NOVEL FRAMEWORK FOR HANDWRITTEN
DIGIT RECOGNITION THROUGH NEURAL
NETWORKS
Manjot Kaur
Bharati Vidyapeeth’s Institute of Computer Applications and Management
(BVICAM). New Delhi (India)
E–mail: manjot.kaur97@gmail.com
Tanya Garg
Bharati Vidyapeeth’s Institute of Computer Applications and Management
(BVICAM). New Delhi (India)
E–mail: tanya.pathak@gmail.com
Ritika Wason
Bharati Vidyapeeth’s Institute of Computer Applications and Management
(BVICAM). New Delhi (India)
E–mail: rit_2282@yahoo.co.in
Vishal Jain
Bharati Vidyapeeth’s Institute of Computer Applications and Management
(BVICAM). New Delhi (India)
E–mail: drvishaljain83@yahoo.com
Recepción: 05/03/2019 Aceptación: 09/04/2019 Publicación: 17/05/2019
Citación sugerida:
Kaur, M., Garg, T., Wason, R. y Jain, V. (2019). Novel framework for handwritten digit
recognition through neural networks. 3C Tecnología. Glosas de innovación aplicadas a la pyme.
Edición Especial, Mayo 2019, pp. 448–467. doi: http://dx.doi.org/10.17993/3ctecno.2019.
specialissue2.448–467
Suggested citation:
Kaur, M., Garg, T., Wason, R. & Jain, V. (2019). Novel framework for handwritten digit
recognition through neural networks. 3C Tecnología. Glosas de innovación aplicadas a la pyme.
Special Issue, May 2019, pp. 448–467. doi: http://dx.doi.org/10.17993/3ctecno.2019.
specialissue2.448–467
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254–4143
450
ABSTRACT
The biggest challenge for natural language processing systems is to accurately
identify and classify the hand–written characters. Accurate Handwritten
Character recognition is a challenging task for humans too as the style, size
and other handwriting parameters may vary from human to human. Though a
relatively straightforward machine vision task but improved accuracy as compared
to the existing implementations is still desirable. This manuscript aims to propose
a novel neural network based framework for handwritten character recognition.
The proposed neural network based framework, transforms the raw data set to a
NumPy array to achieve image attening and feeds the same into a pixel vector
before feeding it into the network. In the neural network, the activation function
is applied to transfer the resultant value to the hidden layer where it is further
minimized through the use of minimized mean square and back propagation
algorithms before applying a stochastic gradient on the resultant mini–batches.
After a detailed study, the optimal algorithm for eective handwritten character
recognition was proposed. Initially, the framework has been simulated only on
digits through 50,000 training data samples, 10,000 validation data set and
10,000 test data set, the accuracy of 96.08.
This manuscript aims to give the reader an insight into how the proposed neural
network based framework has been applied for handwritten digit recognition. It
highlights the successful applications of the same while laying down the directions
for the enhancements possible.
KEYWORDS
Natural Language Processing, Handwritten Character Recognition, Neural
Networks, Machine Vision; Digit Recognition.
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1. INTRODUCTION
Many literate humans eortlessly recognize the decimal digit set (0–9). A sample
of the same is depicted in Figure 1 below. This natural attribute of mankind
is actually due to the seemingly simple human brain. The human brain is a
supercomputer in itself as each of its hemispheres has a visual cortex containing
140 million neurons with approximately tens of billions of connections between
them (LeCun, et al., 1990). So this supercomputer tuned by evolution over
hundreds of millions of years on this earth is superbly adapted to understand this
complex, colourful visual world.
This masterpiece–human brain can solve a tough problem like recognizing any
entity in this world in moments of seconds. The diculty bubbles up when we
attempt to automate the same task by writing a computer program and applying
computer vision for character/digit recognition (Bottou, et al., 1994) (Nielsen,
2018). Recognizing digits, in particular, is a simple task as the input is simple
black and white pixels with only 10 well–dened outputs. However, the accurate
recognition of the handwritten shapes in dierent styles, fonts etc is a complex
task in itself. A simple 6 has a loop on bottom and vertical or curved stroke on
top which can be written in varied styles and is dicult to express algorithmically
to a machine which is none other than a newborn baby born after every turn
o (Bottou, et al., 1994; Nielsen, 2018; Hegen, Demuth, & Beale, 1996). Neural
networks solve the above problem in a much simpler way (LeCun, et al., 1990;
Bottou, et al., 1994; Nielsen, 2018; Hegen, et al., 1996; Widrow, Rumelhart, &
Lehr, 1994; Mishra & Singh, 2016). The strategy is to take huge data set of black
and white handwritten digits from real life people and build a neural network to
train from those data sets and learn to recognize those digits (Shamim, Miah,
Sarker, Rana, & Jobair, 2018; Patel, Patel, & Patel, 2011; Ganea, Brezovan, &
Ganea, 2005).
