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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME
19
ECG INTERPRETATION USING BACKWARD PROPAGATION NEURAL
NETWORKS
Kritika Parganiha#1
, Prasanna Kumar Singh#2
#1
M.Tech student, Dept. of ECE, Lingayas University, Faridabad, India
#2
Associate Professor, E&C Dept., Lingayas University, Faridabad, India
ABSTRACT
Electro Cardiogram (ECG) is a non invasive technique and is used as a primary diagnostic
tool for cardiovascular diseases. ECG Signal provides necessary information about electrophysiology
of heart diseases and ischemic changes that may occur. Arrhythmias are amongst the most common
ECG abnormalities. There are various Arrhythmias like Ventricular Premature Beats, Asystole,
Couplet, Fusion beats etc. This information can be extracted from ECG but its diagnosis simply
depends on the experience of the physician. Previously many methods have been used for the
analysis and automisation of analysis. In this paper we make use of MATLAB based Artificial
Neural Networks (ANN) to judge whether the patient is normal or not. We use Back Propagation
Neural Networks “Levenberg Marquardt (LM) Algorithm” by taking the ECG input in the form of
digital time series signal. These results are compared with previous neural network techniques and
found that the method proposed in this paper gives best results.
Keywords: Arrhythmia, MATLAB, Artificial Neural Networks, Radon Transform,
Back Propagation, Levenberg Marquardt Algorithm.
1. INTRODUCTION
Heart related problems are the major concern now-a-days. Monitoring heart helps to
determine the abnormalities of a cardiac patient. Electrocardiography (ECG) is used for this purpose
in the hospitals since a long time. ECG plays an important role in healthcare and with time its
volume has increased by a large amount.
ECG is printed in a thermal paper and is kept in hospitals for further diagnosis and as records.
This requires immense storage space and manpower requirement which is time consuming and not
economical. This can be eliminated by converting.
INTERNATIONAL JOURNAL OF ELECTRONICS AND
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 5, Issue 4, April (2014), pp. 19-24
© IAEME: www.iaeme.com/ijecet.asp
Journal Impact Factor (2014): 7.2836 (Calculated by GISI)
www.jifactor.com
IJECET
© I A E M E
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME
20
ECG records into digital time series signal[1]. Now these ECG samples are analysed by
experienced doctors who depending upon their knowledge predict the problems associated with
patient. This experience based analysis gives different interpretations. Hence there is a need of
system that could analyse ECG signals properly and accurately so that there is a less chance of
mistake and the problem gets spotted in its early stage.
For this purpose many works in the field of Image processing, Digital signal processing etc
has been done making use of Artificial Neural Networks [11] which has given effective results to
such complex problems.
This paper has been divided into five sections. Section 1 gives basic Introduction. Section 2
depicts the Methodology used. Section 3 gives information about the Database. Section 4 represents
the type of Input taken. Section 5 shows the Results obtained and in Section 6 we discuss the
Conclusion.
2. METHODOLOGY
The database provided by MIT-BIH Arrhythmia database [3] regarding different kinds of
heart rhythm abnormalities for different class of patients is used for training, testing and validation of
neural networks. In this paper, 12 lead ECG signals were recorded at 25mm/sec and printed in
thermal paper. These ECG trace are scanned at 600dpi (dots per inch) black and white images and
stored in jpeg format. Then using Radon Transform the skewness of images is detected and
corrected, which may have incurred during scanning. The de-skewed or corrected image is then
adaptively binarized by choosing local thresholds and then it is filtered by morphological filters. In
this work Otsu’s algorithm [9] has been performed for image adaptive binarization. Finally the peaks
of ECG signal input are detected and these peaks are used as an input for ‘ECG Classification Using
Neural Networks’. Then the parameters namely, Standard Deviation, Correlation and Wavelet
Coefficient are extracted which helps to decide the performance of the algorithm. The features are
then encrypted and testing process is done to determine whether the signal is normal or abnormal.
3. DATABASE
The database used in this paper to train and test the neural network, is the standard MIT-BIH
arrhythmia database [3].The input database consists of 48 half-hour excerpts of two channel
ambulatory ECG recordings, obtained from subjects studied by BIH Arrhythmia Laboratory. The
recordings were digitized and then taken as input in the network.
