{
 "cells": [
  {
   "attachments": {
    "simple-neural-network.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "d8e474c0",
   "metadata": {},
   "source": [
    "Neural networks (NN), also called artificial neural networks (ANN) are a subset of learning algorithms within the machine learning field that are loosely based on the concept of biological neural networks.\n",
    "\n",
    "see https://victorzhou.com/blog/intro-to-neural-networks/\n",
    "\n",
    "Basically, an artifical neutral net (ANN) comprises of the following components:\n",
    "\n",
    "- An input layer that receives data and pass it on\n",
    "- A hidden layer\n",
    "- An output layer\n",
    "- Weights between the layers\n",
    "- A deliberate activation function for every hidden layer, we’ll employ the Sigmoid activation function.\n",
    "\n",
    "There are several types of neural networks. Here we are going to create the feed-forward or perception neural networks. This type of ANN relays data directly from the front to the back.\n",
    "\n",
    "Training the feed-forward neurons often need back-propagation, which provides the network with corresponding set of inputs and outputs. When the input data is transmitted into the neuron, it is processed, and an output is generated.\n",
    "\n",
    "Here is a diagram that shows the structure of a simple neural network (single neuron):\n",
    "\n",
    "![simple-neural-network.png](attachment:simple-neural-network.png)\n",
    "\n",
    "And, the best way to understand how neural networks work is to learn how to build one from scratch (without using any library).\n",
    "\n",
    "Here is a table that shows the problem.\n",
    "\n",
    "|                   | In\tput \t| Output|\n",
    "| ---------------   | ----- | -- |\n",
    "| Training data #1\t|0\t 0\t 1\t|0|\n",
    "| Training data #2\t|1\t 1\t 1\t|1|\n",
    "| Training data #3\t|1\t 0\t 1\t|1|\n",
    "| Training data #4\t|0\t 1\t 1\t|0|\n",
    "| New Situation\t    |1\t 0\t 0\t|?|\n",
    "\n",
    "We are going to train the neural network such that it can predict the correct output value when provided with a new set of data.\n",
    "\n",
    "As you can see on the table, the value of the output is always equal to the first value in the input section. Therefore, we expect the value of the output (?) to be 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50f543c2",
   "metadata": {},
   "source": [
    "Creating a NeuralNetwork Class\n",
    "We’ll create a NeuralNetwork class in Python to train the neuron to give an accurate prediction. The class will also have other helper functions.\n",
    "\n",
    "Even though we’ll not use a neural network library for this simple neural network example, we’ll import the numpy library to assist with the calculations."
   ]
  },
  {
   "attachments": {
    "sigmoid-function-1.png": {
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   },
   "cell_type": "markdown",
   "id": "5cdfcc3b",
   "metadata": {},
   "source": [
    "We’ll use the Sigmoid function, which draws a characteristic “S”-shaped curve, as an activation function to the neural network.\n",
    "\n",
    "![sigmoid-function-1.png](attachment:sigmoid-function-1.png)\n",
    "\n",
    "This function can map any value to a value from 0 to 1. It will assist us to normalize the weighted sum of the inputs.\n",
    "\n",
    "Thereafter, we’ll create the derivative of the Sigmoid function to help in computing the essential adjustments to the weights.\n",
    "\n",
    "The output of a Sigmoid function can be employed to generate its derivative. For example, if the output variable is “x”, then its derivative will be x * (1-x)"
   ]
  },
  {
   "attachments": {
    "t-function.png": {
     "image/png": "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"
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   "cell_type": "markdown",
   "id": "c8a84e13",
   "metadata": {},
   "source": [
    "This is the stage where we’ll teach the neural network to make an accurate prediction. Every input will have a weight—either positive or negative.\n",
    "\n",
    "This implies that an input having a big number of positive weight or a big number of negative weight will influence the resulting output more.\n",
    "\n",
    "Remember that we initially began by allocating every weight to a random number.\n",
    "\n",
    "Here is the procedure for the training process we used in this neural network example problem:\n",
    "\n",
    "- We took the inputs from the training dataset, performed some adjustments based on their weights, and siphoned them via a method that computed the output of the ANN.\n",
    "- We computed the back-propagated error rate. In this case, it is the difference between neuron’s predicted output and the expected output of the training dataset.\n",
    "- Based on the extent of the error got, we performed some minor weight adjustments using the Error Weighted Derivative formula.\n",