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Figure 1. Sample of Handwritten Digits gure.
In Neural Networks, each node performs some simple computation on the input
and conveys a signal to next node through a connection having a weight and
a bias associated with it which amplies or diminishes a signal (Nielsen, 2018;
Shamim, Miah, Sarker, Rana, & Jobair, 2018). Dierent choices for weights and
bias results in dierent functions evaluated by networks. An appropriate learning
algorithm must be used to determine the optimal values of weights and bias
(Widrow, et al., 1994; Knerr, Personnaz, & Dreyfus, 1992).
All neural networks have these following common following attributes (Widrow,
et al., 1994; Alwzwazy, Albe–Hadili, Alwan & Islam, 2016; Matan, et al., 1990).
• A set of processing units
• A set of connections
• A computing procedure
• A training procedure
The Processing Units
The processing units in a Neural Network are the smallest units just like neurons
in a brain. These nodes work in a similar fashion and operate simultaneously.
There is no master procedure to coordinate them all (Cardoso & Wichert, 2013).
These units compute a scalar function of its input and broadcast the results to
units connected to it as output. The result is called the activation value and the
scalar function is called activation function (Widrow, et al., 1994).
There are three types of inputs:
• Input unit, which receives data from the environment as input.
• The hidden unit, which transforms internal data of network and broadcast
to the next set of units.
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• Output unit, which represents a decision as the output of all system (Widrow,
et al., 1994).
The Connections
The connections are essential to determine the topology of a neural network.
There are three types of topologies (Gattal, Djeddi, Chibani & Siddiqi, 2016):
• Unstructured networks for pattern completion.
• Layered networks for pattern association.
• Modular networks for building complex systems.
The topology used in this paper for the proposed system is layered networks
(Widrow, et al., 1994).
A Computing Procedure
Computations feed input vectors to processing units from the input layer (Sakshica
& Gupta, 2015). Then the activation value of remaining units is computed
synchronously or asynchronously. In a layered network, this is done by feedforward
propagation method. The activation functions used are mathematical functions.
The most common function is a sigmoidal function (Mishra & Singh, 2016).
A Training Procedure
Training a network implies adapting its connections according to the input
environment so the network can exhibit optimized computational behaviour for
all input patterns (Arel, Rose & Karnowski, 2010). The process used in this paper
is modifying weights and biases with respect to the desired output. The cost of
error is calculated using a mean square error method (Mishra & Singh, 2016).
2. DATA COLLECTION
Handwritten digit data set is vague in nature because they may not always
be sharp straight lines of pixels (LeCun, et al., 1990). The main goal in digit
recognition of feature extraction is to remove the ambiguity from data (Bottou,
et al., 1994; Cireşan, Meier, Gambardella & Schmidhuber, 2010). It deals with
extracting essential information from normalized images of isolated digits that
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serve as raw data in the form of vectors (Cireşan, et al., 2010). The numbers in
the images can be of dierent sizes, styles and orientation (Patel, et al., 2011).In
this study, a subset of MNIST dataset is used which contains ten thousands of
scanned images of handwritten digits from 250 people. This data is divided into
three parts, the rst part contains 50,000 images to be used as training data. The
second part is 10,000 images to be used as testing data. The third part contains
10,000 images for validation data. There are 28X28 pixels in size gray scale
images. The training set, validation set and testing set are kept distinct to help
neural network to learn from training set , validate the results from validation
test and generate output from test set (LeCun, et al., 1990; Liu, Nakashima,
Sako & Fujisawa, 2003; LeCun, et al., 1995). These are an example of digits of
MNIST dataset collected in dierent hand writings. For example – a digit 2 can
be represented in a dierent orientation with or without a loop at the bottom or
straight line or curved line at the bottom.
Figure 2. A sample set of MNIST dataset.
These are the 100 examples out of 60,000 used in the input of neural network
in this paper.
3. PROPOSED DETECTION ALGORITHM
We now discuss this feed–forward neural network that was applied in this work to
achieve highest possible accuracy in handwritten digit recognition (LeCun, et al.,
1989; Knerr, et al., 1992).
