nn-mlp_from_scratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "20c69952",
   "metadata": {},
   "source": [
    "# Neural Network (Multilayered Perceptron) From Scratch\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "53be8a03",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(69420)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7e0d3f6",
   "metadata": {},
   "source": [
    "## Neuron Representation\n",
    "```\n",
    "[ A    B <- Input Neurons\n",
    " [w00 w01] O1\n",
    " [w10 w11] O2\n",
    " [w20 w21] O3   <- Outputs to next layer\n",
    "]\n",
    "                 \n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "077bbe5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "W1 = np.array([\n",
    "    [0.1,0.2], \n",
    "    [0.2,0.1],\n",
    "    [0.3,0.5]\n",
    "])\n",
    "\n",
    "bias1 = np.array([0.2,0.1,0.4])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfebe7fd",
   "metadata": {},
   "source": [
    "### XOR function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0af70846",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array([\n",
    "    [0,0],\n",
    "    [0,1],\n",
    "    [1,0],\n",
    "    [1,1]\n",
    "])\n",
    "\n",
    "t = np.array([\n",
    "    [0],\n",
    "    [1],\n",
    "    [1],\n",
    "    [0]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "199a9e0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def neuron_sum(x,W,b):\n",
    "    return W@x +b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "15b48d9d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.2 0.1 0.4]\n",
      "[0.4 0.2 0.9]\n",
      "[0.3 0.3 0.7]\n",
      "[0.5 0.4 1.2]\n"
     ]
    }
   ],
   "source": [
    "for x in X:\n",
    "    print(neuron_sum(x,W1,bias1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2deab714",
   "metadata": {},
   "source": [
    "so our formula to compute the activation of a neuron is\n",
    "$$\n",
    "y_i = g(\\mathbf W \\cdot x + bias)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e543aa31",
   "metadata": {},
   "source": [
    "## Neural Network Representation\n",
    "\n",
    "NN(MLP) = $[(W^1,bias^1),...,(W^l,bias^l),...(W^L,bias^L)]$, where $l = 1,\\dots,L$.\n",
    "\n",
    "let's add two more layers,\n",
    "\n",
    "\n",
    "arch: (3x2)-(4x3)-(1x4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "74b9e594",
   "metadata": {},
   "outputs": [],
   "source": [
    "W2 = np.array([\n",
    "    [0.1,0.2,0.1],\n",
    "    [0.1,0.4,0.2],\n",
    "    [0.2,0.5,0.4],\n",
    "    [0.3,0.1,0.3]\n",
    "])\n",
    "\n",
    "bias2  = np.array([0.2,0.3,0.5,0.3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fa00ae80",
   "metadata": {},
   "outputs": [],
   "source": [
    "W3 = np.array([\n",
    "    [0.1,0.5,0.1,0.4],\n",
    "])\n",
    "\n",
    "bias3  = np.array([0.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c303b81d",
   "metadata": {},
   "outputs": [],
   "source": [
    "NN = [(W1,bias1),(W2,bias2),(W3,bias3)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd62e603",
   "metadata": {},
   "source": [
    "## Forward Phase\n",
    "\n",
    "For the first hidden layer:\n",
    "$$\n",
    "z^1 = x \\cdot \\mathbf W^1 + bias^1 \\\\\n",
    "y^1 = g(z^1)\n",
    "$$\n",
    "For subsequent hidden layers:\n",
    "$$\n",
    "z^l = y^{l-1} \\cdot \\mathbf W^l + bias^l \\\\\n",
    "y^l = g(z^l)\n",
    "$$\n",
    "For the output layer:\n",
    "$$\n",
    "z^L =  y^{L-1} \\cdot W^L + bias^L \\\\\n",
    "y^L = g(z^L)\n",
    "$$\n",
    "\n",
    "for activation function lets use sigmoid($\\sigma$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b82ebf81",
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = 1 #global"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6d7d128f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z*beta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8ff51b18",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0]\n",
      "to\n",
      "[0.549834   0.52497919 0.59868766]\n",
      "to\n",
      "[0.60344688 0.66478969 0.75248902 0.66753438]\n",
      "to\n",
      "[0.69741158]\n"
     ]
    }
   ],
   "source": [
    "A = [X[0]]\n",
    "for Weight,b in NN:\n",
    "    print(A[-1],end = \"\\nto\\n\")\n",
    "    A.append(sigmoid(neuron_sum(A[-1],Weight,b)))\n",
    "    \n",
    "print(A[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03a13efb",
   "metadata": {},
   "source": [
    "## Error Calculation\n",
    "MSE,\n",
    "$$\n",
    "E = \\frac 12 \\sum_{i=1}^N (y^L_i - y_i)^2\n",
    "$$\n",
    "\n",
    "Using Mean Squared Error, lets compute the error between the predicted output and the desired output.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f6084fd2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MSE(t,y):\n",
