3 - Fully Connected Neural network.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation of Fully connected Neural Network\n",
    "A. Implementation of Error Back propagation algorithm for fully connected neural network to solve two input XOR classification problem.  <br/>\n",
    "B. Implementation of Error Back propagation algorithm for fully connected neural network to solve three input XNOR classification problem. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Importing the libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating the base layer\n",
    "class Layer:\n",
    "    def __init__(self):\n",
    "        self.input = None\n",
    "        self.output = None\n",
    "\n",
    "    def forward(self, input):\n",
    "        pass\n",
    "    def backward(self, output_gradient, learning_rate):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating the Dense layer\n",
    "class Layer_Dense(Layer):\n",
    "    def __init__(self, input_size, output_size):\n",
    "        self.weights = np.random.randn(output_size,input_size)\n",
    "        self.biases = np.random.randn(output_size,1)\n",
    "\n",
    "    def forward(self, input):\n",
    "        self.input = input\n",
    "        return np.dot(self.weights, self.input ) + self.biases\n",
    "\n",
    "    def backward(self, output_gradient, learning_rate):\n",
    "        weights_gradient = np.dot(output_gradient,self.input.T )\n",
    "        input_gradient = np.dot(self.weights.T, output_gradient)\n",
    "        self.weights -= learning_rate * weights_gradient\n",
    "        self.biases -=learning_rate * output_gradient\n",
    "        return input_gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating the activation layer\n",
    "class Activation(Layer):\n",
    "    def __init__(self, activation, activation_prime):\n",
    "        self.activation = activation\n",
    "        self.activation_prime = activation_prime\n",
    "\n",
    "    def forward(self, input):\n",
    "        self.input = input\n",
    "        return self.activation(self.input)\n",
    "\n",
    "    def backward(self, output_gradient, learning_rate):\n",
    "        return np.multiply(output_gradient, self.activation_prime(self.input))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating the activation functions\n",
    "# Tanh function\n",
    "class Tanh(Activation):\n",
    "    def __init__(self):\n",
    "        def tanh(x):\n",
    "            return np.tanh(x)\n",
    "        def tanh_prime(x):\n",
    "            return 1 - np.tanh(x)**2\n",
    "        super().__init__(tanh, tanh_prime)\n",
    "\n",
    "class Linear(Activation):\n",
    "    def __init__(self):\n",
    "        def linear(x):\n",
    "            return x\n",
    "        \n",
    "        def linear_prime(x):\n",
    "            return 1\n",
    "        \n",
    "        super().__init__(linear, linear_prime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating the loss function\n",
    "def mse(y_true, y_pred):\n",
    "    return np.mean(np.power(y_true - y_pred, 2))\n",
    "\n",
    "# creating the loss function derivative\n",
    "def mse_prime(y_true, y_pred):\n",
    "    return 2 * (y_pred - y_true) / np.size(y_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 Error 6.218354908263778\n",
      "Epoch 1000 Error 0.002364625407872958\n",
      "Epoch 2000 Error 0.00100194048260467\n",
      "Epoch 3000 Error 0.0006328332711532491\n",
      "Epoch 4000 Error 0.00046169478658533193\n",
      "Epoch 5000 Error 0.00036310486360948985\n",
      "Epoch 6000 Error 0.00029905816624631895\n",
      "Epoch 7000 Error 0.00025413175843269956\n",
      "Epoch 8000 Error 0.00022088809491722174\n",
      "Epoch 9000 Error 0.0001953013979187904\n",
      "------------------------------------------------------\n",
      "Final error:  4.3755428853937046e-05\n"
     ]
    }
   ],
   "source": [
    "# creating the neural network\n",
    "X = np.reshape(([-1,-1],[-1,1],[1,-1],[1,1]),(4,2,1))\n",
    "Y = np.reshape(([-1],[1],[1],[-1]),(4,1,1))\n",
    "\n",
    "network = [\n",
    "    Layer_Dense(2, 3),\n",
    "    Tanh(),\n",
    "    Layer_Dense(3, 1),\n",
    "    Tanh()\n",
    "]\n",
    "epochs = 10000\n",
    "learning_rate = 0.1\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    error = 0\n",
    "    for x, y in zip(X, Y):\n",
    "        # Forward pass\n",
    "        output = x\n",
    "        for layer in network:\n",
    "            output = layer.forward(output)\n",
    "\n",
    "        error += mse(y, output)\n",
    "        # Backward pass\n",
    "        output_gradient = mse_prime(y, output)\n",
    "        for layer in reversed(network):\n",
    "            output_gradient = layer.backward(output_gradient, learning_rate)\n",
    "\n",
    "    if epoch % 1000 == 0:\n",
    "        print(\"Epoch\",epoch,\"Error\",error)\n",
    "    \n",
    "error/= len (X)\n",
    "print (\"------------------------------------------------------\")\n",
    "print(\"Final error: \",error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input\t Actual Output\t Predicted Output\n",
      "_____________________________________________\n",
      "[[-1]\n",
      " [-1]] \t     [-1] \t -0.9946931880901012\n",
      "----------------------------------------------------\n",
      "[[-1]\n",
      " [ 1]] \t     [1] \t 0.992842850074133\n",
      "----------------------------------------------------\n",
      "[[ 1]\n",
      " [-1]] \t     [1] \t 0.9917447809668798\n",
