CHAPTER 4 MODIFIED ARTIFICIAL NEURAL NETWORKS FOR...

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43 CHAPTER 4 MODIFIED ARTIFICIAL NEURAL NETWORKS FOR IMAGE CLASSIFICATION 4.1 INTRODUCTION Image classification is one of the pattern recognition applications in which the images are classified into different categories based on some similarity measures. Several computational techniques are available in the literature for classification but Artificial Neural Network (ANN) has outperformed other automated techniques because of the various advantages such as high accuracy and quick convergence. But, an interesting fact is that these advantages are not simultaneously available in the same network. The networks such as Counter Propagation Networks (CPN) are accurate but less efficient in terms of computational complexity. On the other hand networks such as Self-Organizing Map (SOM) are less accurate but quickly converge to the results. These drawbacks are eliminated in this research work by proposing few modified neural networks which has the ability of yielding accurate results within quick time. The ability of these networks is tested in the context of abnormal MR brain image classification. Experimental results have verified the efficiency of these proposed networks in terms of the performance measures. 4.2 PROPOSED METHODOLOGY OF IMAGE CLASSIFICATION SYSTEM The framework of the proposed automated system for image classification is shown in Figure 4.1. Real-time MR brain images from four categories such as Meningioma, Astrocytoma, Metastasis and Glioma are used in this work. The details of pre-processing technique and the feature extraction techniques have been already discussed in Chapter 3.

Transcript of CHAPTER 4 MODIFIED ARTIFICIAL NEURAL NETWORKS FOR...

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CHAPTER 4

MODIFIED ARTIFICIAL NEURAL NETWORKS FOR IMAGE

CLASSIFICATION

4.1 INTRODUCTION

Image classification is one of the pattern recognition applications in which the

images are classified into different categories based on some similarity measures.

Several computational techniques are available in the literature for classification

but Artificial Neural Network (ANN) has outperformed other automated

techniques because of the various advantages such as high accuracy and quick

convergence. But, an interesting fact is that these advantages are not

simultaneously available in the same network. The networks such as Counter

Propagation Networks (CPN) are accurate but less efficient in terms of

computational complexity. On the other hand networks such as Self-Organizing

Map (SOM) are less accurate but quickly converge to the results. These

drawbacks are eliminated in this research work by proposing few modified neural

networks which has the ability of yielding accurate results within quick time. The

ability of these networks is tested in the context of abnormal MR brain image

classification. Experimental results have verified the efficiency of these proposed

networks in terms of the performance measures.

4.2 PROPOSED METHODOLOGY OF IMAGE CLASSIFICATION

SYSTEM

The framework of the proposed automated system for image classification is

shown in Figure 4.1. Real-time MR brain images from four categories such as

Meningioma, Astrocytoma, Metastasis and Glioma are used in this work. The

details of pre-processing technique and the feature extraction techniques have

been already discussed in Chapter 3.

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Figure 4.1 Framework of the image classification system

In this work, five different types of ANN are used among which two are

conventional networks and three are the proposed modified networks. The focus

is on the modified networks but the conventional networks are also implemented

to aid the comparative analysis. These networks are implemented for abnormal

MR brain image classification and the classifiers are analyzed in terms of

classification accuracy and convergence rate. The rest of the chapter is organized

as follows: Section 4.3 deals with the conventional neural networks, Section 4.4

covers the modified neural networks, Section 4.5 illustrates the experimental

results and Section 4.6 concludes the chapter by providing the highlights of this

work.

4.3 CONVENTIONAL ARTIFICIAL NEURAL NETWORKS

In this research work, the applicability of the conventional neural networks such

as CPN and SOM for MR brain image classification is explored.

Performance analysis

Image Pre-processing

(Skull removal)

Feature Extraction

(Image based)

MR brain images

CPN

classifier

SOM

classifier

MCPN

classifier

MSOM1

classifier

MSOM2

classifier

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4.3.1 Counter Propagation Neural Network

One of the prime hybrid neural networks is the CPN in which both the

supervised and unsupervised training methodology are used for weight

estimation. It consists of the input Kohonen layer which uses the “winner take-

all” strategy and the output Grossberg layer which uses the error signal for weight

adjustment. The error signal is used to update only the output layer weights unlike

BPN where error is used to update weights of both the layer. Thus, this network is

named as Counter Propagation Neural Network to show that it is contrary to the

conventional BPN.

