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CHAPTER 5

SOFTWARE DEFECTS CLASSIFICATION USING

FB-MLP NEURAL NETWORK

5.1 Introduction

High quality of software is ensured by Software reliability and

Software quality assurance. Both these concepts are drawn in

throughout the software development and maintenance process. The

activities like the performance analysis, functional tests, quantifying

time and budget along with measurement of metrics are used to

ensure quality [24]. In addition; code reviews, key personnel

assignment and automatic test-case generation are the other

strategies that are applied to reach the high reliability [19].

Time, budget and mean time to failure are some of the factors

with which software quality is gauged. Software quality becomes too

expensive when Alpha and Beta testing is used to improve the quality

of software, though achieving zero defects is not possible. So software

quality modeling deals not only with the software being of desired

quality and defect free to the possible extent but also keeps budget

and time in control. Quantifiable software metrics used in defect

prediction models are successful in predicting defects in modules.

Defect prediction models are based on comparing two variables; one

independent variable captured in the form of process metric and one

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dependent variable which indicates whether there could be fault or

not in the module. Researchers use independent variables either from

previous projects or from the current project and use it in the model

to predict fault in the module.

When it is not possible to replace legacy systems, the

enhancement of predicting is widely practised. It is also cost effective

method of maintaining legacy systems.

5.2 Proposed Neural Network model – Fuzzy Bell Multi Layer

Perceptron Neural Network (FB-MLP Neural Network)

The proposed neural network Fuzzy Bell Multi Layer Perceptron

(FB-MLP) Neural network is a modification of existing Multi layer

perceptron (MLP) model wherein with the introduction of bell function,

a fuzzy logic based hidden layer exploiting the advantages of

membership function.

Fuzzy logic advantages:

The main advantage of fuzzy logic is that it mimics human decision

making to handle vague concepts and ability to deal with imprecise or

imperfect information. And the ability to rapid compute due to its

intrinsic parallel processing nature. Fuzzy logic resolves conflicts by

collaboration, propagation and aggregation. It also handles improved

knowledge representation and uncertainty reasoning, modeling of

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complex, non-linear problems and natural language

processing/programming capability

Fuzzy logic limitations:

Though fuzzy logic finds numerous applications it is highly

abstract and heuristic and thus need experts for rule discovery (data

relationships). The major disadvantage is the lack of self-organizing &

self-tuning mechanisms of neural networks.

Advantages of Neural network:

The main advantage of neural networks is that there is no need

to know data relationships. It has self-learning capability and self-

tuning capability. Neural networks are applicable to model various

systems.

Limitations of Neural network:

Critics of NN say neural network is a "garbage in garbage out"

system, which is extreme. The limitations faced by neural network are

that it is unable to handle linguistic information and cannot manage

imprecise or vague information. The inability to combine numeric data

with linguistic or logical data is another major disadvantage of neural

network. It is difficult to reach global minimum even by complex BP

learning and relys on trial-and-errors to determine hidden layers and

nodes.

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Neurofuzzy:

Neurofuzzy refers to the combination of fuzzy set theory and neural

networks with the advantages of both. Neuro fuzzy can handle any

kind of information (numeric, linguistic, logical, etc.). It can manage

imprecise, partial, vague or imperfect information and resolve conflicts

by collaboration and aggregation self-learning, self-organizing and

self-tuning capabilities. There is no need of prior knowledge of

relationships of data and mimics human decision making process.

Fast computation using fuzzy number operations is obtained in

neurofuzzy systems.

5.2.1 Methodology

The proposed neural network consists of two layers with the

first layer being a tanh activation function and the second layer

containing the bell fuzzy activation function. Figure 5.1 shows the

scaled down version of the proposed model. Table 5.1 shows the

actual input neurons, hidden neurons and other parameters of the

proposed model.

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Figure 5.1 : The proposed MLP model

Multilayer Perceptrons (MLPs) are feed forward neural networks

trained with the standard backpropagation algorithm. MLP can be

trained to learn to transform input data into a preferred response, and

are widely used for modeling prediction problems (K. Hornik, et al.,

1989) [48]. Backpropagation computes the sensitivity of the output

with respect to each weight in the network, and modifies each weight

by a value that is proportional to the sensitivity.

Suppose the total number of hidden layers is L. The input layer

is considered as layer 0. Let the number of neurons in hidden layer l

be Nl, l = 1,2,. . . . L. Let l

ijw represents the weight of the link between

the jth neuron of the l − 1th hidden layer and ith neuron of the lth

hidden layer, and l

i be the bias parameter of ith neuron of the lth

Output Input layer

Hidden layer with tanh activation

Weight

kijw

( )ju n

( )y n

Hidden layer with proposed Bell fuzzy

activation and fuzzy membership

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hidden layer. Let xi represent the ith input parameter to the MLPNN.