    "    return np.sum((y-t)**2)/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "226915b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24319145273888504"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSE(t[0],A[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c68aa6b0",
   "metadata": {},
   "source": [
    "## Backward Phase (Error back propagation)\n",
    "\n",
    "For the output layer:\n",
    "$$\n",
    "δ^L = (y^L - y) * g'(z^L)\n",
    "$$\n",
    "For the hidden layers:\n",
    "$$\n",
    "δ^l = g'(z^l) * W^{l+1} \\cdot δ^{i+1}\n",
    "$$\n",
    "where $δ^l$ is the error of neuron in the l-th layer, and g'(z) is the derivative of the activation function.\n",
    "\n",
    "\n",
    "The partial derivative of the error with respect to a weight is:\n",
    "$$\n",
    "\\frac {\\partial E}{\\partial W^l} = y^{l-1} * δ^l\n",
    "$$\n",
    "The partial derivative of the error with respect to a bias is:\n",
    "$$\n",
    "\\frac {\\partial E}{\\partial b^l} = δ^l\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "22378ab0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid_d(y): # here instead of the input z^l we directly given y^l because 𝜎' = 𝜎(z) * (1 - 𝜎(z))\n",
    "    return beta*y * (1 - y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "00dda2df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.14717384])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_o = (A[-1] - t[0]) * sigmoid_d(A[-1])\n",
    "delta_o"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7bc3aa15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00352185, 0.01639843, 0.0027411 , 0.01306505])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_h = (W3.T @ delta_o) * sigmoid_d(A[-2])\n",
    "delta_h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "672e8d38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.0015989 , 0.002479  , 0.00207773])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_i = (W2.T @ delta_h) * sigmoid_d(A[-3])\n",
    "delta_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "bd937985",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.08881159],\n",
       "       [0.09783965],\n",
       "       [0.1107467 ],\n",
       "       [0.0982436 ]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dE_dW3 = A[-2].reshape(-1,1) * delta_o\n",
    "dE_dW3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "414d03fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.01118841,  0.40216035, -0.0107467 ,  0.3017564 ]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W3 - dE_dW3.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e24bf028",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.549834  , 0.52497919, 0.59868766]),\n",
       " array([[0.549834  ],\n",
       "        [0.52497919],\n",
       "        [0.59868766]]))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[-3],A[-3].reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c7644217",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.00193643, 0.00901641, 0.00150715, 0.00718361],\n",
       "       [0.0018489 , 0.00860883, 0.00143902, 0.00685888],\n",
       "       [0.00210849, 0.00981754, 0.00164106, 0.00782188]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dE_dW2 = A[-3].reshape(-1,1) * delta_h\n",
    "dE_dW2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "025f8bc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dE_dW1 = A[-4].reshape(-1,1) * delta_i\n",
    "dE_dW1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c896c047",
   "metadata": {},
   "source": [
    "## Summing all up!!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6eeedd2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "143fc5f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# NN Initializer\n",
    "def init_network(arch):\n",
    "    return [ (\n",
    "        np.random.randn(arch[i],arch[i-1]) * np.sqrt(1 / arch[i-1]),\n",
    "        np.random.rand(arch[i])\n",
    "    ) for i in range(1,len(arch))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a4bc838c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Feed Forward the input\n",
    "def forward(x,NN):\n",
    "    A = [x]\n",
    "    for w,b in NN:\n",
    "        A.append(sigmoid(neuron_sum(A[-1],w,b)))\n",
    "    return A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "d789f2dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Back Propagate the error\n",
    "def backward(A,NN,t):\n",
    "    L = len(NN)\n",
    "    deltas = [None]* L\n",
    "    dE_dW = [None] * L\n",
    "    L-=1\n",
    "    \n",
    "    for i in range(L,-1,-1):\n",
    "        if i != L:deltas[i] = (NN[i+1][0].T @ deltas[i+1]) * sigmoid_d(A[i+1])\n",
