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Introduction

The present session will introduce the Python classes and how to create your own Artificial Neural Network (ANN) class. The class will implement the __init__, feedforward, and backpropagation methods.

Each method will be described in detail to understand the ANN’s inner work. Then, the handwriting MNIST dataset will be used to train and test our ANN.

Objectives

Learn the basics of using Python Classes
Create methods for: create, feedforward, and backpropagation
Train the ANN
Test the ANN

Classes and methods

A class defines the structure, data and methods that an object will have. There is possible to have public and private variables to operate in the methods.

Argument
Initialitation
Methods
Destroy

class Dog:
    # init method
    def __init__(self, dogName, dogAge):
        self.name = dogName
        self.age = dogAge
        pass 
    
    def status(self):
        print("The dog's name is: ", self.name)
        print("The dog's age is: ", self.age)

dog1 = Dog("firulais", 8)
dog2 = Dog("Perro", 2)
dog3 = Dog("cuadrado", 5)

dog3.status()

The dog's name is:  cuadrado
The dog's age is:  5

ANN class implementation

The next chunk of code defines the Neural Network's basic structure. We are going to implement and define the methods one at time to understand them in a better way.

class Neurona:
    # init
    def __init__():
        pass
    # feedforward (cálculo)
    def feedforward():
        pass
    # backpropagation (entrenamiento)
    def backpropagation():
        pass

Initialization or creation Method

Let’s begin with the initialization. We know we need to set the number of input, hidden and output layer nodes. That defines the shape and size of the neural network. Thus, we’ll let them be set when a new neural network object is created by using the class' parameters. That way we retain the choice to create new neural networks of different sizes with simple methods.

A good programmers, computer scientists and mathematicians, try to create more general code rather than specific code. It is a good habit, because it forces us to think about solving problems in a deeper and more general way. This means that our code can be used in more general scenarios.

Then, let us see how our code should look like:

import numpy as np

class Neurona:
    # init
    def __init__(self, inputNodes, hiddenNodes, outputNodes):
        self.inN = inputNodes
        self.hN = hiddenNodes
        self.outN = outputNodes
        ## 
        ## W = w11 w21
        self.wih = np.random.rand(self.hN, self.inN)
        self.who = np.random.rand(self.outN, self.hN)
        pass
    # feedforward (cálculo)
    def feedforward():
        pass
    # backpropagation (entrenamiento)
    def backpropagation():
        pass

At this point were are only creating an object, but the class can't do any useful yet. Also, this is a good technique to start coding somethig, by keeping it small at the begining (make commits), and then grow the methods.

Next, we should add more code to allow our ANN class finish its initialization by creating the weight matrixes.

Feedfordward method

So the next step is to create the network of nodes and links. The most important part of the network is the link weights. They’re used to calculate the signal being fed forward, the error as it’s propagated backwards, and it is the link weights themselves that are refined in an attempt to to improve the network.

For the basic NN, the weight matrix consist of:

A matrix that links the input and hidden layers, Wih, of size hidden nodes by input nodes (hn×in)
and another matrix for the links between the hidden and output layers, Who, of size on×hn (output nodes by hidden nodes)

X_h=W_{ih}I

O_h=\sigma{X_h}

For the basic NN, the weight matrix consist of:

A matrix that links the input and hidden layers, Wih, of size hidden nodes by input nodes (hn×in)
and another matrix for the links between the hidden and output layers, Who, of size on×hn (output nodes by hidden nodes)

X_h=W_{ih}I

O_h=\sigma{X_h}

Backpropagation

 \frac{\partial E}{\partial w*{jk}}= -e_j\cdot \sigma\left(\sum_i w*{ij} o*i\right) \left(1-\sigma\left(\sum_i w*{ij} o_i\right) \right) o_i

import numpy as np
class Neurona:
    # init
    def __init__(self, inputNodes, hiddenNodes, outputNodes):
        self.inN = inputNodes
        self.hN = hiddenNodes
        self.outN = outputNodes
        ## 
        ## W = w11 w21
        self.wih = np.random.rand(self.hN, self.inN)-0.5
        self.who = np.random.rand(self.outN, self.hN)-0.5
        pass
    # feedforward (cálculo)
    def feedforward(self, Inputs):
        #Xh
        self.inputs = np.array(Inputs, ndmin=2).T
        self.Xh = np.dot(self.wih, self.inputs)
        self.af = lambda x:1/(1+np.exp(-x))
        #Oh
        self.Oh = self.af(self.Xh)
        
        #Xo
        self.Xo = np.dot(self.who, self.Oh)
        #Oh
        self.Oo = self.af(self.Xo)
        #Oo
        pass
    # backpropagation (entrenamiento)
    def backpropagation(self, Inputs, Targets, Learning):
        lr = Learning
        self.inputs = np.array(Inputs, ndmin=2).T
        self.targets = np.array(Targets, ndmin=2).T
        #Xh
        self.Xh = np.dot(self.wih, self.inputs)
        self.af = lambda x:1/(1+np.exp(-x))
        #Oh
        self.Oh = self.af(self.Xh)
        
        #Xo
        self.Xo = np.dot(self.who, self.Oh)
        #Oh
        self.Oo = self.af(self.Xo)
        #Oo

