ABSTRACT with an aim to determine the characters

ABSTRACT

 

Recognition of
Handwriting by humans may seem as a very easy task but when done by a machine
is a very complex one. It is impossible for humans to expend so much of their
time to interpret characters apart from them analyzing the collected data. Our
main focus should be on analyzing the data rather than trying to interpret the
data in the first place. Apart from this, the manual interpretation of data may
not yield the right results since it may wary from person to person and hence it
is not accurate to a great extent and may take a lot of time and energy.
Algorithms using neural networks have made this task a lot easier and more
accurate. Therefore neural networks have been utilized with an aim to determine
the characters by recognizing them using algorithms, which use various rules
for prediction of handwritten characters. In this paper we discuss the recognition of handwritten
digits taken from the MNIST data set and calculate the efficiency of our
algorithm.

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Keywords

 

Introduction

 

Handwriting is a form
of writing peculiar to a person which it varying in size, shape of letters,
spacing between letters. There are different styles of handwriting including
cursive, block letters, calligraphy, signature etc.It makes the task of
recognizing handwritten characters a bit complex for neural networks since it
has to predict the characters based on its ability to learn rather than being
explicitly programmed.

Arthur Samuel and Tom
Mitchell offer the definitions of machine learning. An informal definition given
by Arthur Samuel is “the field of study that gives computers the ability
to learn without being explicitly programmed.” The more modern definition
is given by Tom Mitchell states: “A computer program is said to learn from
experience E with respect to some class of tasks T and performance measure P,
if its performance at tasks in T, as measured by P, improves with experience
E.”

Proposed Methodology

Digit recognition is done by training a multi-layer
feedforward neural network by using mini batch stochastic gradient descent and
backpropagation algorithm.

The MNIST data set obtained from link1 contains a
modified version of the original training set of 60,000 images. The original
training set is split into a training set with 50,000 examples and a validation
set with 10,000 examples. This set is then used to train the neural network. Each image is represented
as numpy 1-dimensional array of 784 float values between 0 and 1. The labels
are numbers between 0 and 9 indicating which digit the image represents. link1

 

The
neural network is an artificial neural network with sigmoid neurons. Therefore,
the output of each neuron is calculated using the sigmoid function.

The output is given as. Where, w is the
weight, b is the bias and x is the input.

Initially, the weights and biases of the neural
network are initialized randomly using Gaussian distribution. They are later
adjusted by applying mini batch stochastic gradient descent.

 

The training data is split into a number of mini
batches. In each epoch, the training data is shuffled and split into mini
batches of a fixed size and gradient descent is applied. The neural network is
trained over a number of epochs. The gradient of the cost function is calculated
by using the backpropagation algorithm. This calculated gradient is then used
to update the weights and biases of the neural network

 

 

Results

The settings of hyerparameters,

On taking epochs=30, mini-batch size=10 and learning
rate=3.0, we get the following accuracy for 10,000 test images in the MNIST
data set.

On taking epochs=20, mini-batch size=15 and learning
rate=2.8, we get the following accuracy for 10,000 test images in the MNIST
data set.