RBF_VS_MLP.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "RBF VS MLP.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eQEE9TkImzIW"
      },
      "source": [
        "#MLP \"y = x ^ 2\n",
        "Training a MLP Neural Network for function approximation. Using this network and predict the F(x) = x^2 , then compare the output of the network with the results of the function F(x) and plot the comparison for the data in range of x ∈ [-3, 3]."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZENxlWgxgvg9"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import tensorflow as tf\n",
        "from tensorflow import keras\n",
        "from tensorflow.keras.models import Sequential\n",
        "from tensorflow.keras.layers import Dense , Activation\n",
        "from tensorflow.keras.layers import Dropout\n",
        "\n",
        "from keras.utils import np_utils, to_categorical\n",
        "\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "from sklearn.metrics import mean_squared_error"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dipWLobWZbaP"
      },
      "source": [
        "x = np.asarray([i for i in np.linspace(-3, 3, 100)])\n",
        "y = np.asarray([i**2.0 for i in x])\n",
        "\n",
        "x = x.reshape((len(x), 1))\n",
        "y = y.reshape((len(y), 1))\n",
        "\n",
        "scale_x = MinMaxScaler()\n",
        "x = scale_x.fit_transform(x)\n",
        "\n",
        "scale_y = MinMaxScaler()\n",
        "y = scale_y.fit_transform(y)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V8nG9Vkqgyp8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "0ff4ff11-b6f9-40d5-d176-3d338602a476"
      },
      "source": [
        "model = Sequential()\n",
        "model.add(Dense(16, input_dim=1, activation='relu'))\n",
        "model.add(Dense(16, activation='relu'))\n",
        "model.add(Dense(1))\n",
        "model.compile(loss='mse', optimizer='adam')\n",
        "model.fit(x, y, epochs=500, batch_size=10, verbose=0)\n",
        "\n",
        "yresult = model.predict(x)\n",
        "\n",
        "x_plot = scale_x.inverse_transform(x)\n",
        "y_plot = scale_y.inverse_transform(y)\n",
        "y_result_plot = scale_y.inverse_transform(yresult)\n",
        "\n",
        "plt.plot(x_plot,y_plot, label='Actual')\n",
        "\n",
        "plt.plot(x_plot,y_result_plot, label='Predicted')\n",
        "plt.legend()\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "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": "26fG6IUipmoN"
      },
      "source": [
        "#RBF \"y = x^2\"\n",
        "Training an RBF(Radial Basis Function) Neural Network for function approximation. Using this network and predict the F(x) = x^2 , then compare the output of the network with the results of the function F(x) and plot the comparison for the data in range of x ∈ [-3, 3]."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YWGVcOm6C4Mf"
      },
      "source": [
        "import numpy as np\n",
        "import random\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HwrJdWtjpp1_"
      },
      "source": [
        "class RBF :\n",
        "     def __init__(self, input_dim, output_dim, centers_number , beta = 0.5):\n",
        "        self.input_dim = input_dim\n",
        "        self.hidden_dim = output_dim\n",
        "        self.centers_number = centers_number\n",
        "        self.center  = [random.uniform(-3, 3) for i in range(self.centers_number)]\n",
        "        self.weight = []\n",
        "        self.beta = beta\n",
        "\n",
        "     def activation_function(self, center, data):\n",
        "         return np.exp(-self.beta * np.linalg.norm(center-data)**2)\n",
        "     \n",
        "     def calculate_matrix (self, x):\n",
        "         matrix = np.zeros((len(x), self.centers_number))\n",
        "         for index_data, data in enumerate(x) :\n",
        "             for index_center, center in enumerate(self.center) :\n",
        "                 matrix[index_data, index_center] = self.activation_function(center, data)\n",
        "         return matrix        \n",
        "\n",
        "     def train(self, x, y):\n",
        "         phi = self.calculate_matrix(x)\n",
        "         self.weight = np.dot(np.linalg.pinv(phi), y)\n",
        "         \n",
        "     def validation(self, x):\n",
        "         matrix = self.calculate_matrix(x)\n",
        "         prediction = np.dot(matrix, self.weight)\n",
        "         return prediction\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Eq5kXFQ49KoN",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "3954d7ba-242e-4b4f-d159-87f433c94510"
      },
      "source": [
        "x_train = np.linspace(-3, 3, 50)\n",
        "y_train = np.power(x_train, 2)\n",
        "\n",
        "rbf = RBF(1, 1, 10)\n",
        "rbf.train(x_train, y_train)\n",
        "predict = rbf.train(x_train, y_train)\n",
        "\n",
        "plt.plot(x_train, y_train, label='Actual')\n",
        "\n",
        "plt.plot(x_train,predict, label='Predicted')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "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"
          }
        }
      ]
    }
  ]
}