Convolutional Neural Network — A Bird’s eye view with an implementation

What is Convolution?

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function that expresses how the shape of one is modified by the other.
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This operation is used in several areas such as probability, statistics, computer vision, natural language processing, image and signal processing, engineering, and differential equations.

This operation is mathematically represented as

Check out this link for a visual understanding of the Convolution operation.

What are Artificial Neural Networks?

Artificial neural networks (ANN) or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains. Such systems “learn” to perform tasks by considering examples, generally without being programmed with any task-specific rules.
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An ANN is a collection of smaller processing units called the artificial neurons which loosely resemble the biological neuron.

Biological Neural Circuit

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A collection of interconnected circuits make a network.

Artificial Neural Network

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Now, we begin with the implementation.

Now, we begin with the implementation

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

import tflearn.data_utils as du
from keras.models import Sequential
from keras.layers import Dense, Dropout, Flatten, Conv2D, MaxPool2D
from keras.optimizers import RMSprop
from keras.preprocessing.image import ImageDataGenerator
from sklearn.metrics import confusion_matrix

Loading the dataset

train_data = pd.read_csv('../input/csvTrainImages 13440x1024.csv', header = None)
train_label = pd.read_csv('../input/csvTrainLabel 13440x1.csv', header = None)
test_data = pd.read_csv('../input/csvTestImages 3360x1024.csv', header = None)
test_label = pd.read_csv('../input/csvTestLabel 3360x1.csv', header = None)

The Dataset

The dataset used here is the Arabic Handwritten Characters Dataset.

The trainImages.csv has 1024 columns and 13440 rows. Each column represents a pixel in an image and each row represents an individual gray-scale image. The value of each pixel varies from 0 to 255.

train_data = train_data.iloc[:,:].values.astype('float32')
train_label = train_label.iloc[:,:].values.astype('int32')-1
test_data = test_data.iloc[:,:].values.astype('float32')
test_label = test_label.iloc[:,:].values.astype('int32')-1

Visualizing the dataset

def row_calculator(number_of_images, number_of_columns):
    if number_of_images % number_of_columns != 0:
        return (number_of_images / number_of_columns)+1
    else:
        return (number_of_images / number_of_columns)

def display_image(x, img_size, number_of_images):
    plt.figure(figsize = (8, 7))
    if x.shape[0] > 0:
        n_samples = x.shape[0]
        x = x.reshape(n_samples, img_size, img_size)
        number_of_rows = row_calculator(number_of_images, 4)
        for i in range(number_of_images):
            plt.subplot(number_of_rows, 4, i+1)
            plt.imshow(x[i])

The training set

display_image(train_data, 32, 16)

The test set

display_image(test_data, 32, 16)

Data preprocessing

Encoding categorical variables

In statistics, a categorical variable is a variable that can take on one of a limited, and usually fixed number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.
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In simple terms, the value of a categorical variable represents a category or class.

Why do we need to Encode Categorical Variables?

There is no meaning in performing operations on a number representing a category. So, categorical encoding needs to be done.

Check out this link on StackOverflow to understand with an example.

There are 28 letters in the Arabic alphabet. Therefore, there are 28 classes.

train_label = du.to_categorical(train_label,28)

Normalization

Normalization is done to bring the entire data into a well-defined range, preferably between 0 and 1

In neural networks, it is good idea not just to normalize data but also to scale them. This is intended for faster approaching to global minima at error surface.
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train_data = train_data/255
test_data = test_data/255

train_data = train_data.reshape([-1, 32, 32, 1])
test_data = test_data.reshape([-1, 32, 32, 1])

Reshaping is done to make the data represent a 2D image

train_data, mean1 = du.featurewise_zero_center(train_data)
test_data, mean2 = du.featurewise_zero_center(test_data)

Feature-wise Zero Center is done to zero center every sample with a specified mean. If not specified, the mean is evaluated over all samples.