Let 1

iy

be the output of ith neuron of the lth hidden layer, which can be

computed according to the standard MLPNN formulas as

LlNiywfy l

l

i

l

j

l

ij

N

j

l

i

l

,...,1,,...1,.1

1

1

,,,...,1, 0

0

NNNixy xxii

where f(.) is the activation function. Let vki represent the

weight of the link between the ith neuron of the Lth hidden layer and

the kth neuron of the output layer, and βk be the bias parameter of the

kth output neuron. The outputs of MLPNN can be computed as,

1

.LN

L

k ki i k

i

y v y

1,......, yk N

A neural network model can be developed through a process

called training. Suppose the training data consists of Np sample pairs,

{ (xp; dp), p=1, 2, . . . N}, where xp and dp are Nx- and Ny-dimensional

vectors representing the inputs and the desired outputs of the neural

network, respectively. Let w be the weight vector containing all the Nw

weights of the neural network. The objective of training is to find w

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such that the error between the neural network predictions and the

desired outputs are minimized, minE(w) where

p yN

p

N

k

pkppk dwxywE1 1

2)),((2

1)(

pN

p

p we1

),(2

1

and dpk is the kth element of vector dp, ypk (xp,w) is the kth output

of the neural network when the input presented to the network is xp.

The term ep(w) is the error in the output due to the pth sample.

The backpropagation algorithm applies a correction jiw n

to

the synaptic weight jiw n

during the nth iteration. The correction

jiw n applied to

jiw n is defined by the delta rule:

ji

ji

e nw n

w n

where is the learning-rate parameter of the backpropagation

algorithm. The negative represents the gradient descent in weight

space to reduce the value of the error.

A good training algorithm will cut down the training time, while

accomplishing better accuracy. Thus training process is a significant

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feature of the ANNs, where representative examples of the information

are continuously presented to the network so that it can incorporate

this information within its structure.

The Fuzzy Bell Multi Layer Perceptron (FB-MLP) Neural network

proposed in this paper uses the criteria specified in Table 5.1.

Table 5.1: Design metrics of the proposed Fuzzy Bell Multi Layer

Perceptron (FB-MLP) Neural network model

Parameters Values

Input Neuron 20

Output Neuron 1

Number of Hidden Layer 2

Number of processing elements – first layer 6

Transfer function of first hidden layer tanh

Learning rule momentum

Number of processing elements-second layer 2

Transfer function of second hidden layer bellfuzzy

Learning Rule of hidden layer Momentum

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The fuzzy bell membership function is given by

F(x)= 12

0

21

1w

w

wx

Where x is the input and wi is the weight.

The membership function of the proposed method is derived

using the input membership function illustrated in Figure 5.2 and

5.3. The definition point is shown in table 5.2 and table 5.3.

Figure 5.2 : Input membership function

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Table 5.2 : Definition points of input membership function.

Term Name Definition Points (x, y)

very_low (0, 1) (0.16666, 1) (0.33334, 0)

(1, 0)

Low (0, 0) (0.16666, 0) (0.33334, 1)

(0.5, 0) (1, 0)

medium (0, 0) (0.33334, 0) (0.5, 1)

(0.66666, 0) (1, 0)

High (0, 0) (0.5, 0) (0.66666, 1)

(0.83334, 0) (1, 0)

very_high (0, 0) (0.66666, 0) (0.83334, 1)

(1, 1)

Figure 5.3 : Weight membership function

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Table 5.3 : Definition points of weight membership function.

Term Name Definition Points (x, y)

very_negative (0, 1) (0.16666, 1) (0.33334, 0)

(1, 0)

negative (0, 0) (0.16666, 0) (0.33334, 1)

(0.5, 0) (1, 0)

Zero (0, 0) (0.33334, 0) (0.5, 1)

(0.66666, 0) (1, 0)

positive (0, 0) (0.5, 0) (0.66666, 1)

(0.83334, 0) (1, 0)

very_positive (0, 0) (0.66666, 0) (0.83334, 1)

(1, 1)

The output membership function obtained is shown in figure

5.4 with the definition point for output illustrated in Table 5.4.

Figure 5.4 : Output membership function

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Table 5.4 : Definition points of output membership function

Term Name Definition Points (x, y)

very_low (0, 0) (0.125, 1) (0.25, 0)

(1, 0)

Low (0, 0) (0.125, 0) (0.25, 1)

(0.375, 0) (1, 0)

medium_low (0, 0) (0.25, 0) (0.375, 1)

(0.5, 0) (1, 0)

medium (0, 0) (0.375, 0) (0.5, 1)

(0.625, 0) (1, 0)

medium_hig

h

(0, 0) (0.5, 0) (0.625, 1)

(0.75, 0) (1, 0)

High (0, 0) (0.625, 0) (0.75, 1)

(0.875, 0) (1, 0)

very_high (0, 0) (0.75, 0) (0.875, 1)

(1, 0)

The rules' 'if' part describes the situation, for which the rules

are designed. The 'then' part describes the response of the fuzzy

system in this situation. The degree of support (DoS) is used to weigh

each rule according to its importance. Using Mean of Maximum

defuzzification the rules obtained are shown in table 5.5. The 3-D plot

of the same is shown in Figure 5.6. Table 5.5 shows the relationship

between linguistic input and the membership function. Rules

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generated improve the processing time as the membership function

reduces the data dimension.