4.3.1.1 Architecture of CPN

The CPN network consists of three layers: the input layer, the competition layer

and the output layer. The configuration of the network is as follows: number of

neurons in the input layer is ‘n’, number of neurons in the competition layer is

‘N’, number of neurons in the output layer is ‘p’. Let U be the weight matrix

between the input layer and the competition layer and V be the weight vector

between the competition layer and the output layer. In this work, the number of

input layer neurons is 8 which are equal to the number of input features. The

number of output layer neurons is 4 which are equal to the number of output

classes. The number of hidden layer neurons is fixed to be 8 to maintain

uniformity between the CPN and Modified CPN (MCPN) which will be discussed

in section 4.4.1.1. The topology of the conventional CPN is shown in Figure 4.2.

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Figure 4.2 Topology of CPN

4.3.1.2 Training algorithm of CPN

The training algorithm of the CPN is explained with the following procedural

steps.

Step 1 : The training instance X is presented to the input layer. Let ijU be the

arbitrary initial weights vector assigned to the links connecting input neuron ‘i’

with the competition neuron ‘j’ and jkV be the arbitrary weights vector assigned to

the links connecting competition neuron ‘j’ and output neuron ‘k’. The Euclidean

distance jD between the weight vector U and the input vector X is calculated

using the following formula

jXUXUD iijij .......21212

=1, 2... N (4.1)

Step 2 : Each neuron in the competition layer is allowed to compete with the

other neurons and the node with the shortest Euclidean distance wins. The output

of the winning node is set to 1 and the rest to 0. Thus, the output of the jth

node in

the competition layer is

0.1jZ if jD is minimum

.........0.0jZ Otherwise (4.2)

.

.

.

.

.

.

.

.

.

. 8

1

2

1

2

8

1

2

4

X

Inp

ut

X

U

Ou

tpu

t

Y

V

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Step 3 : The weight adjustment between the input layer and the competition layer

is given by

j

t

ij

t

ij

t

ij ZUxUU

1

(4.3)

where ‘t’ is the iteration number and ‘ ’ is the learning coefficient.

Step 4 : The weight adjustments for the output layer is given by

j

t

jk

t

jk

t

jk ZVTVV

1

(4.4)

Step 5: This process is repeated for the specified number of iterations and the

stabilized weight matrices are observed.

The number of iterations used for the practical implementation is approximately

1800 and the value of the learning coefficient is 0.7. Though this hybrid network

has been enjoying the merits of both the methodologies, there are some serious

setbacks which limits its practical applications. CPN networks are sufficiently

accurate but the high accuracy is achieved at the cost of high computational

complexity. The computational complexity also increases with the increase in the

number of layers. Also, the accuracy is dependent on the number of iterations

which again raises serious doubts about the robustness of the system. The

accuracy of the results differs with change in the number of iterations which again

has lead to the problem of local minimum. Hence, suitable modifications must be

performed to improve the efficiency of the conventional systems.

4.3.2 Self-Organizing Map

One type of the unsupervised neural networks which posses the self-organizing

property is called Kohonen Self-Organizing Map. Similar to statistical clustering

algorithms, these Kohonen networks are able to find the natural groupings from

the training data set. As the training algorithm follows the “winner take-all”

principle, these networks are also called as competitive learning networks.

4.3.2.1 Architecture of SOM

The topology of the Kohonen self-organizing map is represented as a 2-

Dimensional, one-layered output neural network. Each input neuron is connected

to each output neuron. The number of input layer neurons is based on the

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dimension of the training pattern. During the process of training, the input

patterns are fed into the network sequentially. The ‘trained’ classes are

represented by the output layer neurons and the center of each class is stored in

the connection weights between input and output layer neurons. The architecture

of SOM is shown in Figure 4.3.

Figure 4.3 Topology of SOM

4.3.2.2 Training algorithm of SOM

The kohonen self-organizing map makes use of the competitive learning rule

for training the network. The “winner-take all” principle is used in this network in

which a winner neuron is selected based on the performance metrics. The weight

adjustment is performed for the winner neurons and also the neighboring neurons

of the winner neuron. The weights of all other neurons remain unchanged. The

neighboring neurons are determined using a radius around the winner neuron. In

this work, unit radius is selected which shows the weights of the winner neuron

alone is adjusted during the process. A detailed training algorithm has been given

below:

Step 1: The weight vectors are randomly initialized.

Step 2: While stopping condition is false, do steps 3 to 6.

Step 3: For each ‘j’(output layer neurons), the Euclidean distance is computed.

jD 2 i

iij xw (4.5)

Step 4: The index j is determined such that jD is a minimum.

Step 5: Update the winner neuron’s weight using the rule

.

.

.

.

.

.

. 8

1

2

1

2

4

X

Inp

ut

X

W

Ou

tpu

t Y

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oldwxoldwneww ijijiji (4.6)

‘xi’ denotes the intensity values of input data set.

‘α’ denotes the learning rate.

Step 6: Test for stopping condition which is defined by the maximum number of

iterations.