    "        else: deltas[i] = (A[i+1] - t) * sigmoid_d(A[i+1])\n",
    "        \n",
    "        dE_dW[i] = (A[i].reshape(-1,1) * deltas[i]).T\n",
    "    return deltas, dE_dW"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "7184fe0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Weight update\n",
    "def update_weights(NN,deltas,dE_dw,eta):\n",
    "    for i in range(len(NN)):\n",
    "        W,b = NN[i]\n",
    "        W -= eta * dE_dw[i]\n",
    "        b -= eta * deltas[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "af0867b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# predict function \n",
    "def predict(X,NN):\n",
    "    return np.array([np.round(forward(x,NN)[-1]) for x in X])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "966fde54",
   "metadata": {},
   "source": [
    "### Network Training using Gradient Descent algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "71479409",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(X,y,NN,epoch=1000,eta=0.01,errorcal=10):\n",
    "    mse_l = []\n",
    "    record = True\n",
    "    mse=0\n",
    "    for i in range(1,epoch+1):\n",
    "        if i%errorcal == 0: \n",
    "            record = True\n",
    "            mse=0\n",
    "            \n",
    "        for x,t in zip(X,y):\n",
    "            A = forward(x,NN)\n",
    "            d,gra = backward(A,NN,t)\n",
    "            update_weights(NN,d,gra,eta)\n",
    "            if record: mse += MSE(A[-1],t)\n",
    "        if record:\n",
    "            mse_l.append(mse)\n",
    "            record = False\n",
    "\n",
    "    fig = plt.figure(figsize=(5,5))\n",
    "    plt.plot(range(len(mse_l)),mse_l)\n",
    "    plt.xlabel(f\"Epoch*{errorcal}\")\n",
    "    plt.ylabel(\"MSE\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdbe06a7",
   "metadata": {},
   "source": [
    "## Model XOR function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "2ef01b5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "XOR = init_network([2,3,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da43db86",
   "metadata": {},
   "source": [
    "predictions before training the network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "b86ae550",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.],\n",
       "       [1.],\n",
       "       [1.],\n",
       "       [1.]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(X,XOR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "87b22865",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train(X,t,XOR,eta=0.25,errorcal=10,epoch=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "0b7a896a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.],\n",
       "       [1.],\n",
       "       [1.],\n",
       "       [0.]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(X,XOR)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5693c89c",
   "metadata": {},
   "source": [
    "## Model breast cancer dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "4d65ae01",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.metrics import accuracy_score\n",
    "bc = load_breast_cancer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "1199d11c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train,X_test,y_train,y_test = train_test_split(bc.data,bc.target,test_size=0.3,shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9316f48e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(171, 30)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "83790ad4",
   "metadata": {},
   "outputs": [],
   "source": [
    "bc_NN = init_network([30,10,4,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "f9aa03c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = 0.3 # set global constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "28ef3488",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_9844/854337207.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  return 1 / (1 + np.exp(-z*beta))\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train(X_train,y_train,bc_NN,eta=0.01,epoch=1000,errorcal=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "db8f300d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model Accuracy on Test set: 0.9298245614035088\n",
      "Model Accuracy on Train set: 0.9045226130653267\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_9844/854337207.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  return 1 / (1 + np.exp(-z*beta))\n",
      "/tmp/ipykernel_9844/854337207.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  return 1 / (1 + np.exp(-z*beta))\n"
     ]
    }
   ],
   "source": [
    "y_pred = predict(X_test,bc_NN)\n",
    "print(f\"Model Accuracy on Test set: {accuracy_score(y_test,y_pred)}\")\n",