Table 5.5 : Rules generated using Fuzzy system with Degree of support (DoS)

IF THEN

X W DoS out

very_low very_negative 0.21 very_low

very_low very_negative 0.36 low

very_low very_negative 0.41 medium_low

very_low very_negative 0.64 medium

very_low very_negative 0.82 medium_high

very_low very_negative 0.16 high

very_low very_negative 0.52 very_high

very_low Negative 0.86 very_low

very_low Negative 0.51 low

very_low Negative 0.14 medium_low

very_low Negative 0.16 medium

very_low Negative 0.87 medium_high

very_low Negative 0.26 high

very_low Negative 0.68 very_high

very_low Zero 0.78 very_low

very_low Zero 0.41 low

very_low Zero 0.24 medium_low

very_low Zero 0.56 medium

very_low Zero 0.71 medium_high

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IF THEN

very_low Zero 0.69 high

very_low Zero 0.59 very_high

very_low Positive 0.63 very_low

very_low Positive 0.09 low

very_low Positive 0.95 medium_low

very_low Positive 0.24 medium

very_low Positive 0.57 medium_high

very_low Positive 0.00 high

very_low Positive 0.98 very_high

very_low very_positive 0.13 very_low

very_low very_positive 0.30 low

very_low very_positive 0.93 medium_low

very_low very_positive 0.02 medium

very_low very_positive 0.92 medium_high

very_low very_positive 0.94 high

very_low very_positive 0.56 very_high

Low very_negative 0.43 very_low

Low very_negative 0.82 low

Low very_negative 0.65 medium_low

Low very_negative 0.85 medium

Low very_negative 0.63 medium_high

Low very_negative 0.30 high

Low very_negative 0.30 very_high

Low Negative 0.58 very_low

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IF THEN

Low Negative 0.46 low

Low Negative 0.59 medium_low

Low Negative 0.40 medium

Low Negative 0.25 medium_high

Low Negative 0.79 high

Low Negative 0.63 very_high

Low Zero 0.19 very_low

Low Zero 0.51 low

Low Zero 0.24 medium_low

Low Zero 0.26 medium

Low Zero 0.20 medium_high

Low Zero 0.92 high

Low Zero 0.05 very_high

Low Positive 0.61 very_low

Low Positive 0.37 low

Low Positive 0.41 medium_low

Low Positive 0.81 medium

Low Positive 0.11 medium_high

Low Positive 0.92 high

Low Positive 0.09 very_high

Low very_positive 0.20 very_low

Low very_positive 0.34 low

Low very_positive 0.11 medium_low

Low very_positive 0.80 medium

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IF THEN

Low very_positive 0.38 medium_high

Low very_positive 0.09 high

Low very_positive 0.07 very_high

Medium very_negative 0.16 very_low

Medium very_negative 0.14 low

Medium very_negative 0.76 medium_low

Medium very_negative 0.74 medium

Medium very_negative 0.27 medium_high

Medium very_negative 0.69 high

Medium very_negative 0.61 very_high

Medium Negative 0.36 very_low

Medium Negative 0.09 low

Medium Negative 0.80 medium_low

Medium Negative 0.82 medium

Medium Negative 0.23 medium_high

Medium Negative 0.56 high

Medium Negative 0.56 very_high

Medium Zero 0.02 very_low

Medium Zero 0.38 low

Medium Zero 0.32 medium_low

Medium Zero 0.24 medium

Medium Zero 0.20 medium_high

Medium Zero 0.91 high

Medium Zero 0.38 very_high

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IF THEN

Medium Positive 0.54 very_low

Medium Positive 0.62 low

Medium Positive 0.40 medium_low

Medium Positive 0.38 medium

Medium Positive 0.85 medium_high

Medium Positive 0.70 high

Medium Positive 0.39 very_high

Medium very_positive 0.84 very_low

Medium very_positive 0.64 low

Medium very_positive 0.42 medium_low

Medium very_positive 0.28 medium

Medium very_positive 0.12 medium_high

Medium very_positive 0.69 high

Medium very_positive 0.29 very_high

High very_negative 0.52 very_low

High very_negative 0.44 low

High very_negative 0.26 medium_low

High very_negative 0.41 medium

High very_negative 0.55 medium_high

High very_negative 0.58 high

High very_negative 0.93 very_high

High Negative 0.65 very_low

High Negative 0.45 low

High Negative 0.77 medium_low

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IF THEN

High Negative 0.19 medium

High Negative 0.48 medium_high

High Negative 0.55 high

High Negative 0.41 very_high

High Zero 0.46 very_low

High Zero 0.49 low

High Zero 0.98 medium_low

High Zero 0.80 medium

High Zero 0.77 medium_high

High Zero 0.07 high

High Zero 0.74 very_high

High Positive 0.02 very_low

High Positive 0.58 low

High Positive 0.42 medium_low

High Positive 0.84 medium

High Positive 0.75 medium_high

High Positive 0.14 high

High Positive 0.27 very_high