The training process is carried out with the training image set. The entire process

is repeated for the specified number of iterations in the algorithm. The weights

yielded by the network in the last iteration are stored as the stabilized weights.

Further, the testing images are used to estimate the performance of the neural

network. The number of iterations used for the practical application is 1100 and

the value of the learning rate is 0.7. Like CPN, SOM is also purely dependent on

the number of iterations for convergence due to the lack of standard convergence

condition. This has lead to incorrect weight matrix which ultimately affects the

classification accuracy. Though the complexity is less, these are seldom preferred

for practical applications because of the low quality results. Hence, suitable

modifications must be performed to enhance the accuracy of the network without

compromising the convergence rate.

4.4 MODIFIED ARTIFICIAL NEURAL NETWORKS

The analysis of the conventional ANN has clearly shown the necessity for

modifications in the existing ANN to eliminate the demerits associated with them.

In this work, three modified ANN are proposed with an objective to achieve

performance enhancement over the conventional ANN.

4.4.1 Modified CPN

A modified approach of CPN is implemented in this work which guarantees high

accuracy within low convergence time. An iteration-free technique is used in the

proposed approach for weight estimation which ultimately minimizes the

computational time required for the convergence of the system. Since the weights

are estimated without any iteration, the robustness of the system is highly

guaranteed. The problem of local minimum is also eliminated which improves the

efficiency of the modified approach to high extent. Thus, this innovative approach

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yields high accuracy and superior convergence rate simultaneously which is the

main objective of this work.

Suitable modifications in the architecture and the training algorithm are

performed in the conventional CPN to formulate the MCPN. In terms of

architecture, the number of neurons in the input layer is equal to the number of

neurons in the hidden layer. In terms of training, the algorithm used in the MCPN

does not follow the conventional iterative procedure. Since the number of neurons

in the hidden layer is equal to the number of training sets in MCPN, an

assignment methodology is followed for weight estimation in the network which

overcomes the above mentioned drawbacks of the conventional system. Initially,

the input features are normalized to the range between 0 and 1. The distribution

method of normalization is used in this work which involves the mean and the

standard deviation of the input data. Then, the weights between the input layer

and the hidden layer are automatically assigned to the input and the weights of the

link between the hidden layer and the output layer is assigned to the desired

output. Thus, the weights are estimated without any iterative training procedures.

Since MCPN is devoid of training, the convergence time is highly reduced

besides maintaining substantial accuracy which is evident from the experimental

results. Thus, MCPN function essentially as a partial self-organizing look-up

table and is taught in response to a set of “illustrations” with the help of a

“recording algorithm” rather than through “training examples” with the help of

“learning algorithm”.

4.4.1.1 Architecture of MCPN

The architecture of MCPN is same as Figure 4.2. In this work, an “assignment”

methodology is used for weight estimation and hence the dimensions of the

network must be carefully analyzed. As per the training methodology, the number

of neurons in the hidden layer must be an integral multiple of the number of

classes. The number of hidden layer neurons cannot be lesser than the input layer

neurons and hence an equal number of neurons are used for both the layers. The

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practical implementation is much easier when equal number of neurons is

selected for both the layers. Thus, architecture of size 8-8-4 is used in this work.

4.4.1.2 Training algorithm of MCPN

The training algorithm is summarized as follows:

Step 1:The weight matrices (U and V ) are randomly initialized. Initially, each

component of the training instance X is presented to the input layer. The

neighborhood function of the hidden layer is defined by the Euclidean distance

jd between the weight vector U and the input vector X is estimated using

Equation (4.1).

Step 2: For each input vector, each neuron in the hidden layer competes with the

other neurons and the neuron with the shortest Euclidean distance wins. The

weight adjustment between the input and the hidden layer selects the weight

vector mU such that

j

m UXUX min (4.7)

Here, mU indicates the associated weights of the winning neurons that are closest

approximations to the input X . The minimum value for the right hand side of

Eqn. (11) is obtained when

mUX = 0 (4.8)

i.e., mUX (4.9)

Step 3: Similarly, for the weight adjustments between the hidden layer ‘j’ and the

output layer ‘k’, the weight vector mV is selected such that

k

m VTVT min (4.10)

Here, mV indicates the associated weights of the winning neurons that are closest

approximations to the targetT . The minimum value for the right hand side of

Equation (4.10) is obtained when

TVm (4.11)

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Thus the weight vectors ijU and jkV are calculated without any training algorithm.

The winner node changes for every input vector from different categories. This

process is repeated with all the training images from the four categories. The final

set of weight matrices is stored in an array. These weights are further used for the

testing process. In the testing process, a new test vector is given as input and the

output is calculated using the two weight matrices. Each output neuron

corresponds to a class and hence the input image belongs to the class for which

the corresponding neuron yields the maximum value. This procedure is repeated

for all the test images and the classification accuracy is calculated. Thus, this

network is computationally fast since the training methodology follows an

iteration free technique. The estimated weight values yield promising output

accuracy which is evident from experiment results.

