AutoEncoders_for_dimesionality_reduction.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "AutoEncoders_for_dimesionality_reduction.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qo9Ky8dK7QSm",
        "colab_type": "text"
      },
      "source": [
        "#AutoEncoders\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fBxUUUdo6JM0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#we can use an auto encoder for DR(Dimensionality Reduction) by seperating the data into two parts\n",
        "#1.Encoder\n",
        "#2.Decoder"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TgLskje36gBO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Note: we have same no. of outputs as inputs"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fiBzIdTi6t0N",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        },
        "outputId": "4dfdc512-8e41-4522-ecfc-93dab504a78a"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "64MNLdco7ng6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#let's create our dataset to work on"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UyM5wNhl7sNy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.datasets import make_blobs"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gh83Q5o37wu0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = make_blobs(n_samples=300,\n",
        "                  n_features=2,\n",
        "                  centers=2,\n",
        "                  cluster_std=1.0,random_state=101)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uzHSr_Kf8G_q",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X,y = data"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LSbywUkJ8l_f",
        "colab_type": "text"
      },
      "source": [
        "\"\"**let's create some noise in our dataset**\"\""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iycYAsg_8LuW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "np.random.seed(101)\n",
        "z_noise = np.random.normal(size=len(X))\n",
        "z_noise = pd.Series(z_noise)"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pqo4XFpo8hzv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "feat = pd.DataFrame(X)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DDI5vgnl8zr8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "feat = pd.concat([feat,z_noise],axis=1)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SPUVBZmk81Gk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "feat.columns = ['X1','X2','X3']"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zNgO0Hz69HvV",
        "colab_type": "text"
      },
      "source": [
        "\"**Let's visualize the data**\""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fn_wLan09Dpo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "2dfb7db8-4a28-47bb-e797-338b99ef22b8"
      },
      "source": [
        "plt.scatter(feat[\"X1\"],feat[\"X2\"],c=y)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fbd3a10c940>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "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": "code",
      "metadata": {
        "id": "DC2sB1tC9SV3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#let's visualize with the noise that we added"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "05gZa42K9Zdx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from mpl_toolkits.mplot3d import Axes3D"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EdG0zyz09gTQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "20688408-a0b2-4815-acb7-4714d25a3188"
      },
      "source": [
        "%matplotlib inline\n",
        "fig = plt.figure()\n",
        "ax = fig.add_subplot(111,projection='3d')\n",
        "ax.scatter(feat[\"X1\"],feat[\"X2\"],feat[\"X3\"],c=y)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7fbd37301240>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        },
        {
          "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": "code",
      "metadata": {
        "id": "gVicNIGb9xFg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from tensorflow.keras.models import Sequential\n",
        "from tensorflow.keras.layers import Dense"
      ],
      "execution_count": 65,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dUqNepXGAV_a",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from tensorflow.keras.optimizers import SGD"
      ],
      "execution_count": 66,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sxqDayPHAfIw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#we create the mode such as\n",
        "# we have 3 dimension ---> we reduce it to 2 ------>then again reproduce 3"
      ],
      "execution_count": 67,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HJssITKVAxTI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "encoder = Sequential()\n",
        "encoder.add(Dense(units=2,activation='relu',input_shape=[3]))"
      ],
      "execution_count": 68,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T84cdUA0A8IW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "decoder = Sequential()\n",
        "decoder.add(Dense(units=3,activation='relu',input_shape=[2]))"
      ],
      "execution_count": 69,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "arVTx5UCBH6K",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "autoencoder = Sequential([encoder,decoder])"
      ],
      "execution_count": 70,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JnxcHgVYBQlu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "autoencoder.compile(loss='mse',optimizer=SGD(lr=.1))"
      ],
      "execution_count": 71,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JUS22GShBY3O",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.preprocessing import MinMaxScaler"
      ],
      "execution_count": 72,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3_9h51zZBcd7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "scaler = MinMaxScaler()\n",
        "scaled_data = scaler.fit_transform(feat)"
      ],
      "execution_count": 73,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n5X-5y-3BmJt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 375
        },
        "outputId": "840dd371-779e-455e-8ad1-8da8fac5587b"
      },
      "source": [
        "autoencoder.fit(scaled_data,scaled_data,epochs=10)"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/10\n",
            "10/10 [==============================] - 0s 1ms/step - loss: 0.2047\n",
            "Epoch 2/10\n",
            "10/10 [==============================] - 0s 1ms/step - loss: 0.1636\n",
            "Epoch 3/10\n",
            "10/10 [==============================] - 0s 1ms/step - loss: 0.1555\n",
            "Epoch 4/10\n",
            "10/10 [==============================] - 0s 1ms/step - loss: 0.1510\n",
            "Epoch 5/10\n",
            "10/10 [==============================] - 0s 1ms/step - loss: 0.1479\n",
            "Epoch 6/10\n",
            "10/10 [==============================] - 0s 1ms/step - loss: 0.1453\n",
            "Epoch 7/10\n",
            "10/10 [==============================] - 0s 1ms/step - loss: 0.1434\n",
            "Epoch 8/10\n",
            "10/10 [==============================] - 0s 1ms/step - loss: 0.1419\n",
            "Epoch 9/10\n",
            "10/10 [==============================] - 0s 1ms/step - loss: 0.1407\n",
            "Epoch 10/10\n",
            "10/10 [==============================] - 0s 1ms/step - loss: 0.1396\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tensorflow.python.keras.callbacks.History at 0x7fbd372635c0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_Yo0SCLHBt1p",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "encoded_2dim = encoder.predict(scaled_data)"
      ],
      "execution_count": 75,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r10nsV_YB4IK",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "c8ec1b2d-75b7-4231-cf14-0092a97072fb"
      },
      "source": [
        "encoded_2dim.shape"
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(300, 2)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 76
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QRe8uLzCCAEK",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "7ef1e2c6-803f-43d7-d7fe-711df9ce04b8"
      },
      "source": [
        "scaled_data.shape"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(300, 3)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zB8knIdNCOK_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "4444481a-3a9e-46fd-b318-503e8d95c6b2"
      },
      "source": [
        "plt.scatter(encoded_2dim[:,0],encoded_2dim[:,1],c=y)"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fbcedf69470>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 78
        },
        {
          "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": "code",
      "metadata": {
        "id": "-psynp2DCWMC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#we can see these are clearly seperable"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yL554bwuDmF9",
        "colab_type": "text"
      },
      "source": [
        "#Thanks"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J6zqgj-BDn5e",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}