Vectorized_NN_generic.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Vectorized_NN_generic.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [
        "5DnWvw5JP2YT"
      ],
      "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/AmulyaReddy99/DNN/blob/master/Vectorized_NN_generic.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PQNpWC1Fz9di",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
        "from sklearn.metrics import accuracy_score, mean_squared_error, log_loss\n",
        "import matplotlib.colors\n",
        "from tqdm import tqdm_notebook\n",
        "import seaborn as sns\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "juqpVMk80d7y",
        "colab_type": "text"
      },
      "source": [
        "## 1. Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A7yDnqKq0M7C",
        "colab_type": "code",
        "outputId": "7209ad46-8b59-44f1-84a4-1c39d606366e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "source": [
        "# Create data\n",
        "from sklearn.datasets import make_blobs\n",
        "\n",
        "data, labels = make_blobs(n_samples=1000, centers=4, n_features=2, random_state=0)\n",
        "labels_orig = labels\n",
        "labels = np.mod(labels_orig, 4)\n",
        "\n",
        "my_cmap = matplotlib.colors.LinearSegmentedColormap.from_list(\"\", [\"red\",\"green\"])\n",
        "plt.scatter(data[:,0], data[:,1], c=labels)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ZzRCZBLGfwfwbCCaEwMIQ+kb73xvDyCUzWdx0OBJl7FJRrr0xCoeRdkPULEbKHyPVkArE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eFLNIOMJaEJpj1ZyIUWhLP0r0eRKO4T4xHUwdUF+sqcFVVunjo7qINL5mDLwVReuHU8mXmFTH3m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\nOjo6OhcZemDX0dHRucj4f+Qoy186G+IFAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "87Cu_oSonsXB",
        "colab_type": "code",
        "outputId": "58d087ba-8db4-490a-f56e-99546cf3b759",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 141
        }
      },
      "source": [
        "# onehotencoding of the labels\n",
        "encoder = OneHotEncoder(sparse=False)\n",
        "Y = encoder.fit_transform(labels.reshape(-1,1))\n",
        "Y"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0., 0., 0., 1.],\n",
              "       [1., 0., 0., 0.],\n",
              "       [0., 0., 0., 1.],\n",
              "       ...,\n",
              "       [0., 0., 0., 1.],\n",
              "       [0., 0., 0., 1.],\n",
              "       [0., 1., 0., 0.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eMGScgyV0WMR",
        "colab_type": "code",
        "outputId": "a7e9b1bb-da93-401f-d7f6-8456ef9a6805",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "X_train, X_test, Y_train, Y_test = train_test_split(data, Y, stratify=Y, random_state=0)\n",
        "print(X_train.shape, Y_train.shape, X_test.shape, Y_test.shape)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(750, 2) (750, 4) (250, 2) (250, 4)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dYT_ETtBDzQb",
        "colab_type": "text"
      },
      "source": [
        "## 2. Generic Neural Network Class"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FhX9MLITFQQn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class NeuralNetwork:\n",
        "  \n",
        "  def __init__(self,n_input=2,hidden = [2],output=1, W1=None,W2=None,init_method='random',activation = 'sigmoid',leaky_slope=0.01):\n",
        "    self.neurons = [n_input] + hidden + [output]\n",
        "    \n",
        "    # forward pass\n",
        "    self.W = {}\n",
        "    self.B = {}\n",
        "    self.A = {}\n",
        "    self.H = {}\n",
        "    # grads\n",
        "    self.dA = {}\n",
        "    self.dW = {}\n",
        "    self.dH = {}\n",
        "    self.dB = {}\n",
        "    \n",
        "    # for storing the history \n",
        "    self.error_h = []\n",
        "    self.W_h = []\n",
        "    self.B_h = []\n",
        "    self.output = output\n",
        "    self.accu_train = {}\n",
        "    self.accu_val = {}\n",
        "        \n",
        "    self.accuracy = 0\n",
        "    \n",
        "    # initialize the weights         \n",
        "    if init_method == 'random':\n",