        # output error
        oe = self.targets-self.Oo
        he = np.dot(self.who.T, oe)
        self.who=self.who+lr*np.dot(oe*self.Oo*(1-self.Oo), self.Oh.T)
        self.wih=self.wih+lr*np.dot(he*self.Oh*(1-self.Oh), self.inputs.T)
        pass

mynn = Neurona(3,5,3)
mynn.backpropagation([0.21, 0.39, 0.87], [0.12, 0.10, 0.99], 0.3)
mynn.who

array([[0.89962766, 0.94344371, 0.25520613, 0.50403018, 0.79841922],
       [0.46742312, 0.8497042 , 0.72150451, 0.4832481 , 0.1614701 ],
       [0.07348318, 0.74125584, 0.96294501, 0.6829789 , 0.99122929]])

mynn.backpropagation([0.21, 0.39, 0.87], [0.12, 0.10, 0.99], 0.3)
mynn.who

array([[0.88622924, 0.92904876, 0.24001207, 0.48936863, 0.78475758],
       [0.45035738, 0.83136916, 0.70215163, 0.46457349, 0.14406909],
       [0.07510425, 0.74299748, 0.96478333, 0.68475279, 0.9928822 ]])

Mnist database

data_file = open("mnist_train.csv", 'r')
data_list = data_file.readlines()
data_file.close
data_list

Output ommited due to its length

import numpy as np 
import matplotlib.pyplot as plt
values = data_list[30600].split(',')
image = np.asfarray(values[1:]).reshape((28,28))
plt.imshow(image)
plt.show()

values[0]

'1'

Training

# hyper-parameters:
inputNodes = 784
hiddenNodes = 100
outputNodes = 10
learningRate = 0.1
myANN = Neurona(inputNodes, hiddenNodes, outputNodes)

myANN.wih[:,0]

array([ 3.80810137e-01, -2.76021452e-01,  1.89578510e-01, -4.40622523e-01,
        4.49345620e-04, -2.99576867e-02,  2.88898176e-01,  1.00257001e-01,
       -1.25427321e-01, -4.10841382e-01,  1.01058830e-01, -4.19682107e-01,
       -2.61884751e-01, -4.86639132e-01, -4.10475994e-01,  4.72554845e-01,
       -2.58545906e-01,  2.12843730e-01,  4.77632343e-01,  4.85691685e-01,
       -2.21585439e-01,  1.43760970e-01, -2.23361202e-01, -3.69871226e-01,
       -1.21973032e-01, -4.29052035e-01, -3.97413451e-01,  4.65864914e-01,
       -1.26186271e-01,  2.07401026e-01,  1.05937271e-01,  1.46875776e-01,
        2.95015245e-01,  3.43457017e-02, -3.29510246e-01, -2.48072947e-01,
       -3.64935302e-01,  3.09460892e-01, -5.01871329e-02,  2.98023264e-01,
       -3.19341252e-01, -3.90225500e-02,  3.10060197e-01, -3.13901381e-01,
        3.69558936e-01, -1.38918625e-01, -4.78037558e-01,  9.24705861e-02,
       -1.34122723e-01, -8.70299561e-02, -3.93637460e-02,  3.81876093e-01,
       -8.53474718e-02, -1.29582776e-01, -4.02245397e-01, -4.56054710e-01,
        2.64854223e-02, -1.53704117e-01,  1.90609293e-01,  3.62048289e-01,
       -6.25482544e-02,  3.82745274e-01,  1.43009716e-01,  1.75700493e-01,
        4.09349632e-01, -4.89451563e-01, -9.27621754e-02,  1.41559919e-01,
        1.34585537e-01, -2.86828229e-01,  3.44307471e-01, -4.98223666e-01,
       -4.05137857e-01,  1.81890913e-01, -4.57908080e-01,  4.87169160e-01,
       -2.11761055e-01,  3.18985378e-02, -3.00127711e-01,  4.80807855e-01,
       -2.70966977e-01,  2.36741392e-02, -3.03853361e-01, -4.29846112e-02,
        5.33828969e-02,  2.18366071e-01,  2.13736555e-01, -1.15094147e-01,
       -2.41327435e-02,  3.40917056e-01,  3.76097667e-02, -5.77225150e-03,
       -3.83882298e-01, -2.31975044e-01,  2.44874629e-01,  7.90940279e-02,
       -2.92400249e-01,  4.53702317e-01,  8.09984361e-02, -4.93878547e-02])

epoch = 1
for e in range(epoch):
    for record in data_list:
        values = record.split(',')
        inputData = (np.asfarray(values[1:])/255*0.99) +0.01
        target = np.zeros(outputNodes)+0.01
        target[int(values[0])] = 0.99
        myANN.backpropagation(inputData, target, learningRate)
        pass
    pass

len(data_list)

values = data_list[30600].split(',')
inputData = (np.asfarray(values[1:])/255*0.99) +0.01
myANN.feedforward(inputData)

myANN.Oo

array([[2.42193187e-02],
       [1.11760730e-01],
       [5.09994337e-01],
       [4.44172963e-02],
       [3.37977872e-04],
       [3.97805262e-03],
       [1.06099919e-03],
       [3.15328122e-02],
       [1.33289159e-01],
       [2.44129745e-03]])

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