Introduction_To_RNN.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Introduction To RNN.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNY4HCBpmBU7dqD7v8orF1S",
      "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/Sanket758/Machine-Learning-Projects/blob/master/Introduction_To_RNN.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CgQVFYj5Ao8G"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-MuzXGvJA80G"
      },
      "source": [
        "np.random.seed(0)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "faVeTZmLA_Ym",
        "outputId": "821d6049-0981-4d4a-92f7-8b4ce011f052",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "t = np.arange(0, 1500)\n",
        "actual_x = np.sin(0.02*t)\n",
        "plt.plot(x)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fec6302e240>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        },
        {
          "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": "8Wzarb85BGTA"
      },
      "source": [
        "# Adding noise\n",
        "x_with_noise = x+ np.random.uniform(low=-1, high=1, size=(1500,))"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IXew_t8mBIUO",
        "outputId": "ee11fad7-1ba6-47de-8df1-6ac9a5e26e3c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "plt.plot(x_with_noise)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fec62f0d3c8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        },
        {
          "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": "IOxNjLbnBlsF",
        "outputId": "1fb9f1fe-26ac-47a7-ddcd-f60d1187d90a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "# Plotting both of the data together\n",
        "plt.plot(x_with_noise)\n",
        "plt.plot(actual_x);"
      ],
      "execution_count": 17,
      "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": "code",
      "metadata": {
        "id": "Yp5dheIeCKjF",
        "outputId": "e904d0f4-a2f1-472c-966e-2cbe554cdf88",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        }
      },
      "source": [
        "from sklearn.preprocessing import MinMaxScaler\n",
        "normalizer = MinMaxScaler(feature_range=(0,1))\n",
        "x = (np.reshape(x_with_noise, (-1,1)))\n",
        "x = normalizer.fit_transform(x)\n",
        "print(x)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.51676004]\n",
            " [0.71941794]\n",
            " [0.46273982]\n",
            " ...\n",
            " [0.13850349]\n",
            " [0.28912443]\n",
            " [0.3143337 ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aJ8xsrYBDpey",
        "outputId": "f879165c-126d-4c45-e894-2d88d80ef0e7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "# Creating a dataset\n",
        "training = x[:1200]\n",
        "testing = x[1200:]\n",
        "print(training.shape, testing.shape)"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(1200, 1) (300, 1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YVjZt0ILEJRV"
      },
      "source": [
        "def createDataset(data, step):\n",
        "    X, y = [], []\n",
        "    for i in range(len(data)-step):\n",
        "        X.append(data[i:i+step])\n",
        "        y.append(data[i+step])\n",
        "    return np.array(X), np.array(y)"
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QqsLe7iaEpIb",
        "outputId": "d2f12d69-c538-4504-b930-25579b91b927",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "step = 10\n",
        "X_train, y_train = createDataset(training, step)\n",
        "X_test, y_test = createDataset(testing, step)\n",
        "print(X_train.shape, y_train.shape)\n",
        "print()\n",
        "print(X_test.shape, y_test.shape)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(1190, 10, 1) (1190, 1)\n",
            "\n",
            "(290, 10, 1) (290, 1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6OVPfXZyE7Mj",
        "outputId": "4c8f21fc-1d0b-47cc-fd8c-d41ba88b6e0a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        }
      },
      "source": [
        "X_train[0]"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.51676004],\n",
              "       [0.71941794],\n",
              "       [0.46273982],\n",
              "       [0.54294433],\n",
              "       [0.65898666],\n",
              "       [0.64818247],\n",
              "       [0.62403718],\n",
              "       [0.70166196],\n",
              "       [0.8845315 ],\n",
              "       [0.54037182]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JjPYB-oDE-4y",
        "outputId": "5775cb57-7637-411b-8dbf-65976372a1d9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "y_train[0]"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.49564324])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YMmb2o43FCG4",
        "outputId": "7b532828-f88c-41d7-bbc7-4204c4cd2c05",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "from tensorflow.keras.models import Sequential\n",
        "from tensorflow.keras.layers import Dense, SimpleRNN\n",
        "\n",
        "model = Sequential()\n",
        "model.add(SimpleRNN(units=1, activation='tanh'))\n",
        "model.add(Dense(1))\n",
        "\n",
        "model.compile(loss='mean_squared_error', optimizer='rmsprop')\n",
        "\n",
        "history = model.fit(X_train, y_train, epochs=200, batch_size=16, verbose=2)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/200\n",
            "75/75 - 0s - loss: 0.0344\n",
            "Epoch 2/200\n",
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          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zkuzEst6ICus",
        "outputId": "8cb06ef0-0fa5-4263-d309-065c08a56794",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "loss = history.history['loss']\n",
        "plt.plot(loss)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fec18124f28>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        },
        {
          "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": "YOPnkd9uIK8k"
      },
      "source": [
        "trainPredict = normalizer.inverse_transform(model.predict(X_train))\n",
        "testPredict = normalizer.inverse_transform(model.predict(X_test))\n",
        "predicted = np.concatenate((trainPredict, testPredict))"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_Ad24mwYIyMT",
        "outputId": "e2abd00d-b2b3-4b51-8b57-5b7de97d1536",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "x = normalizer.inverse_transform(x)\n",
        "plt.plot(x)\n",
        "plt.plot(predicted)"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fec1807f128>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        },
        {
          "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": "xkm3tV1MKHeO",
        "outputId": "1ae04b5d-63d7-4c78-cc32-3f215d4ce665",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "plt.plot(predicted);"
      ],
      "execution_count": 33,
      "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": "code",
      "metadata": {
        "id": "TIew0CoAKPjg",
        "outputId": "c449b867-f27b-4823-eaf5-85dee4f960b1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "plt.plot(actual_x)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fec17642940>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        },
        {
          "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"
          }
        }
      ]
    }
  ]
}