In conventional networks such as CPN, the weight adjustment process occurs

across all connection weights for given learning coefficients. Also, a large

number of iterations are required for the connection weights for stability. For each

training instance, a new set of connection weights minimizing the system error

must be calculated. Moreover, the stabilized weights do not guarantee a global

minimum for the system error. These drawbacks are eliminated in MCPN.

4.4.2 Modified SOM1

The proposed MSOM1 is framed by performing suitable modifications in the

conventional SOM network. The same architectural changes and training

procedural changes of MCPN is adopted for MSOM1 also. In terms of

architecture, the number of input layer neurons is equal to the number of output

layer neurons. Unlike MCPN, this modification has limited the size of the input

feature vector. For example, in a 4-level classification system, the number of

input features are only 4 since the number of output neurons is 4. Since less

number of input features yield low accuracy, an alternative arrangement to

increase the size of the input feature vector is used. More than single neuron is

allotted for each class and hence more number of neurons is used in the output

layer which ultimately paves way for a larger input feature set. In terms of

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training, the same iteration-free methodology adopted for MCPN is followed for

weight estimation which ultimately reduces the computational complexity of the

system. Thus, the proposed system is an iteration-free technique which proves to

be more efficient than the conventional SOM systems.

4.4.2.1 Architecture of MSOM1

The architecture used in this work is a single layered network with an input layer

and an output layer. The number of input features is 8 and the number of classes

is 4 for this application. Since the number of neurons in both the layers is equal,

the number of output layer neurons is increased to 8 with 2 neurons representing

each class. The architecture is same as that of Figure 4.3 except for the number of

neurons in the output layer.

4.4.2.2 Training algorithm of MSOM1

A different methodology is employed for the weight calculation procedure for the

MSOM1. The weights of the winner neurons are estimated using an assignment

methodology rather than the conventional iterative procedures. This method has

also avoided the necessity for other parameters such as the learning rate,

momentum, etc. The number of computational operations are also significantly

reduced which improves the efficiency of the system. The training algorithm used

for MSOM1 is explained through the following procedural steps:

Step 1: The random weights are initialized.

Step 2: For each j (output layer neurons), the difference between the weights and

the input vector is computed using Equation (4.5).

Step 3: Find index j such that jD is a minimum.

Step 4: The weight adjustment between the input and the output layer selects the

weight vector mW such that

j

m WXWX min (4.12)

Here, mU indicates the associated weights of the winning neurons that are closest

approximations to the input X . The minimum value is obtained for the right hand

side of Equation (4.12) when

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mWX = 0 (4.13)

i.e., mWX (4.14)

Thus, the weight matrix is obtained without any necessity for the iterations. These

weights are further used for testing the MSOM1 with the test images. The number

of misclassified images is observed and the overall classification accuracy is

calculated. The drawbacks of the conventional SOM are eliminated in this

proposed approach. The significant factor is that the proposed approach is devoid

of any iterations which has made the MSOM1 highly efficient than the

conventional SOM.

4.4.3 Modified SOM2

Another significant drawback of the SOM is the lack of standard convergence

condition. In the second modified approach, suitable modifications are performed

to incorporate the standard convergence condition. This objective is achieved by

concatenating the Hopfield neural network to the conventional SOM. The energy

function used in the Hopfield neural network is used as the convergence condition

for the Modified SOM2.

4.4.3.1 Architecture of MSOM2

The framework of the proposed Modified SOM2 is shown in Figure 4.4.

Figure 4.4 Topology of Modified SOM2

The proposed Modified SOM2 is a 2-layer network with the input layer, hidden

layer and an output layer. The number of neurons in the input layer is equal to the

number of input features. The number of neurons in the hidden and output layer is

also eight in order to satisfy the following two conditions. Since the output layer

represents the Hopfield layer, there shall not be any one-to-one connection

1

2

8

1 1

2 2

8 8

W U

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between the hidden layer and the output layer to ensure stability of the network.

Hence, equal number of neurons is used. Secondly, the feedback from the output

layer neuron is given to the corresponding input layer neuron. Thus, the number

of neurons used in all the layers must be same in the proposed network.

4.4.3.2 Training algorithm of MSOM2

The training procedures of the conventional SOM and the Hopfield networks are

used in this modified network. The training inputs are given to the input layer and

the hidden layer output is calculated using the “winner take-all algorithm” in a

single step. These outputs are given as inputs to the Hopfield layer where the

output values of each neuron is estimated with the help of fixed set of weights

‘U’. These outputs are further fed back to the input layer and the winner neuron’s

weights of the previous iteration are changed using the weight adjustment

equations. With the new set of weights, the output values are once again

calculated and given as input to the Hopfield layer. This procedure continues till

the change in energy value becomes zero. The following mathematical steps

illustrate the training algorithm.

