Handwritten Digit Recognition
using Multilayer Neural Network

Sneha Reddy, Tanishka Vegunta

of Information Technology, Chaitanya Bharathi Institute of Technology,
Hyderabad, India



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of Handwriting by humans may seem as a very easy task but when done by a
machine, it is a very complex one. It is unproductive for humans to spend a lot
of time trying to recognize characters in order to analyze any collected data.

Our main focus should be on analyzing the data rather than trying to recognize
the characters. Apart from this, the manual recognition of characters may not
yield the right results since it may vary from person to person. 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 training a neural network. In this paper, we
discuss the recognition of handwritten digits taken from the MNIST data set and
check the accuracy of our implementation. This is done by training a neural
network using stochastic gradient descent and backpropagation.



Digit recognition, Backpropagation, Mini batch
Stochastic Gradient



is a form of writing peculiar to a person with variations in size, shape of
letters, spacing between letters. There are different styles of handwriting
including cursive, block letters, calligraphy, signature etc. This makes the
task of recognizing handwritten characters complex when using traditional rule
based programming. The task becomes more natural when it is approached from a
machine learning perspective by using neural networks. According to Tom
Mitchell “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.”1

neural network consists of neurons which are simple processing units and there
are directed, weighted connections between these neurons.

For a
neuron j, propagation function receives the outputs of other neurons and
transforms them in consideration of the weights into the network input that can
be further processed by the activation function. 2

batch gradient descent used in the paper is a combination of batch gradient
descent and stochastic gradient descent algorithms. It calculates model error
rate by splitting data set into small batches.

backpropagation algorithm used in this paper is used for adjusting the weights
in the neural network. The algorithm works by comparing the actual output and
the desired output for a given input and calculates error value. The weights
are adjusted based on the error value. The error is first calculated at the
output layer and then distributed for the other layers.



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 3 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. 3

mnist data set example

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

The output of each neuron 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 and backpropagation.

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 for a number of epochs. The labels generated for the training data in
each epoch are compared to the actual labels and cost function is calculated. 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. Starting from the output layer and moving
backwards, the biases and weights between connections are adjusted.  The digits are labelled based on which neuron has
the highest activation out of the output layer neurons.

After training the network during each epoch,
the trained network is tested using the 10,000 test images. The labels
generated by the neural network are compared to the class labels given in the
MNIST test data. The number of correctly generated labels is identified.



2 Results

The above results are obtained when the number
of epochs is set to 30, the mini batch size is 10 and the learning rate is 3.0.

The accuracy is calculated by identifying the number of correctly identified
images out of the 10,000 test images in the MNIST data set. The given results
are taken as the best out of five trials.

The accuracy peaks at 95.00 % at the 28th
epoch. The accuracy increases rapidly in the beginning with each successive
epoch. The accuracy becomes steady after a certain point and it continues with
approximately the same accuracy.



Neural networks are an effective technique for
identification of handwritten digits. The accuracy of a neural network in
handwriting recognition is quite high and they can still achieve higher
accuracy by optimizing certain parameters. In the current implementation using
mini batch stochastic gradient descent and backpropagation, an accuracy of 95%
was obtained in one of the trial runs.



Thanks to our project guide Ms K. Sugamya, CBIT.



1 Machine Learning: Hands-On for Developers and Technical Professionals

2 A Brief
Introduction to Neural Networks : David Kriesel




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