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Figure 3. Proposed Algorithm.
Above elaborates the steps of the proposed framework used in this study. The
next section details this simulation.
4. PROPOSED METHODOLOGY
A. Neural Network
Figure 3 describes the architecture of the proposed neural network. It consists of
an input layer, a hidden layer and an output layer. Each layer contains a number
of neurons represented by a sigmoid function. So, the output of each neuron lies
in the range of [0,1]. Every neurons output is determined by a weighted sum.
jwjxj w is the weight of jthneurone having x input. The sum of the weighted
sum and bias value determines the output value. The input layer consists of 784
neurons with each neuron representing each pixel value. Since each digit should
be between 0and 9. So, the output layer consists of 10 neurons represented by the
matrix (LeCun, et al., 1990; Lauer, Suen & Bloch, 2007).
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g(x) =
1
1+ e
− x
(1)
Equation 1: Sigmoid Function.
Equation 1 dened shows the sigmoid function used. Here, g(x) represents the
sigmoid function and the net value of the weighted sum is x. So, x is areal number.
If the value of x is a very large positive number then the value of g(x) will be 1.
And if the value of x is a very negative number then the value of g(x) is 0. Hence
the graph shown by sigmoid function is
Figure 4. Graph of Sigmoid function.
But the problem with sigmoid function is that the for negative values the speed
of neural networks become slow. That is in the second quadrant of the graph.
Figure 5. Neural Network Layer Architecture.
Figure 4 represents the whole multiple layered structures used in the neural
network. The input layer contains 784 neurons that are each neuron for every
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pixel. The intensity of each pixel is the input to the neurons of the rst layer. The
activation function is performed on that input and the reuniting activation value
is passed on to every neuron in the next layer. This same procedure is performed
on the next layer. The output layer having 10 neurons So, the neuron with the
highest activation value is the result. Figure 5 represents the output matrix where
each row and column represents the output of the node in the output layer.
Figure 6. Output Matrix for output Layer.
B. Gradient descent back propagation algorithm (LeCun, et al., 1990)
This algorithm helps in nding weights and biases so that output from network
approximates the ideal output for all training input x. This is done by the cost
function. The cost function is a measure of how wrong the model is in terms
of its ability to estimate the relationship between weights and biases (Widrow,
et al., 1994; Patel, et al., 2011; Ganea, et al., 2005; Lee, 1991). ((LeCun, et al.,
1990), equation 2) is also called mean squared error for the cost function.
C w,b
( )
=
1
2n
x
∑
y x
( )
− a
2
2
( )
Equation 2: Cost Function.
C(w,b) is non–negative since the sum of squared terms is always positive. If C(w,b)
is approximately equal to 0 the ideal output is equal to obtained output. So, our
algorithm is doing a good job. So, this algorithm minimizes the cost function
which is represented by a graph (Shamim, Miah, Sarker, Rana & Jobair, 2018;
Knerr et., 1992; LeCun, et al., 1989).
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Figure 7. Curve Representing the Cost Function.
Figure 7 shows the 2D curve representing the linear equation depending on the
two variables x and y same as weights and biases. Consider this curve as a valley
in the mountains to reach the minimum height we have to reach the bottom of
the valley. Similarly, if we roll down a ball from the above of the valley the ball
will roll down and reach to the lower point in the valley. Neglecting the friction
by air and ground and further physics laws of momentum.The minimum cost is
the point of the lowest point in the valley. Hence the below two equations gives
the minimum cost by partial dierentiating the cost with respect to weight and
bias. Solving this equation through this algorithm gives two ((Bottou, et al., 1994),
equations 3) for weight and bias as:
w
k
→
′
w
k
= w
k
−
η
δ
C
δ
w
k
3
( )
b
l
→ b'
l
= b
l
−
η
δ
C
δ
w
k
4
( )
Equation 3, 4: Cost with respect to weights and biases.
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Figure 8. 2D Curve Representing the Cost Function.
C. Stochastic Gradient Descent
Stochastic Gradient Descent helps in speed up the gradient descent algorithm by
dividing the training input into mini batches of each size m.
Step 1: Initialize the parameters
The cost function of this algorithm is dependent on two parameters that are
weight and bias. So, random values are initialized to weight and bias vector for
each input of neuron of each layer. The values of weights and biases are not
initialized to 0 because that will be equivalent to the deletion of connections
between the nodes.