    "print(f\"Model Accuracy on Train set: {accuracy_score(y_train,predict(X_train,bc_NN))}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68a41c99",
   "metadata": {},
   "source": [
    "# Full Implementation of Neural Network with Momentum in Weight Updating Step\n",
    "\n",
    "In this simple implementation of Multilayered Perceptron, the `train` function performs normal Gradient Descent during training. The `train_on_batch` function, on the other hand, considers the given input as a batch and updates the model parameters accordingly.\n",
    "\n",
    "So, there is no implementation of SGD using mini-batches in this code, as it is not necessary for this small project. \n",
    "\n",
    "However, if you wish to implement SGD with mini-batches, a straightforward approach would be to create a simple function that divides the dataset into smaller batches, randomly selects one batch, and applies `train_on_batch` with `epoch=1` for a $N$ epochs. This approach can be more computationally efficient when working with larger datasets, as it allows the model to update its parameters using smaller subsets of the data at a time.\n",
    "\n",
    "Pseudo code SGD with mini-batches:\n",
    "\n",
    "```py\n",
    "Function train(X, y, NN, batch_size, num_epochs):\n",
    "    losses = []\n",
    "    for epoch in range(num_epochs):\n",
    "        X_batch, y_batch = sample_a_minibatch(X, y, batch_size) # Randomly sample a mini-batch with or without replacement\n",
    "        losses += NN.train_on_batch(X_batch, y_batch, epoch=1)\n",
    "            \n",
    "    return losses\n",
    "```\n",
    "## Momentum $\\alpha$ \n",
    "Momentum is a concept in optimization algorithms that governs how much weight is given to previous weight updates when computing the current update. In the context of SGD, momentum can be thought of as a ball rolling down a hill. Without momentum, the ball may get stuck in a local minimum on its way to the steepest point. However, by giving the ball a little momentum, it can more easily escape the local minimum and continue rolling towards the global minimum.\n",
    "\n",
    "At first the $\\Delta W^l$ is set to 0,\n",
    "\n",
    "Then, the current updates calculated and stored in $\\Delta W^l = \\eta * \\frac {\\partial E}{\\partial W^l} + \\alpha * \\Delta W^l$ \n",
    "\n",
    "Finally the Network weights updated by, $W^l =  W^l - \\Delta W^l$.\n",
    "\n",
    "where $l = 1,\\dots,L$ (number of layers), and the same process is used for updating the biases $\\Delta b^l$.\n",
    "\n",
    "**File**: `nn.py`\n",
    "- **Classes**: `NeuralNetwork`,`sigmoid`,`linear` &`relu`.\n",
    "\n",
    "- **Functions**: `MSE`&`neuron_sum`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "fb26a7aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "from nn import NeuralNetwork\n",
    "from sklearn.datasets import load_iris"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6986fdda",
   "metadata": {},
   "source": [
    "## Lets model the Iris dataset with our NeuralNetwork"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "d1e59771",
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "85b452cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train,X_test,y_train,y_test = train_test_split(iris.data,iris.target,test_size=0.5,shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "56bdbf09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(75, 4)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "37db53c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "iris_model = NeuralNetwork([4,3,1],[\"sigmoid\",\"linear\"],eta=0.1,momentum=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "d0e96448",
   "metadata": {},
   "outputs": [],
   "source": [
    "mse_l = iris_model.train(X_train,y_train,epoch=100,errorcal=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "c449f517",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5))\n",
    "plt.plot(range(len(mse_l)),mse_l)\n",
    "plt.xlabel(f\"Epoch\")\n",
    "plt.ylabel(\"MSE\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "c8d21440",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of the model (Test set): 0.96\n"
     ]
    }
   ],
   "source": [
    "y_preds = [np.round(y) for y in iris_model.predict(X_test)]\n",
    "print(f\"Accuracy of the model (Test set): {accuracy_score(y_test,y_preds)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "34c8b8fe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of the model (Train set): 0.9333333333333333\n"
     ]
    }
   ],
   "source": [
    "y_preds = [np.round(y) for y in iris_model.predict(X_train)]\n",
    "print(f\"Accuracy of the model (Train set): {accuracy_score(y_train,y_preds)}\")"
   ]
  }
 ],
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