    "- We iterated this process an arbitrary number of 15,000 times. In every iteration, the whole training set is processed simultaneously.\n",
    "\n",
    "We used the “.T” function for transposing the matrix from horizontal position to vertical position. Therefore, the numbers will be stored this way:\n",
    "\n",
    "![t-function.png](attachment:t-function.png)\n",
    "\n",
    "Ultimately, the weights of the neuron will be optimized for the provided training data. Consequently, if the neuron is made to think about a new situation, which is the same as the previous one, it could make an accurate prediction. This is how back-propagation takes place.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "38318bbf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beginning Randomly Generated Weights: \n",
      "[[-0.16595599]\n",
      " [ 0.44064899]\n",
      " [-0.99977125]]\n",
      "Ending Weights After Training: \n",
      "[[10.08740896]\n",
      " [-0.20695366]\n",
      " [-4.83757835]]\n",
      "prediction [0.9999584]\n"
     ]
    }
   ],
   "source": [
    "# https://python-course.eu/machine-learning/simple-neural-network-from-scratch-in-python.php\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "class NeuralNetwork():\n",
    "    \n",
    "    def __init__(self):\n",
    "        # seeding for random number generation\n",
    "        np.random.seed(1)\n",
    "        \n",
    "        #converting weights to a 3 by 1 matrix with values from -1 to 1 and mean of 0\n",
    "        self.synaptic_weights = 2 * np.random.random((3, 1)) - 1\n",
    "\n",
    "    def sigmoid(self, x):\n",
    "        #applying the sigmoid function\n",
    "        return 1 / (1 + np.exp(-x))\n",
    "\n",
    "    def sigmoid_derivative(self, x):\n",
    "        #computing derivative to the Sigmoid function\n",
    "        return x * (1 - x)\n",
    "\n",
    "    def train(self, training_inputs, training_outputs, training_iterations):\n",
    "        \n",
    "        #training the model to make accurate predictions while adjusting weights continually\n",
    "        for iteration in range(training_iterations):\n",
    "            #siphon the training data via  the neuron\n",
    "            output = self.think(training_inputs)\n",
    "\n",
    "            #computing error rate for back-propagation\n",
    "            error = training_outputs - output\n",
    "            \n",
    "            #performing weight adjustments\n",
    "            adjustments = np.dot(training_inputs.T, error * self.sigmoid_derivative(output))\n",
    "\n",
    "            self.synaptic_weights += adjustments\n",
    "\n",
    "    def think(self, inputs):\n",
    "        #passing the inputs via the neuron to get output   \n",
    "        #converting values to floats\n",
    "        \n",
    "        inputs = inputs.astype(float)\n",
    "        output = self.sigmoid(np.dot(inputs, self.synaptic_weights))\n",
    "        return output\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "\n",
    "    #initializing the neuron class\n",
    "    neural_network = NeuralNetwork()\n",
    "\n",
    "    print(\"Beginning Randomly Generated Weights: \")\n",
    "    print(neural_network.synaptic_weights)\n",
    "\n",
    "    #training data consisting of 4 examples--3 input values and 1 output\n",
    "    training_inputs = np.array([[0,0,1],\n",
    "                                [1,1,1],\n",
    "                                [1,0,1],\n",
    "                                [0,1,1]])\n",
    "\n",
    "    training_outputs = np.array([[0,1,1,0]]).T\n",
    "\n",
    "    #training taking place\n",
    "    neural_network.train(training_inputs, training_outputs, 15000)\n",
    "\n",
    "    print(\"Ending Weights After Training: \")\n",
    "    print(neural_network.synaptic_weights)\n",
    "    \n",
    "    print('prediction',neural_network.think(np.array([1, 0, 0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "bec4bf1c-8a5b-4c7d-9398-ba5919be7103",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "prediction [0.5]\n",
      "prediction [0.99994884]\n",
      "prediction [0.00640321]\n",
      "prediction [0.44844546]\n"
     ]
    }
   ],
   "source": [
    "print('prediction',neural_network.think(np.array([0, 0, 0])))\n",
    "print('prediction',neural_network.think(np.array([1, 1, 0])))\n",
    "print('prediction',neural_network.think(np.array([0, 1, 1])))\n",
    "print('prediction',neural_network.think(np.array([0, 1, 0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "556035b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# https://python-course.eu/machine-learning/simple-neural-network-from-scratch-in-python.php\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "n_samples = 1000\n",
    "samples, labels = make_blobs(n_samples=n_samples, \n",
    "                             centers=([2.5, 3], [6.7, 7.9]), \n",