Step 2: Feed–forward Algorithm
In this algorithm, the output from one layer is input to the next layer. That is
there are no loops and information is fed forward not backward. This is achieved
by the ((LeCun, et al., 1990), equation 5).
′
a =
σ
wa + b
( )
5
( )
Equation 5: Feed forward equation
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Here, a is the vector of activations of the second layer of neurons. To obtain
a, a is multiplied by weight matrix w and vector b of biases is added. And then
the function is applied element–wise to vector w.a+b. This is how inputs are fed
forward. This equation gives the following results
Equation 6: Output Equation
Step 3: Calculate the gradient
The gradient for output and hidden layers are obtained by updating the weights
and biases. This is done by shuing the training data and then dividing into mini
batches and then updating weights and biases for each mini batch.
Step 4: Update the weights
In the beginning, weights and biases are initialized some random values. Now,
this model gives the output using those values which is far dierent from the ideal
output. This gives a huge error. So, to reduce the error we will minimize the
cost function and get the desired values of weight and biases. This is how back
propagation works. ((LeCun, et al., 1990), equation 7) is used.
w
k
→ w'
k
= w
k
−
η
m
j
∑
δ
C
X
j
δ
w
k
7
( )
b
l
→ b'
l
= b
l
−
η
m
j
∑
δ
C
X
j
δ
b
l
8
( )
Equation 7,8: Update weights and biases.
5. EXPERIMENTAL RESULTS
The number of neurons in hidden rate and learning rate are called hyper
parameters of neural network (Gattal, et al., 2016). So, changing the number of
neurons and training the network again and again until the highest accuracy is
achieved.
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Table 1. Hidden Neurons Vs Accuracy.
Hidden Neurons Accuracy(%)
10 91.46
30 95.07
50 95.86
60 95.16
65 96.30
70 87.56
80 87.33
100 78.37
Table 1 shows the analysis of data when the network is trained with a dierent
number of neurons in the hidden layer and the accuracy they achieved. Figure
6 shows the graph of accuracy vs a number of hidden neurons. With 65 hidden
neurons, mini–batch size of 10 and learning rate of 3 the highest accuracy
achieved is at 96.30 Learning rate describes how quickly or slowly the network
learns. Low learning rate slows down the learning process but converges smoothly.
Larger learning rate speeds up the learning but may to converge. So, the desired
learning rate is decaying learning rate. Table 2 shows the analysis data with
dierent learning rate with their accuracy.Learning Rate should not be too low
or too high. If it is too low then the neural network will take time to train and if it
is too high the neural network will quickly forget the previous training and adapts
new training faster. Both of which are of no use.
Figure 9. Accuracy Vs Hidden Neurons Graph.
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Figure 10. Accuracy Vs Learning Rate Graph.
Table 2. Learning Rate Vs Accuracy.
Learning Rate Accuracy (%)
3 95.16
3.5 96.06
4 96.35
4.5 87.45
5 96.32
5.5 96.58
6 96.36
6.5 96.33
6. CONCLUSION
Performance of a neural network depends upon factors like the number of
hidden neurons, learning rate, number of layers etc which are called hyper
parameters of a network (Sakshica & Gupta, 2015; Lee, 1991). This research
paper creates experiential support to showcase the eectiveness and eciency
of the neural networks to recognize handwritten digits. The main objective of
this paper is to show the highest possible accuracy achieved for recognition of
handwritten digit using the technique of feed forward and back propagation in
neural networks. Although research is still going on in this eld in many forms of
LeNetarchitecture like LeNet–1, LeNet–4, Boosted LeNet–4.The main aim of
the paper is to implement one of the methods of various methods. This branch
of articial intelligence is to develop a better network for all kinds of data sets
with better performance.
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7. FUTURE WORK
Neural networks have been applied to many applications like character
recognition, signature recognition, and leaf decoding. The more training samples
give more accuracy of the networks. By changing the model of the network from
feed–forward to convolutional network the process can be faster and accuracy
can be improved although it must be tried for dierent activation functions.
Dropout technique which is turning o part of networks layers randomly to
increase the regularization and decrease over tting. In this case, accuracy for
training data is much higher than testing data. It can be improvised for colored
digits and can be used for code on post cards for sorting of letters. The proposed
framework in this manuscript can also be further applied to some well–dened
digit sets to accurately validate them. For example, the proposed framework in
this manuscript can be applied on zip code digits, university enrollment numbers
or mobile numbers of a given set in a given setting to automate their machine
recognition or identication.
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