4. INPUT
The input for network was selected keeping in view following criteria[2]:
a. The input must be of standard size so that it is neither too small nor too large.
b. The input must be arranged in such a way that the R-peak in QRS complex is placed at centre
of signal cycle.
International Journal of Electronics and Communication Engineering & Techno
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp.
Figure 1: Schematic representation of normal ECG waveform
Here in figure 1, A clear P wave
of P waves may suggest atrial fibrillation,
is the largest voltage deflection of approximately 10
and gender. The voltage amplitude of QRS complex may also give information about the cardiac
disease. T wave represents ventricular repolarization
5. RESULTS
The following table represents the results obtained using
Propagation Neural Networks.
Table 1: Back Propagation Neural Network Design Analysis Results
‘TRAINLM’ Training Algorithm
HN
Time ( in Sec)
Epochs ( Max: 30)
MSE (0.0001)
Gradient
Result
HN- Hidden neurons, representing the number of neurons in the Hidden layer
Time- Maximum Training Time.
MSE- Mean Squared Error the error goal being fixed at 0.0001 and hence here the
0.0001 is being tabulated.
TRAINLM-Levenberg Marquardt Back propagation training algorithm.
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976
6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME
21
Schematic representation of normal ECG waveform
P wave before the QRS complex represents sinus rhythm.
of P waves may suggest atrial fibrillation, junction rhythm or ventricular rhythm. The
is the largest voltage deflection of approximately 10–20 mV but may vary in size depending on age,
and gender. The voltage amplitude of QRS complex may also give information about the cardiac
epresents ventricular repolarization.
sents the results obtained using Levenberg Marquardt Back
Back Propagation Neural Network Design Analysis Results
‘TRAINLM’ Training Algorithm
10
Time ( in Sec) 0:00:02
Epochs ( Max: 30) 6
MSE (0.0001) 0.00753
Gradient 0.110
Passed
Hidden neurons, representing the number of neurons in the Hidden layer.
Mean Squared Error the error goal being fixed at 0.0001 and hence here the
Levenberg Marquardt Back propagation training algorithm.
logy (IJECET), ISSN 0976 –
© IAEME
before the QRS complex represents sinus rhythm. Absence
rhythm. The QRS complex
20 mV but may vary in size depending on age,
and gender. The voltage amplitude of QRS complex may also give information about the cardiac
Levenberg Marquardt Back
Back Propagation Neural Network Design Analysis Results
Mean Squared Error the error goal being fixed at 0.0001 and hence here the difference MSE-
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME
22
The following images are analysis plots for this work, each representing different properties
about the network.
Figure 2: Training Process Results
In the above figure 2, less number of epochs means that network is a good learner and it
learns in small repetitions. Less time means network achieving goal easily and in short span of time.
Performance indicates final Mean Square Error (MSE) achieved in which lower value corresponds to
higher network accuracy.
Figure 3: Mean Squared Error ( MSE) Plot
In Figure 3, the Mean Squared Error (MSE) Plot shows achieved error value. Lower value
depicts less probability of false predictions. Hence, our network achieved quite low error probability.
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME
23
Figure 4: Gradient & Validation Check Plots
In Figure 4, Lower value of Gradient plot shows that network is learning upto large extent
representing fine adjustments in weights and biases making the network more accurate and reliable
avoiding any false predictions. Validation plot represents the point where network learned
sufficiently and has passed the validation. The magnitude of the gradient and the number of
validation checks are used to terminate the training. The gradient will become very small as the
training reaches a minimum of the performance. The number of validation checks represents the
number of successive iterations that the validation performance fails to decrease.
6. CONCLUSION
This network gives quite low value of MSE and is near 0.00753 in just 6 epochs. Levenberg
Marquardt Algorithm proves to be fastest method for training moderate sized neural networks. The
network based on Back Propagation Neural network algorithm with trainlm training algorithm was
best for case of normal beat analysis giving an accuracy of about 99.9% as well as low memory
requirement. Hence this method was preferred for normal beat analysis. By this work we conclude
that by using MATLAB based Neural network design [6]; such networks can be made with
capability to understand different class of inputs which are fed to be analyzed. Though the objective
of this research was not to use MATLAB or Neural Networks and these were used to get higher
accuracy for analysis of ECG which is more useful for the mankind.