        "      for i in range(len(self.neurons)-1):\n",
        "        self.W[i+1] = np.random.rand(self.neurons[i],self.neurons[i+1])\n",
        "        self.B[i+1] = np.random.rand(1,self.neurons[i+1])\n",
        "     \n",
        "    if init_method == 'zeros':\n",
        "      for i in range(len(self.neurons)-1):\n",
        "        self.W[i+1] = np.zeros(shape=(self.neurons[i],self.neurons[i+1]))\n",
        "        self.B[i+1] = np.zeros(shape=(1,self.neurons[i+1]))\n",
        "       \n",
        "    if init_method == 'xavier':\n",
        "      for i in range(len(self.neurons)-1):\n",
        "        self.W[i+1] = np.random.rand(self.neurons[i],self.neurons[i+1]) / np.sqrt(self.neurons[i])\n",
        "        self.B[i+1] = np.random.rand(1,self.neurons[i+1]) / np.sqrt(self.neurons[i])\n",
        "                \n",
        "    if init_method == 'he':\n",
        "      for i in range(len(self.neurons)-1):\n",
        "        self.W[i+1] = np.random.rand(self.neurons[i],self.neurons[i+1]) / np.sqrt(self.neurons[i]/2)\n",
        "        self.B[i+1] = np.random.rand(1,self.neurons[i+1]) / np.sqrt(self.neurons[i])\n",
        "        \n",
        "    self.activation = activation\n",
        "    self.leaky_slope = leaky_slope\n",
        "\n",
        "  def activation_function(self,X):\n",
        "    \n",
        "    if self.activation == 'sigmoid':\n",
        "      return 1.0/(1.0+np.exp(-X))\n",
        "      \n",
        "    if self.activation == 'tanh':\n",
        "      return np.tanh(X)\n",
        "    \n",
        "    if self.activation == 'relu':\n",
        "      return np.maximum(0,X)  # Element-wise maximum of array elements\n",
        "    \n",
        "    if self.activation == 'leaky_relu':\n",
        "      return np.maximum(self.leaky_slope*X,X)\n",
        "    \n",
        "    \n",
        "  def grad_activation(self,X):\n",
        "    if self.activation == 'sigmoid':\n",
        "      return np.multiply(X,(1-X))\n",
        "    elif self.activation == 'tanh':\n",
        "      return (1-np.square(X))\n",
        "    elif self.activation == 'relu':\n",
        "      return 1.0*(X>0)\n",
        "    elif self.activation == 'leaky_relu':\n",
        "      out = np.zeros(shape=X.shape)\n",
        "      out[X<=0] = self.leaky_slope\n",
        "      out[X>0] = 1\n",
        "      return out\n",
        "      \n",
        "  def softmax(self,X):\n",
        "    exps = np.exp(X)\n",
        "    sums = np.sum(exps,axis=1).reshape(-1,1)\n",
        "    return exps/sums\n",
        "    \n",
        "  def forward_pass(self,X):\n",
        "    self.H[0] = X\n",
        "    for i in self.W.keys():\n",
        "      self.A[i] = np.matmul(self.H[i-1],self.W[i]) + self.B[i]\n",
        "      \n",
        "      if i == len(self.neurons)-1 and self.output > 1:\n",
        "        self.H[i] = self.softmax(self.A[i])\n",
        "      else:\n",
        "        self.H[i] = self.activation_function(self.A[i])\n",
        "           \n",
        "    return self.H[len(self.neurons)-1]\n",
        " \n",
        "  def grad(self,X,Y,W=None,B=None):\n",
        "    \n",
        "    if W is None:\n",
        "      W = self.W\n",
        "    if B is None:\n",
        "      B = self.B\n",
        "    \n",
        "    self.forward_pass(X)\n",
        "    Y = Y.reshape(-1,self.output)\n",
        "    \n",
        "    # Backpropation for the last layer \n",
        "    self.dA[len(self.neurons)-1] = np.multiply((self.H[len(self.neurons)-1] - Y), self.grad_activation(self.H[len(self.neurons)-1]))  # (M,N).*(M,N) = (M,N)\n",
        "    \n",
        "    if self.loss == 'ce':\n",
        "      self.dA[len(self.neurons)-1] = self.H[len(self.neurons)-1] - Y # (N,1) \n",
        "    \n",
        "    self.dW[len(self.neurons)-1] = np.matmul(self.H[len(self.neurons)-2].T,self.dA[len(self.neurons)-1]) \n",
        "    self.dB[len(self.neurons)-1] = np.sum(self.dA[len(self.neurons)-1],axis=0).reshape(1,-1)\n",
        "    \n",
        "    \n",
        "    # backpropation for hidden layers to input\n",
        "    for i in range(len(self.neurons)-2,0,-1):\n",
        "      self.dH[i] = np.matmul(self.dA[i+1],W[i+1].T) \n",