      "----------------------------------------------------\n",
      "[[1]\n",
      " [1]] \t     [-1] \t -0.9947609911473744\n",
      "----------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "# testing the neural network\n",
    "\n",
    "input_arr = np.reshape(([-1,-1],[-1,1],[1,-1],[1,1]),(4,2,1))\n",
    "output_arr = np.array(([-1],[1],[1],[-1]))\n",
    "predicted_arr = np.array([])\n",
    "for x, y in zip(input_arr, output_arr):\n",
    "    output = x\n",
    "    for layer in network:\n",
    "        output = layer.forward(output)\n",
    "    predicted_arr = np.append(predicted_arr,output)\n",
    "\n",
    "print (\"Input\\t Actual Output\\t Predicted Output\")\n",
    "print (\"_____________________________________________\")\n",
    "for i in range (len (input_arr)):\n",
    "    print (input_arr[i],\"\\t    \",output_arr[i],\"\\t\",predicted_arr[i])\n",
    "    print (\"----------------------------------------------------\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotted the predicted output and actual output\n",
    "\n",
    "x = np.arange(0,4,1)\n",
    "plt.scatter(x, predicted_arr, linewidths = 2,marker =\"s\",edgecolor =\"green\",s = 50)\n",
    "plt.scatter(x, output_arr, linewidths = 1,marker =\"^\",edgecolor =\"red\",s = 100)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Predicted and Actual Output\")\n",
    "plt.legend([\"Predicted Output\", \"Actual Output\"])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "x = np.arange(0,4,1)\n",
    "z = np.arange(0,4,1)\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.scatter(x,predicted_arr,z, c='r', marker='s')\n",
    "ax.scatter(x,output_arr,z, c='b', marker='o')\n",
    "ax.set_xlabel('X Label')\n",
    "ax.set_ylabel('Y Label')\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3B -  Implement Error Back propagation algorithm for fully connected neural network to solve three input XNOR classification problem. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 Error 19.867590625290017\n",
      "Epoch 1000 Error 0.005709402253928425\n",
      "Epoch 2000 Error 0.005709402253928425\n",
      "Epoch 3000 Error 0.005709402253928425\n",
      "Epoch 4000 Error 0.005709402253928425\n",
      "Epoch 5000 Error 0.005709402253928425\n",
      "Epoch 6000 Error 0.005709402253928425\n",
      "Epoch 7000 Error 0.005709402253928425\n",
      "Epoch 8000 Error 0.005709402253928425\n",
      "Epoch 9000 Error 0.005709402253928425\n",
      "-------------------------------------------\n",
      "Final error:  0.0008156288934183465\n"
     ]
    }
   ],
   "source": [
    "# creating the neural network\n",
    "\n",
    "X = np.array([[0.1],[0.2],[0.3],[0.4],[0.5],[0.6],[0.7]])\n",
    "Y = np.array([[1.2],[1.4],[1.55],[1.75],[2.01],[2.2],[2.35]])\n",
    "\n",
    "network = [\n",
    "    Layer_Dense(1, 1),\n",
    "    Linear()\n",
    "]\n",
    "\n",
    "epochs = 10000\n",
    "learning_rate = 0.1\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    error = 0\n",
    "    for x, y in zip(X, Y):\n",
    "        # Forward pass\n",
    "        output = x\n",
    "        for layer in network:\n",
    "            output = layer.forward(output)\n",
    "\n",
    "        error += mse(y, output)\n",
    "        # Backward pass\n",
    "        output_gradient = mse_prime(y, output)\n",
    "        for layer in reversed(network):\n",
    "            output_gradient = layer.backward(output_gradient, learning_rate)\n",
    "\n",
    "    if epoch % 1000 == 0:\n",
    "        print(\"Epoch\",epoch,\"Error\",error)\n",
    "\n",
    "    \n",
    "error/= len (X)\n",
    "print (\"-------------------------------------------\")\n",
    "print(\"Final error: \",error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input: [0.1] Output: [[1.19031205]] Actual: [1.2]\n",
      "Input: [0.2] Output: [[1.386833]] Actual: [1.4]\n",
      "Input: [0.3] Output: [[1.58335395]] Actual: [1.55]\n",
      "Input: [0.4] Output: [[1.7798749]] Actual: [1.75]\n",
      "Input: [0.5] Output: [[1.97639585]] Actual: [2.01]\n",
      "Input: [0.6] Output: [[2.1729168]] Actual: [2.2]\n",
      "Input: [0.7] Output: [[2.36943775]] Actual: [2.35]\n",
      "-------------------------------------------\n",
      "Predicted: [1.19031205 1.386833   1.58335395 1.7798749  1.97639585 2.1729168\n",
      " 2.36943775]\n"
     ]
    }
   ],
   "source": [
    "# testing the neural network\n",
    "\n",
    "input_arr = np.array([[0.1],[0.2],[0.3],[0.4],[0.5],[0.6],[0.7]])\n",
    "output_arr = np.array([[1.2],[1.4],[1.55],[1.75],[2.01],[2.2],[2.35]])\n",
    "predicted_arr = np.array([])\n",
    "\n",
    "for x, y in zip(input_arr, output_arr):\n",
    "    output = x\n",
    "    for layer in network:\n",
    "        output = layer.forward(output)\n",
    "    predicted_arr = np.append(predicted_arr,output)\n",
    "    print(\"Input:\",x,\"Output:\",output,\"Actual:\",y)\n",
    "print (\"-------------------------------------------\")\n",
    "print (\"Predicted:\",predicted_arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(input_arr, output_arr, color='green' )  # Actual data\n",
    "plt.plot(input_arr, predicted_arr, color='red', linewidth=2, label='Predicted')  # Predicted data\n",
    "plt.xlabel('Input')\n",
    "plt.ylabel('Output')\n",
    "plt.title('Actual vs Predicted')\n",
    "plt.legend(\"\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.1"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "a9cff5a362bc38ef45d817ae74b1af54d6a076e3d773891282bce078b815ba34"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}