    "                             cluster_std=1.4,\n",
    "                             random_state=0)\n",
    "                             \n",
    "colours = ('green', 'magenta', 'blue', 'cyan', 'yellow', 'red')\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "\n",
    "for n_class in range(2):\n",
    "    ax.scatter(samples[labels==n_class][:, 0], samples[labels==n_class][:, 1], \n",
    "               c=colours[n_class], s=40, label=str(n_class))\n",
    "plt.xlabel('$x_1$')\n",
    "plt.ylabel('$x_2$');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "61866e2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from collections import Counter\n",
    "\n",
    "class Perceptron:\n",
    "    \n",
    "    def __init__(self, \n",
    "                 weights,\n",
    "                 bias=1,\n",
    "                 learning_rate=0.3):\n",
    "        \"\"\"\n",
    "        'weights' can be a numpy array, list or a tuple with the\n",
    "        actual values of the weights. The number of input values\n",
    "        is indirectly defined by the length of 'weights'\n",
    "        \"\"\"\n",
    "        self.weights = np.array(weights)\n",
    "        self.bias = bias\n",
    "        self.learning_rate = learning_rate\n",
    "        \n",
    "    @staticmethod\n",
    "    def unit_step_function(x):\n",
    "        if  x <= 0:\n",
    "            return 0\n",
    "        else:\n",
    "            return 1\n",
    "        \n",
    "    def __call__(self, in_data):\n",
    "        in_data = np.concatenate( (in_data, [self.bias]) )\n",
    "        result = self.weights @ in_data\n",
    "        return Perceptron.unit_step_function(result)\n",
    "    \n",
    "    def adjust(self, \n",
    "               target_result, \n",
    "               in_data):\n",
    "        if type(in_data) != np.ndarray:\n",
    "            in_data = np.array(in_data)  # \n",
    "        calculated_result = self(in_data)\n",
    "        error = target_result - calculated_result\n",
    "        if error != 0:\n",
    "            in_data = np.concatenate( (in_data, [self.bias]) )\n",
    "            correction = error * in_data * self.learning_rate\n",
    "            self.weights += correction\n",
    "            \n",
    "    def evaluate(self, data, labels):\n",
    "        evaluation = Counter()\n",
    "        for sample, label in zip(data, labels):\n",
    "            result = self(sample) # predict\n",
    "            if result == label:\n",
    "                evaluation[\"correct\"] += 1\n",
    "            else:\n",
    "                evaluation[\"wrong\"] += 1\n",
    "        return evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a9c0c35e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counter({'correct': 784, 'wrong': 16})\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "res = train_test_split(samples, labels, \n",
    "                       train_size=0.8,\n",
    "                       test_size=0.2,\n",
    "                       random_state=1)\n",
    "\n",
    "train_data, test_data, train_labels, test_labels = res \n",
    "\n",
    "p = Perceptron(weights=[0.3, 0.3, 0.3],\n",
    "               learning_rate=0.8)\n",
    "\n",
    "for sample, label in zip(train_data, train_labels):\n",
    "    p.adjust(label,\n",
    "             sample)\n",
    "\n",
    "evaluation = p.evaluate(train_data, train_labels)\n",
    "print(evaluation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "39267976",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.4277135509226737 10.516023065099064\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# plotting learn data\n",
    "colours = ('green', 'blue')\n",
    "for n_class in range(2):\n",
    "    ax.scatter(train_data[train_labels==n_class][:, 0], \n",
    "               train_data[train_labels==n_class][:, 1], \n",
    "               c=colours[n_class], s=40, label=str(n_class))\n",
    "    \n",
    "# plotting test data\n",
    "colours = ('lightgreen', 'lightblue')\n",
    "for n_class in range(2):\n",
    "    ax.scatter(test_data[test_labels==n_class][:, 0], \n",
    "               test_data[test_labels==n_class][:, 1], \n",
    "               c=colours[n_class], s=40, label=str(n_class))\n",
    "\n",
    "\n",
    "    \n",
    "X = np.arange(np.max(samples[:,0]))\n",
    "m = -p.weights[0] / p.weights[1]\n",
    "c = -p.weights[2] / p.weights[1]\n",
    "print(m, c)\n",
    "ax.plot(X, m * X + c )\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "414b4576-e824-4867-8e5a-d2b2b2d315a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://beckernick.github.io/neural-network-scratch/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "45281d83-d622-4f8a-901e-8ee437d3badc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://towardsdatascience.com/neural-networks-forward-pass-and-backpropagation-be3b75a1cfcc"
   ]
  }
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