        "      self.dA[i] = np.multiply(self.dH[i],self.grad_activation(self.H[i]))\n",
        "      self.dW[i]= np.matmul(self.H[i-1].T,self.dA[i])\n",
        "      self.dB[i] = np.sum(self.dA[i],axis=0).reshape(1,-1)\n",
        "      \n",
        "  def initialise_params(self,algo='GD',gamma=0.9):\n",
        "    if algo != 'GD':\n",
        "      self.V_W = {}\n",
        "      self.V_B = {}\n",
        "      for j in self.W.keys():\n",
        "        self.V_W[j] = 0\n",
        "        self.V_B[j] = 0\n",
        "        \n",
        "    if algo == 'NAG':\n",
        "      self.W_T = {}\n",
        "      self.B_T = {}\n",
        "      for j in self.W.keys():\n",
        "        self.W_T[j] = self.W[j] - gamma*self.V_W[j]\n",
        "        self.B_T[j] = self.B[j] - gamma*self.V_B[j]\n",
        "        \n",
        "    if algo == \"Adam\":\n",
        "      self.M_W = {}\n",
        "      self.M_B = {}\n",
        "      \n",
        "      for j in self.W.keys():\n",
        "        self.M_W[j] = 0\n",
        "        self.M_B[j] = 0\n",
        "        \n",
        "  def get_accuracy(self,X=None,Y=None):\n",
        "    \n",
        "    if X is None:\n",
        "      X = self.X\n",
        "    if Y is None:\n",
        "      Y = self.Y\n",
        "      \n",
        "    if self.output > 1:\n",
        "      accuracy = accuracy_score(np.argmax(Y,axis=1),np.argmax(self.predict(X),axis=1))\n",
        "    else:\n",
        "      accuracy = accuracy_score(Y,(self.predict(X)>=0.5).astype(int))\n",
        "\n",
        "    return accuracy\n",
        "\n",
        "        \n",
        "  def error(self,X=None,Y=None):\n",
        "    if X is None:\n",
        "      X = self.X\n",
        "    if Y is None:\n",
        "      Y = self.Y\n",
        "    Y_pred = self.forward_pass(X)\n",
        "    \n",
        "    if self.loss == 'ce':\n",
        "      return log_loss(Y,Y_pred)\n",
        "\n",
        "    return mean_squared_error(Y,Y_pred)\n",
        "    \n",
        "  \n",
        "  def fit(self,X,Y,X_val=None,Y_val=None,epochs=100,learning_rate=0.1,display_loss=True,loss='mse',algo='GD',batch_size=32,gamma=0.9,eps=1e-8,beta=0.9,beta1=0.9,beta2=0.99):\n",
        "    \n",
        "    self.loss = loss      \n",
        "    self.X = X\n",
        "    self.Y = Y.reshape(-1,self.output)\n",
        "    m = self.X.shape[0]\n",
        "    \n",
        "    self.initialise_params(algo,gamma=gamma)\n",
        "       \n",
        "    if algo == \"GD\":\n",
        "      for epoch in range(epochs):\n",
        "        self.grad(X,Y)\n",
        "        for i in self.W.keys():\n",
        "          self.W[i] -= learning_rate*self.dW[i]/m\n",
        "          self.B[i] -= learning_rate*self.dB[i]/m\n",
        "        self.append_log()\n",
        "        self.accu_train[epoch] = self.get_accuracy()\n",
        "        if X_val is not None and Y_val is not None:\n",
        "          self.accu_val[epoch] = self.get_accuracy(X_val,Y_val)\n",
        "      \n",
        "    if algo == 'MiniBatch':\n",
        "      X_batch,Y_batch = X[0:batch_size], Y[0:batch_size]\n",
        "      for epoch in range(epochs):\n",
        "        j = 0\n",
        "        while (len(X[j:j+batch_size]) != 0):\n",
        "          X_batch,Y_batch = X[j:j+batch_size], Y[j:j+batch_size]\n",
        "          self.grad(X_batch,Y_batch)\n",
        "          for i in self.W.keys():\n",
        "            self.W[i] -= learning_rate*self.dW[i]/batch_size\n",
        "            self.B[i] -= learning_rate*self.dB[i]/batch_size\n",
        "          j = j + batch_size\n",
        "        self.append_log(X_batch,Y_batch)\n",
        "        self.accu_train[epoch] = self.get_accuracy()\n",
        "        if X_val is not None and Y_val is not None:\n",
        "          self.accu_val[epoch] = self.get_accuracy(X_val,Y_val)\n",
        "        \n",
        "    if algo == \"Momentum\":\n",
        "      for epoch in range(epochs):\n",
        "        self.grad(X,Y)\n",
        "        for j in self.W.keys():\n",
        "          self.V_W[j] = gamma*self.V_W[j] + learning_rate*self.dW[j]/m\n",