The results obtained with other methods are compared with our results [4][5][7][8][10]. Table
2 shows the comparison of results.
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME
24
Table 2: Comparison of Results
METHOD % OF CORRECT
CLASSIFICATION
Multilayer Perceptron
(MLP)
98.87
Hybrid Neuro- Fuzzy System
(HFNS)
98.68
Principal Component Analysis
(PCA)
98.73
Weightless 99.63
Our Method 99.9
These networks are not tested with the current real patients record but it will give the same
high accuracy, the network being trained and tested with sufficient number of inputs. In this research
paper, all arrhythmias are not classified by their name, they are just tested as normal or abnormal.
The classification needs to be done as the next step of the research.
REFERENCES
[1] A. R. Gomes e Silva, H.M. de Oliveira, R.D. Lins., “Converting ECG and other paper legated
biomedical maps into digital signals,” XXV Simposio Brasileiro de Telecomunicacoes,
Setembro 3-6, Recife –PE, Brasil.
[2] Ayub and Saini / International Journal of Engineering, Science and Technology, Vol. 3, No.
3, 2011, pp. 41-4.
[3] Brown G., 2006, MIT-BIH Arrhythmia database, MIT.
[4] Chickh M. A.N. Belgacem, F. Bereksi-Reguig, 2002, Neural classifier to classify ectopic
beats. Acte des IX emes rencontre de la Societe Francophone de Classification, Toulouse, le
16-18.
[5] Chow H.S,. Moody G. B., and Mark R.G.1993, Detection of ventricular ectopic beats using
neural networks, Computers in Cardiology, pp 659-662.
[6] Demuth Horward, Beale Mark, Hagan Martin, 2008, MATLAB Neural Network Toolbox,
MATHWORKS INC., MATLAB Version R2008b, October.
[7] Gao D, Kinouchi Y, Ito K, Zhao X, 2003, Neural Networks for Event extraction from Time
Series, A back propagation Algorithm Approach, Future generation , Computer System.
[8] Nadal J. and Bosson M.C.,1993, Classification of cardiac arrhythmias based on principal
component analysis and feedforward neural networks, Computers m Cardiology,
pp 341- 344.
[9] Rafael C. Gonzalez and Richard E. Woods,, “Digital Image Processing (3rd Edition)”,
Prentice Hall, 2008.
[10] Thomson D. C., Soraghan J. J, and Durrani T.S, 1993, An artificial neural-network based
SVT/VT classification system, Computers in Cardiology,(pp 333-336.
[11] Zurada, 1999, Introduction to Artificial Neural Systems, West Publishing House.
[12] Shivajirao M. Jadhav, Sanjay L. Nalbalwar and Ashok A. Ghatol, “Performance Evaluation
of Multilayer Perceptron Neural Network Based Cardiac Arrhythmia Classifier”,
International Journal of Computer Engineering & Technology (IJCET), Volume 3, Issue 2,
2012, pp. 1 - 11, ISSN Print: 0976 – 6367, ISSN Online: 0976 – 6375.