Step 1: The weights are randomly initialized.

Step 2: The input features are supplied to the input layer and output values are

determined using Equation (4.5).

Step 3: Determine j for which jD is minimum. This neuron is selected as the

winner neuron and stored separately.

Step 4: The weight matrix of output layer is calculated using the following

equations.

kjjk DDu (4.15)

kjuu kjjk ; (4.16)

ju jj ;0 (4.17)

Step 5: The output value of Hopfield layer is calculated using following formula

kj

jjkk DuNET (4.18)

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kNET

k eOUT

11 (4.19)

Step 6: The Liapunov energy function E for the continuous Hopfield network is

further calculated using the output values.

kj

j k

jk OUTDuE 21 (4.20)

This equation is framed from the standard energy function for continuous systems

but without the external inputs. This equation is specified by Hopfield in his

earlier research works.

Step 7: The change in energy is estimated by partially differentiating the above

equation with respect to kOUT . The change in energy is given by

k

ji

jjk OUTDuE

(4.21)

= kk OUTNET (4.22)

Step 8: The values kOUT are fed back to the input layer if rE where ‘r’ is the

error tolerance value. The value of ‘r’ in this work is 0.01.

Step 9: The weights of the winner neuron of the previous iteration is then adjusted

using the following equation

twOUTtwtw ijkijij 1 (4.23)

Step 10: After weight adjustment, the new values of jD is calculated with the new

weights and Steps 3-7 is repeated till the convergence condition ( 01.0E ) is

reached. The number of iterations required for convergence is 1430.

The above training methodology is repeated for training images from all

categories and the final weight matrix ‘W’ represents all the four stored patterns.

The testing process is then carried out with the stabilized weights and the

performance measures are estimated for the testing images. In this method, since

the convergence condition is available, the weights of this method are more

accurate than the weights obtained by conventional SOM.

In this work, accuracy is given more emphasis than the computational

complexity. The accuracy is higher than the conventional SOM since better

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stabilized weights are obtained through this technique. Even though the

mathematical analysis is slightly complex, the convergence time of this approach

is nominal for practical applications due to the reduction in the number of

iterations.

4.5 EXPERIMENTAL RESULTS AND DISCUSSIONS

The experiments are carried out on the Pentium processor with speed 1.66 GHz

and 1 GB RAM. The software used for the implementation is MATLAB (version

7.0), developed by Math works Laboratory. The five classifiers are trained and

tested individually with the dataset shown in Table 4.1.

Table 4.1 Dataset for brain image classification

Tumor type Training data Testing data No.of

images/class

Meningioma 60 82 142

Glioma 60 76 136

Astrocytoma 60 64 124

Metastasis 60 78 138

Total abnormal

images

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The efficiency of the classifiers is analyzed in terms of performance measures

such as Classification Accuracy (CA), sensitivity and specificity. A brief analysis

on the computational complexity and the convergence rate is also performed in

this work. These performance measures are estimated for each abnormal category

and then the average measures of all the four categories is determined to judge the

performance of the classifier. The same process is repeated for all the five

classifiers. The formulae for calculating these performance measures are given

by:

FNFPTNTPTNTPCA (4.24)

FNTPTPySensitivit (4.25)

FPTNTNySpecificit (4.26)

In the above equations, TP corresponds to True Positive, TN corresponds to

True Negative, FP corresponds to False Positive and FN corresponds to False

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Negative. These parameters for a specific category, say, meningioma are as

follows: TP=True Positive (an image of ‘meningioma’ type is categorized

correctly to the same type), TN=True Negative (an image of ‘Non-meningioma’

type is categorized correctly as ‘Non-meningioma’ type), FP= False Positive (an

image of ‘Non-meningioma’ type is categorized wrongly as ‘meningioma’ type)

and FN=False Negative (an image of ‘meningioma’ type is categorized wrongly

as ‘Non-meningioma’ type). ‘Non-meningioma’ actually corresponds to any of

the three categories other than ‘meningioma’. Thus, ‘TP and TN’ corresponds to

the correctly classified images and ‘FP and FN’ corresponds to the misclassified

images The same parameters are determined for all the categories by replacing

‘meningioma’ in the above definitions with other abnormal categories. Thus,

different parameter values are obtained for each class and also for the different

classifiers. These parameters are estimated from the confusion matrix which

provides the details about the false and successful classification of images from

all categories for each classifier.