        "          self.V_B[j] = gamma*self.V_B[j] + learning_rate*self.dB[j]/m    \n",
        "          self.W[j] -= self.V_W[j]\n",
        "          self.B[j] -= self.V_B[j]\n",
        "        self.append_log()\n",
        "        self.accu_train[epoch] = self.get_accuracy()\n",
        "        if X_val is not None and Y_val is not None:\n",
        "          self.accu_val[epoch] = self.get_accuracy(X_val,Y_val)\n",
        "        \n",
        "        \n",
        "    if algo == 'NAG':      \n",
        "      for epoch in range(epochs):\n",
        "        self.grad(X,Y,W=self.W_T,B=self.B_T)\n",
        "        for j in self.W.keys():\n",
        "          self.V_W[j] = gamma*self.V_W[j] + learning_rate*self.dW[j]/m\n",
        "          self.V_B[j] = gamma*self.V_B[j] + learning_rate*self.dB[j]/m\n",
        "          \n",
        "          self.W_T[j] = self.W[j] - gamma*self.V_W[j]\n",
        "          self.B_T[j] = self.B[j] - gamma*self.V_B[j]\n",
        "          \n",
        "          self.W[j] -= self.V_W[j]\n",
        "          self.B[j] -= self.V_B[j]\n",
        "        self.append_log()\n",
        "        self.accu_train[epoch] = self.get_accuracy()\n",
        "        if X_val is not None and Y_val is not None:\n",
        "          self.accu_val[epoch] = self.get_accuracy(X_val,Y_val)\n",
        "        \n",
        "        \n",
        "    if algo == 'Adagrad':        \n",
        "      for epoch in range(epochs):\n",
        "        self.grad(X,Y)\n",
        "        for j in self.W.keys():\n",
        "          self.V_W[j] += np.square(self.dW[j])\n",
        "          self.V_B[j] += np.square(self.dB[j])\n",
        "          self.W[j] -= learning_rate * self.dW[j] / (np.sqrt(self.V_W[j])+eps)\n",
        "          self.B[j] -= learning_rate * self.dB[j] / (np.sqrt(self.V_B[j])+eps)\n",
        "      \n",
        "        self.append_log()\n",
        "        self.accu_train[epoch] = self.get_accuracy()\n",
        "        if X_val is not None and Y_val is not None:\n",
        "          self.accu_val[epoch] = self.get_accuracy(X_val,Y_val)\n",
        "        \n",
        "    if algo == 'RMSProp':        \n",
        "      for epoch in range(epochs):\n",
        "        self.grad(X,Y)\n",
        "        for j in self.W.keys():\n",
        "          self.V_W[j] = beta*self.V_W[j] + (1-beta)*np.square(self.dW[j])\n",
        "          self.V_B[j] = beta*self.V_B[j] + (1-beta)*np.square(self.dB[j])\n",
        "          \n",
        "          self.W[j] -= learning_rate * self.dW[j] / (np.sqrt(self.V_W[j])+eps)\n",
        "          self.B[j] -= learning_rate * self.dB[j] / (np.sqrt(self.V_B[j])+eps)\n",
        "      \n",
        "        self.append_log()\n",
        "        self.accu_train[epoch] = self.get_accuracy()\n",
        "        if X_val is not None and Y_val is not None:\n",
        "          self.accu_val[epoch] = self.get_accuracy(X_val,Y_val)\n",
        "      \n",
        "    if algo == 'Adam':        \n",
        "      for epoch in range(epochs):\n",
        "        self.grad(X,Y)\n",
        "        for j in self.W.keys():\n",
        "          self.M_W[j] = beta1*self.M_W[j] + (1-beta1)*self.dW[j]\n",
        "          self.M_B[j] = beta1*self.M_B[j] + (1-beta1)*self.dB[j]\n",
        "          self.V_W[j] = beta2*self.V_W[j] + (1-beta2)*np.square(self.dW[j])\n",
        "          self.V_B[j] = beta2*self.V_B[j] + (1-beta2)*np.square(self.dB[j])\n",
        "          \n",
        "          self.W[j] -= learning_rate * self.M_W[j] / (np.sqrt(self.V_W[j])+eps)\n",
        "          self.B[j] -= learning_rate * self.M_B[j] / (np.sqrt(self.V_B[j])+eps)\n",
        "      \n",
        "        self.append_log()\n",
        "        self.accu_train[epoch] = self.get_accuracy()\n",
        "        if X_val is not None and Y_val is not None:\n",
        "          self.accu_val[epoch] = self.get_accuracy(X_val,Y_val)\n",
        "        \n",
        "    if display_loss:\n",
        "      plt.plot(self.accu_train.values())\n",
        "      plt.plot(self.accu_val.values())\n",
        "      plt.xlabel('Iterations')\n",
        "      plt.ylabel('Accuracy')\n",