Building the CNN

recognizer = Sequential()

recognizer.add(Conv2D(filters = 32, kernel_size = (5,5),padding = 'Same', activation ='relu', input_shape = (32,32,1)))
recognizer.add(Conv2D(filters = 32, kernel_size = (5,5),padding = 'Same', activation ='relu'))
recognizer.add(MaxPool2D(pool_size=(2,2)))
recognizer.add(Dropout(0.25))

recognizer.add(Conv2D(filters = 64, kernel_size = (3,3),padding = 'Same', activation ='relu'))
recognizer.add(Conv2D(filters = 64, kernel_size = (3,3),padding = 'Same', activation ='relu'))
recognizer.add(MaxPool2D(pool_size=(2,2), strides=(2,2)))
recognizer.add(Dropout(0.25))

recognizer.add(Flatten())
recognizer.add(Dense(units = 256, input_dim = 1024, activation = 'relu'))
recognizer.add(Dense(units = 256, activation = "relu"))
recognizer.add(Dropout(0.5))
recognizer.add(Dense(28, activation = "softmax"))

What is Max Pooling?

Pooling means combining a set of data. The process of combining data follows some rules. By definition, max pool takes the maximum value of a defined grid. Max pooling is used to reduce the dimensions. It can also avoid over-fitting. Check out this blog for a better understanding of Max Pooling.

What is Dropout?

Dropout is a regularization technique for reducing overfitting in neural networks by preventing complex co-adaptations on training data. It is a very efficient way of performing model averaging with neural networks. The term “dropout” refers to dropping out units (both hidden and visible) in a neural network.
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What is Flatten?

Flattening is done to convert the multidimensional data into a 1D feature vector to be used by the next layer which is the Dense Layer

What is a Dense Layer?

The Dense layer is just a layer of the Artificial Neural Network Optimizer for the CNN

What is an optimizer?

Optimization algorithms helps us to minimize (or maximize) an Objective function (another name for Error function) E(x) which is simply a mathematical function dependent on the Model’s internal learnable parameters which are used in computing the target values(Y) from the set of predictors(X) used in the model. For example — we call the Weights(W) and the Bias(b) values of the neural network as its internal learnable parameters which are used in computing the output values and are learned and updated in the direction of optimal solution i.e minimizing the Loss by the network’s training process and also play a major role in the training process of the Neural Network Model.
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optimizer = RMSprop(lr=0.001, rho=0.9, epsilon=1e-08, decay=0.0)

The optimizer used here is an RMSprop. Click here to know more about RMSprop

recognizer.compile(optimizer = optimizer , loss = "categorical_crossentropy", metrics=["accuracy"])

What is ImageDataGenerator?

An Image data generator is used to generate batches of tensor image data with real-time augmentation. This data is looped over in batches.

It is used to load the images in batches.

datagen = ImageDataGenerator(
        featurewise_center=False, 
        samplewise_center=False,  
        featurewise_std_normalization=False,
        samplewise_std_normalization=False,
        zca_whitening=False,
        rotation_range=10,
        zoom_range = 0.1,  
        width_shift_range=0.1, 
        height_shift_range=0.1,
        horizontal_flip=False,
        vertical_flip=False)

datagen.fit(train_data)

Fitting the CNN to the training data

recognizer.fit_generator(datagen.flow(train_data,train_label, batch_size=100), epochs = 30, verbose = 2, steps_per_epoch=train_data.shape[0] // 100)

Making the predictions

predictions = recognizer.predict(test_data)
predictions = np.argmax(predictions,axis = 1)

Generating a confusion matrix

A confusion matrix is a technique for summarizing the performance of a classification algorithm. Classification accuracy alone can be misleading if you have an unequal number of observations in each class or if you have more than two classes in your dataset. Calculating a confusion matrix can give you a better idea of what your classification model is getting right and what types of errors it is making.
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cm = confusion_matrix(test_label, predictions)

Calculating the accuracy

accuracy = sum(cm[i][i] for i in range(28)) / test_label.shape[0]
print("accuracy = " + str(accuracy))

An accuracy of 97% was obtained.

Seeing a CNN in action

To see the working of a CNN in real-time, check out this link. It shows the working of a CNN that is trained to recognize handwritten digits.