In the confusion matrix, the row-wise elements correspond to the four

categories and the column-wise elements correspond to the target class associated

with that abnormal category. Hence, the number of images correctly classified

(TP) under each category is determined by the diagonal elements of the matrix.

The row-wise summation of elements for each category other than the diagonal

elements corresponds to the ‘FN’ of that category. The column-wise summation

of elements for each category other than the diagonal elements corresponds to the

‘FP’ of that category. Similarly, ‘TN’ of the specific category is determined by

summing the elements of the matrix other than the elements in the corresponding

row and column of the specific category. The results of the individual classifiers

are discussed in the next section.

The computational complexity of the system is determined by the amount of

mathematical calculations. The computational calculations must be minimal for

an efficient system. In this section, an analysis is performed between the

classifiers based on the number of mathematical operations. The convergence

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time is directly proportional to the number of operations. The following 2-step

procedure is used to determine the number of mathematical operations for each

classifier.

Step 1: Sub-divide the training algorithm into small segments.

Step 2: Determine the number of mathematical calculations in each segment.

Only the number of calculations is used to determine the computational

complexity. Even though all the mathematical operations are not unique, the

impact of these operations on the modified networks is almost zero except for

Modified SOM2. Hence, it is sufficient to estimate the number of calculations

rather than the effect of these operations.

The convergence time is also dependent on the number of iterations. The

number of iterations required by each network for convergence is different since

the mode of convergence is different. In this work, the convergence time is

calculated based on the number of iterations required for convergence. If the

network converge quickly, then the convergence time is less and vice-versa.

Hence, the analysis is performed with non-uniform iterations but with uniform

values for convergence parameters.

4.5.1 Results of SOM

The performance analysis is performed individually for the SOM classifier.

4.5.1.1 Accuracy measures of SOM

The confusion matrix of the conventional SOM is shown in Table 4.2.

Table 4.2 Confusion Matrix of SOM

Class 1 Class 2 Class 3 Class 4

Meningioma 58 9 8 7

Glioma 7 52 8 9

Astrocytoma 7 7 44 6

Metastasis 8 6 6 58 Class 1=Meningioma; Class 2=Glioma; Class 3 = Astrocytoma; Class 4=Metastasis

The misclassification rate is quite high for the conventional SOM which is

evident from Table 4.2. The performance measures calculated from the confusion

matrix is shown in Table 4.3.

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Table 4.3 Performance Measures of SOM

TP TN FP FN Sensitivity Specificity CA (%)

Meningioma 58 196 22 24 0.71 0.89 85

Glioma 52 202 22 24 0.68 0.90 85

Astrocytoma 44 214 22 20 0.69 0.91 86

Metastasis 58 200 22 20 0.74 0.90 86

Average value 0.71 0.90 86

The low classification accuracy results of the SOM are clearly shown in Table

4.3. The lack of standard convergence condition is the main drawback of this

network. The stopping condition is quite unclear which results in un-stabilized

weights. The testing process with these weights ultimately fails which accounts

for the inaccurate results. These networks are also forced to depend on iterations

since these networks do not have the assistance of the target vector.

4.5.1.2 Computational complexity and convergence rate of SOM

The mathematical operations involved in the training algorithm are as follows:

(a) Euclidean distance calculation

This technique involves basically 1 subtraction and 1 multiplication

operations. For an input vector of size a, the number of operations required for

calculating the distance of 1 neuron is equal to 2a. Since the Euclidean distance is

calculated for p output layer neurons, the number of mathematical operations

increases to 2ap.

(b) Weight adjustment procedure between the input and the hidden layer

This technique involves 1 subtraction, 2 multiplications and 1 addition

operations. These operations are performed individually for a matrix of size a×p

and hence the total number of operations increases to 4ap.

Thus, the total number of operations involved in SOM is 6ap. This

conventional network is also an iterative network and hence the total number of

operations increases to ‘t(6ap)’. Thus, the complexity of the algorithm is based on

the number of neurons in each layer and the number of iterations used in the

training process. The convergence time requirement is approximately 650 CPU

seconds. Even though the training is performed beyond the specified number of

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iterations, there is no significant improvement in the accuracy. Thus, the

conventional SOM is quick but the results are less accurate.

4.5.2 Results of CPN

The accuracy measures and the convergence rate analysis are discussed in this

section.

4.5.2.1 Accuracy measures of CPN

The confusion matrix of the conventional CPN is shown in Table 4.4.

Table 4.4 Confusion Matrix of CPN

Class1 Class 2 Class 3 Class 4

Meningioma 71 4 3 4

Glioma 3 65 3 5

Astrocytoma 4 3 55 2

Metastasis 2 5 4 67

The level of misclassification has been slightly reduced in comparison to the

conventional SOM. The performance measure analysis is shown in Table 4.5.