        "      plt.title('Algorithm: '+algo+' | Activation Function: '+self.activation)\n",
        "      \n",
        "    \n",
        "  \n",
        "  def predict(self,X):\n",
        "    return self.forward_pass(X)\n",
        "    \n",
        "  def append_log(self,X=None,Y=None):\n",
        "    if X is None:\n",
        "      X = self.X\n",
        "    if Y is None:\n",
        "      Y = self.Y\n",
        "    self.W_h.append(self.W)\n",
        "    self.B_h.append(self.B)\n",
        "    self.error_h.append(self.error(X,Y))\n",
        "    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d3RBcFD4SQ4N",
        "colab_type": "text"
      },
      "source": [
        "##3. Modelling"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MQhQbkVCSi_O",
        "colab_type": "code",
        "outputId": "a9f43517-99b6-483c-f5ed-b747efa7d684",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        }
      },
      "source": [
        "NN = NeuralNetwork(hidden=[2], output=4,init_method='random',activation='sigmoid',leaky_slope=0.01)\n",
        "NN.fit(X_train,Y_train,X_test,Y_test,loss='ce',learning_rate=0.1,epochs=1000,display_loss=True,algo='NAG',batch_size=128,gamma=0.8,beta=0.9,beta1=0.5,beta2=0.5)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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+DRKeT51znU86v2wDgWmS3gXuAqam8zxlSQngZuAooDhcxmQzmx0pMwa4AjjI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\nc87V8aTgnHOuzv8DWmdE/aRol5gAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nB6-nsb0yNLE",
        "colab_type": "code",
        "outputId": "59bd3331-b372-43e9-c89b-dc86523ce8b2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "def accuracy(X,Y,model):\n",
        "  Y_pred = model.predict(X)\n",
        "  \n",
        "  if model.output > 1:\n",
        "      accuracy = accuracy_score(np.argmax(Y,axis=1),np.argmax(model.predict(X),axis=1))\n",
        "  else:\n",
        "      accuracy = accuracy_score(Y,(model.predict(X)>=0.5).astype(int))\n",
        " \n",
        "  return accuracy\n",
        "\n",
        "\n",
        "print('Accuracy score for training data set: ',accuracy(X_train,Y_train,NN))\n",
        "print('Accuracy score for test data set: ',accuracy(X_test,Y_test,NN))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy score for training data set:  0.9306666666666666\n",
            "Accuracy score for test data set:  0.924\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3HpY6jKlSNyd",
        "colab_type": "text"
      },
      "source": [
        "##4. Visualisation of the network"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zRvd_h68-IyU",
        "colab_type": "code",
        "outputId": "45479309-9016-4dd0-b394-56d929c4225b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 582
        }
      },
      "source": [
        "fig = plt.figure(figsize=(10,10))\n",
        "\n",
        "for i,n in enumerate(NN.neurons):\n",
        "  X = np.linspace(0,10,n+2)\n",
        "  Y = [i+1]*len(X[1:-1])\n",
        "  plt.scatter(X[1:-1],Y,s=1000)\n",
        "\n",
        "plt.xticks([])\n",
        "\n",
        "plt.yticks(list(range(1,len(NN.neurons)+1)))\n",
        "plt.ylabel('Layer Number')\n",
        "plt.grid(b=True)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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h6+xpukrYYl1785Y3Z3pieqQ1pyem86YtbxppTegLe5ouErZY17actSVbz9o6spNqJ8tk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\nsAUA0JCwBQDQ0P8Pz3qMYtNaBEwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nXiv3XqXhSeh",
        "colab_type": "code",
        "outputId": "3d25aaa5-ddea-4d9a-8648-0c2f162347d2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 660
        }
      },
      "source": [
        "algos = ['GD','MiniBatch','Momentum','NAG','Adagrad','RMSProp','Adam']\n",
        "\n",
        "\n",
        "loss = 'ce'\n",
        "iterations = 200\n",
        "\n",
        "fig = plt.figure(figsize=(15,10))\n",
        "plt.xlabel('Iterations',fontsize=15)\n",
        "plt.ylabel(loss,fontsize=15)\n",
        "plt.title('Comparison of all the algorithms\\n'+\", \".join(algos))\n",
        "plt.xlim(0,iterations)\n",
        "plt.ylim(0,2)\n",
