434.46535668, 1256.71136136, 1237.84064945,  862.82704985,\n",
              "       1309.34040893,  363.03385523])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    }
  ]
}