High very_positive 0.19 very_low

High very_positive 0.27 low

High very_positive 0.82 medium_low

High very_positive 0.45 medium

High very_positive 0.16 medium_high

High very_positive 0.63 high

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IF THEN

High very_positive 0.67 very_high

very_high very_negative 0.71 very_low

very_high very_negative 1.00 low

very_high very_negative 0.85 medium_low

very_high very_negative 0.92 medium

very_high very_negative 0.09 medium_high

very_high very_negative 0.19 high

very_high very_negative 0.46 very_high

very_high Negative 0.44 very_low

very_high Negative 0.94 low

very_high Negative 0.10 medium_low

very_high Negative 0.19 medium

very_high Negative 0.91 medium_high

very_high Negative 0.13 high

very_high Negative 0.91 very_high

very_high Zero 0.97 very_low

very_high Zero 0.88 low

very_high Zero 0.52 medium_low

very_high Zero 0.01 medium

very_high Zero 0.13 medium_high

very_high Zero 0.29 high

very_high Zero 0.05 very_high

very_high Positive 0.01 very_low

very_high Positive 0.07 low

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IF THEN

very_high Positive 0.61 medium_low

very_high Positive 0.76 medium

very_high Positive 0.70 medium_high

very_high Positive 0.10 high

very_high Positive 0.39 very_high

very_high very_positive 0.96 very_low

very_high very_positive 0.77 low

very_high very_positive 0.87 medium_low

very_high very_positive 0.23 medium

very_high very_positive 0.94 medium_high

very_high very_positive 0.77 high

very_high very_positive 0.99 very_high

Figure 5.5: Plot of the inputs vs the output

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The learning capability and the generalization capability of the

proposed neural network model is calculated using the performance

measure of the mean square error(MSE). The MSE is given by

EN

yO

MSE

E

J

n

I

ijij

0 0

2

where

E is the number of processing elements.

N is the number of examplars.

O is the desired output for examplar i at processing element j.

Y is the obtained output for examplar i at processing element j.

The tanh will squash the range of each neuron between -1 and 1. The

tanh activation function is given by

where i is the sum of the input patterns.

5.3 Results and Discussions

The proposed FB-MLP neural network algorithm was implemented

using Visual Studio and the classification accuracy measured. Figure

5.7 shows the plot of MSE vs Epoch for various alpha (learning rate)

and momentum values.

tanh( )i i

i i

e ei

e e

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Figure 5.6 : MSE versus No.of Epoch

From figure 5.6 it is seen that that for a very high learning rate of 0.3 (

typical values being 0.001 to 1) and 0.6 momentum ( Normal values

between 0 to 1) the convergence is fast and efficient with as low as

150 iterations.

The classification accuracy obtained along with the accuracy

obtained from previous chapter is tabulated in Table 5.6 and Figure

5.7.

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Table 5.6 : Classification accuracy for Random tree, CART and

BL regression Vs FB-MLP on KC1 dataset

KC1 dataset with

proposed

Normalization

Random tree 94.55

CART 96.79

Bayesian logistic

regression 95.67

Existing MLP 94.28

Proposed FB- MLP 98.2

The proposed method classification accuracy improves over existing

MLP network by 3.92% which is considerable. However the

convergence of the proposed method is faster due to fuzzification.

Figure 5.7 : The classification accuracies obtained and compared with

other methods.

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The sensitivity and specificity plot is shown in figure 5.8

Figure 5.8 : The sensitivity and specificity

The sensitivity and specificity of the proposed method converges

very efficiently. This is highly desirable as the variance is extremely

low and the capability of the software to detect faulty modules is

extremely high. The proposed model performance is better than other

techniques found in literature.

5.4 Conclusion

In this chapter it was proposed to implement a modified Multi

Layer Perceptron Neural Network (MLP-NN) for software defect

classification based on metrics that can be easily measured from

software modules. The proposed method is compared with other

methods found in literature and is shown in Figure 5.9.

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Figure 5.9 : Proposed method compared with other methods

found in literature.