        "for algo in algos:\n",
        "  NN = NeuralNetwork(hidden=[5,2])\n",
        "  NN.fit(X_train,Y_train,loss=loss,learning_rate=0.1,epochs=iterations,display_loss=False,algo=algo,batch_size=128,gamma=0.8,beta=0.9,beta1=0.9,beta2=0.99)\n",
        "  plt.plot(range(len(NN.error_h)),NN.error_h,label=algo)\n",
        "\n",
        "  \n",
        "plt.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fa498dc8710>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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hzz33LBzpGzRoEJMnTwbge9/7HhdeeCE333wz77zzDqNGjeIf//gHEcGqVatq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\n76/hvVfO56H1LVz3f5/ik79ar8lyRERERERkxI3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6lfVKmUp5F8Zy9T9vucvviQvjcvWV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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1080x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5DnWvw5JP2YT",
        "colab_type": "text"
      },
      "source": [
        "## 5. Comparison of the algorithms and the activation functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kTagWWBVP7gQ",
        "colab_type": "code",
        "outputId": "3099e539-a5e3-43cf-baeb-457b48fd1a91",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1034
        }
      },
      "source": [
        "algos = ['GD',\"MiniBatch\",'Adagrad','RMSProp','Adam']\n",
        "activation = ['sigmoid','tanh','relu','leaky_relu']\n",
        "\n",
        "def compare_params(row,column,epochs=1000,learning_rate=0.1,init='random'):\n",
        "  X1,Y1 = np.meshgrid(row,column)\n",
        "  accuracies = np.zeros(shape=(len(row),len(column)))\n",
        "  for i,r in enumerate(row):\n",
        "    for j,c in enumerate(column):\n",
        "      print(r,c)\n",
        "      model = NeuralNetwork(hidden=[5,2],init_method='xavier',activation=c,leaky_slope=0.01)\n",
        "      model.fit(X_test,Y_test,loss='ce',learning_rate=learning_rate,epochs=epochs,display_loss=False,algo=r,batch_size=128,gamma=0.9,beta=0.5,beta1=0.9,beta2=0.99)\n",
        "      accuracies[i,j] = model.accuracy\n",
        "\n",
        "  data = pd.DataFrame(accuracies,index=row,columns=column)\n",
        "  plt.figure(figsize=(15,10))\n",
        "  plt.title('**Accuarcy Scores for leaky_relu with '+init+' initialisation**\\n\\nNeural Network | Epochs: '+str(epochs))\n",
        "  s = sns.heatmap(data,annot=True)\n",
        "  s.set_xticklabels(labels = column, rotation=90)\n",
        "  plt.show()\n",
        "  return data\n",
        "  \n",
        "  \n",
        "data = compare_params(row=algos,column=activation,epochs=200,learning_rate=0.1)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "GD sigmoid\n",
            "GD tanh\n",
            "GD relu\n",
            "GD leaky_relu\n",
            "MiniBatch sigmoid\n",
            "MiniBatch tanh\n",
            "MiniBatch relu\n",
            "MiniBatch leaky_relu\n",
            "Adagrad sigmoid\n",
            "Adagrad tanh\n",
            "Adagrad relu\n",
            "Adagrad leaky_relu\n",
            "RMSProp sigmoid\n",
            "RMSProp tanh\n",
            "RMSProp relu\n",
            "RMSProp leaky_relu\n",
            "Adam sigmoid\n",
            "Adam tanh\n",
            "Adam relu\n",
            "Adam leaky_relu\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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8UDP9wcQP6NG7+0L1tt1jG64a9jfOueIsevbtAcDI517jhf+9yB3P38odL9zC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\nSVIh/h8Wb1G2DoDNFgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1080x720 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NWx9Zo90kkhP",
        "colab_type": "text"
      },
      "source": [
        "## 6. Practice"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2i03XhvbzjnD",
        "colab_type": "code",
        "outputId": "85eaf7e1-1248-4d23-b7cc-657717290ff0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "Y_true = np.array([1,0,0,0])\n",
        "Y_pred = [0.09,0.01,0.02,0.02]\n",
        "mean_squared_error(Y_true,Y_pred)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.20725"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 190
        }
      ]
    }
  ]
}