Table 4.5 Performance Measures of CPN

TP TN FP FN Sensitivity Specificity CA (%)

Meningioma 71 209 9 11 0.86 0.95 93

Glioma 65 212 12 11 0.85 0.94 92

Astrocytoma 55 226 10 9 0.86 0.95 93

Metastasis 67 211 11 11 0.86 0.95 92

Average value 0.86 0.95 92.5

The overall performance measures are better than the conventional SOM. The

reason is the presence of the supervised mode of training in the output layer. But,

this accuracy is again dependent on the number of iterations which limits the

robustness of the system. Hence, iteration independent CPN can lead to better

efficiency measures.

4.5.2.2 Computational complexity and convergence rate of CPN

The mathematical calculations involved in the training algorithm are:

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(a) Euclidean distance calculation

This technique involves basically 1 subtraction and 1 multiplication

operations. For an input vector of size ‘a’, the number of operations required for

calculating the distance of 1 neuron is equal to 2a. Since the Euclidean distance is

calculated for ‘N’ hidden neurons, the number of mathematical operations

increases to 2aN.

(b) Weight adjustment procedure between the input and the hidden layer

This technique involves 1 subtraction, 2 multiplications and 1 addition

operations. These operations are performed individually for a matrix of size a×N

and hence the total number of operations increases to 4aN.

(c) Weight adjustment procedure between the hidden and the output layer

This technique involves 1 subtraction, 2 multiplications and 1 addition

operations. These operations are performed individually for a matrix of size N×p

and hence the total number of operations increases to 4Np. In this calculation, p

denotes the size of the output layer neurons.

The total number of basic mathematical operations per iteration is given by

6aN+4Np. Since CPN is iterative in nature, the system must be trained for

sufficient number of iterations. If ‘t’ is the number of iterations, then the overall

mathematical operations increase to t(6aN+4Np). Usually, the value of ‘t’ is very

high which implicates the high computational complexity of CPN. The time

requirement for CPN is approximately 1280 CPU seconds. In comparison to

SOM, the number of required iterations ‘t’ is high for the conventional CPN.

Thus, CPN is computationally heavy but the results are quite accurate.

4.5.3 Results of MCPN

The MCPN is also tested with the same dataset and the results are tabulated in

this section.

4.5.3.1 Accuracy measures of MCPN

The confusion matrix of the MCPN is shown in Table 4.6.

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Table 4.6 Confusion Matrix of MCPN

Class1 Class 2 Class 3 Class 4

Meningioma 80 1 0 1

Glioma 1 72 1 2

Astrocytoma 3 1 60 0

Metastasis 0 2 2 74

The number of correctly classified images is significantly high which is evident

from Table 4.6. The performance measures of the MCPN are displayed in Table

4.7.

Table 4.7 Performance Measures of MCPN

TP TN FP FN Sensitivity Specificity CA (%)

Meningioma 80 214 4 2 0.97 0.98 98

Glioma 72 220 4 4 0.95 0.98 97

Astrocytoma 60 233 3 4 0.94 0.99 98

Metastasis 74 219 3 4 0.95 0.98 98

Average value 0.95 0.98 98

The superior classification accuracy of the proposed MCPN is clearly depicted in

Table 4.7. The weight matrices calculated using the proposed approach have

yielded a substantial increase in the classification accuracy. One of the main

reasons is that the modified network is an iteration-free technique. Hence, the

weight matrices are almost error-free unlike conventional CPN in which the

quality of the output weight matrices is dependent on iterations. The requirement

for exact selection of modifiable parameters such as learning rate is also avoided

in this network. Thus, the modified approach is much superior to the CPN in

terms of classification accuracy.

4.5.3.2 Computational complexity and convergence rate of MCPN

The Euclidean distance calculation procedure alone is involved in the training

algorithm of MCPN since there is no necessity for the weight adjustment

equations. Hence, the number of mathematical operations is only 2aN. The

difference between the output layer weights and the target vector is also

calculated in this algorithm which accounts for another 2Np operations. Hence,

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the total number of operations is given by 2aN+2Np. The impact of the iterations

is also completely minimized since MCPN is an iteration-free technique. The

convergence rate is typically less than 2 seconds. Thus, high accuracy within

quick time is guaranteed in MCPN.

4.5.4 Results of Modified SOM1

The results of the Modified SOM1 are discussed in this section.

4.5.4.1 Accuracy measures of MSOM1

The confusion matrix of the Modified SOM1 is shown in Table 4.8.

Table 4.8 Confusion Matrix of Modified SOM1

Class 1 Class 2 Class 3 Class 4

Meningioma 75 2 2 3

Glioma 2 68 3 3

Astrocytoma 3 2 57 2

Metastasis 2 2 4 70

The level of misclassification is reduced in comparison to the conventional SOM.

The performance measure analysis is shown in Table 4.9.

Table 4.9 Performance Measures of Modified SOM1

TP TN FP FN Sensitivity Specificity CA (%)

Meningioma 75 211 7 7 0.91 0.96 95

Glioma 68 218 6 8 0.89 0.97 95

Astrocytoma 57 227 9 7 0.89 0.96 94

Metastasis 70 214 8 8 0.90 0.96 95

Average value 0.90 0.96 95

The improvement in the correct classification rate of Modified SOM1 over the

conventional SOM is evident from Table 4.9. A more accurate weight matrix is

obtained since the training methodology is different from the conventional

system. The probability of the results being trapped in local minima is low since

the training algorithm does not involve any iterative convergence equations.

4.5.4.2 Computational complexity and convergence rate of MSOM1

The Euclidean distance calculation procedure alone is involved in the training

algorithm of MSOM1 since there is no necessity for the weight adjustment

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equations. Hence, the total number of mathematical operations is only 2ap. The

number of operations required for the Modified SOM1 is very much lesser than

the other networks proposed in this work. The convergence rate is typically less

than 1 second. Thus, the proposed network has provided quick convergence

without compromising the accuracy.

4.5.5 Results of Modified SOM2

The accuracy measures and the convergence rate analysis are detailed in this

section.

4.5.5.1 Accuracy measures of MSOM2

The confusion matrix of the Modified SOM2 is shown in Table 4.10.

Table 4.10 Confusion Matrix of Modified SOM2

Class1 Class 2 Class 3 Class 4

Meningioma 80 1 0 1

Glioma 0 74 1 1

Astrocytoma 1 1 62 0

Metastasis 0 1 1 74

The number of misclassified images has been highly reduced in comparison to

other classifiers. The performance measures of the Modified SOM2 are displayed

in Table 4.11.

Table 4.11 Performance Measures of Modified SOM2

TP TN FP FN Sensitivity Specificity CA (%)

Meningioma 80 215 1 2 0.98 0.99 99

Glioma 74 219 3 2 0.98 0.98 98

Astrocytoma 62 232 2 2 0.97 0.99 99

Metastasis 74 220 2 2 0.97 0.99 99

Average value 0.98 0.99 99

The classification accuracy of conventional SOM is enhanced due to the inclusion

of the Hopfield network in the architecture and training algorithm. Thus, the basic

drawback (low accuracy) of conventional SOM has been eliminated by this

modified network. Though iteration dependent, the presence of the stable

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convergence condition is the main reason for the high accuracy of the proposed

approach.

4.5.5.2 Computational complexity and convergence rate of MSOM2

The computational complexity is slightly higher than the other modified networks

due to the inclusion of the Hopfield network. But, the complexity is still lesser

than the conventional multi-layer neural networks. The various operations

involved in this network are:

(a) Euclidean distance calculation

The input layer is similar to the Kohonen layer and hence the number of required

operations is ‘2aN’.

(b) Weight adjustment for the hidden layer neurons.

Basically, the number of mathematical operations involved is 1 subtraction, 1

multiplication and 1 addition. Hence, the total number of operations is ‘3aN’.

(c) Calculation of output value and energy function

But, the output value in the weight adjustment equation is determined by 2

additions, 1 multiplication and 1 division. These operations are performed in the

output layer and hence the total number of operations is ‘4Np’. The calculation of

energy values requires 2 addition operations and 2 multiplication operations

additionally. Hence, the number of mathematical operations is ‘8Np’.

The total number of operations required is‘t(5aN+8Np)’ with ‘t’ being the

number of iterations required for convergence. The complexity is higher than the

modified networks and the conventional single layer networks but it is better than

the conventional multi-layer networks. The first reason is that only one weight

adjustment equation is involved unlike two weight adjustment equations in the

conventional multi-layer networks. Another factor is that the number of iterations

required for convergence is lesser than the number of iterations required for

conventional networks. Even though computational operations required for the

algorithm is high, the convergence rate is better than the conventional multi-layer

networks. The convergence rate of this network is 990 CPU seconds. Thus, high

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accuracy is guaranteed for the proposed approach within reasonable convergence

time.

4.6 CONCLUSION

In this work, three modified networks are proposed for MR brain image

classification. The performance of these networks is analyzed in terms of

classification accuracy and convergence rate. The results of these networks are

compared with the performance measures of two conventional neural networks.

Experimental results have verified the superior nature of the proposed networks

over the conventional neural networks. The modified networks are found to

possess the capability of accurately classifying the images within nominal

convergence time which is the main objective of this work. Thus, this work has

suggested suitable alternates for the conventional neural networks for practical

medical imaging applications.