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  • 1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME 19 ECG INTERPRETATION USING BACKWARD PROPAGATION NEURAL NETWORKS Kritika Parganiha#1 , Prasanna Kumar Singh#2 #1 M.Tech student, Dept. of ECE, Lingayas University, Faridabad, India #2 Associate Professor, E&C Dept., Lingayas University, Faridabad, India ABSTRACT Electro Cardiogram (ECG) is a non invasive technique and is used as a primary diagnostic tool for cardiovascular diseases. ECG Signal provides necessary information about electrophysiology of heart diseases and ischemic changes that may occur. Arrhythmias are amongst the most common ECG abnormalities. There are various Arrhythmias like Ventricular Premature Beats, Asystole, Couplet, Fusion beats etc. This information can be extracted from ECG but its diagnosis simply depends on the experience of the physician. Previously many methods have been used for the analysis and automisation of analysis. In this paper we make use of MATLAB based Artificial Neural Networks (ANN) to judge whether the patient is normal or not. We use Back Propagation Neural Networks “Levenberg Marquardt (LM) Algorithm” by taking the ECG input in the form of digital time series signal. These results are compared with previous neural network techniques and found that the method proposed in this paper gives best results. Keywords: Arrhythmia, MATLAB, Artificial Neural Networks, Radon Transform, Back Propagation, Levenberg Marquardt Algorithm. 1. INTRODUCTION Heart related problems are the major concern now-a-days. Monitoring heart helps to determine the abnormalities of a cardiac patient. Electrocardiography (ECG) is used for this purpose in the hospitals since a long time. ECG plays an important role in healthcare and with time its volume has increased by a large amount. ECG is printed in a thermal paper and is kept in hospitals for further diagnosis and as records. This requires immense storage space and manpower requirement which is time consuming and not economical. This can be eliminated by converting. INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME: www.iaeme.com/ijecet.asp Journal Impact Factor (2014): 7.2836 (Calculated by GISI) www.jifactor.com IJECET © I A E M E
  • 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME 20 ECG records into digital time series signal[1]. Now these ECG samples are analysed by experienced doctors who depending upon their knowledge predict the problems associated with patient. This experience based analysis gives different interpretations. Hence there is a need of system that could analyse ECG signals properly and accurately so that there is a less chance of mistake and the problem gets spotted in its early stage. For this purpose many works in the field of Image processing, Digital signal processing etc has been done making use of Artificial Neural Networks [11] which has given effective results to such complex problems. This paper has been divided into five sections. Section 1 gives basic Introduction. Section 2 depicts the Methodology used. Section 3 gives information about the Database. Section 4 represents the type of Input taken. Section 5 shows the Results obtained and in Section 6 we discuss the Conclusion. 2. METHODOLOGY The database provided by MIT-BIH Arrhythmia database [3] regarding different kinds of heart rhythm abnormalities for different class of patients is used for training, testing and validation of neural networks. In this paper, 12 lead ECG signals were recorded at 25mm/sec and printed in thermal paper. These ECG trace are scanned at 600dpi (dots per inch) black and white images and stored in jpeg format. Then using Radon Transform the skewness of images is detected and corrected, which may have incurred during scanning. The de-skewed or corrected image is then adaptively binarized by choosing local thresholds and then it is filtered by morphological filters. In this work Otsu’s algorithm [9] has been performed for image adaptive binarization. Finally the peaks of ECG signal input are detected and these peaks are used as an input for ‘ECG Classification Using Neural Networks’. Then the parameters namely, Standard Deviation, Correlation and Wavelet Coefficient are extracted which helps to decide the performance of the algorithm. The features are then encrypted and testing process is done to determine whether the signal is normal or abnormal. 3. DATABASE The database used in this paper to train and test the neural network, is the standard MIT-BIH arrhythmia database [3].The input database consists of 48 half-hour excerpts of two channel ambulatory ECG recordings, obtained from subjects studied by BIH Arrhythmia Laboratory. The recordings were digitized and then taken as input in the network. 4. INPUT The input for network was selected keeping in view following criteria[2]: a. The input must be of standard size so that it is neither too small nor too large. b. The input must be arranged in such a way that the R-peak in QRS complex is placed at centre of signal cycle.
  • 3. International Journal of Electronics and Communication Engineering & Techno 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. Figure 1: Schematic representation of normal ECG waveform Here in figure 1, A clear P wave of P waves may suggest atrial fibrillation, is the largest voltage deflection of approximately 10 and gender. The voltage amplitude of QRS complex may also give information about the cardiac disease. T wave represents ventricular repolarization 5. RESULTS The following table represents the results obtained using Propagation Neural Networks. Table 1: Back Propagation Neural Network Design Analysis Results ‘TRAINLM’ Training Algorithm HN Time ( in Sec) Epochs ( Max: 30) MSE (0.0001) Gradient Result HN- Hidden neurons, representing the number of neurons in the Hidden layer Time- Maximum Training Time. MSE- Mean Squared Error the error goal being fixed at 0.0001 and hence here the 0.0001 is being tabulated. TRAINLM-Levenberg Marquardt Back propagation training algorithm. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME 21 Schematic representation of normal ECG waveform P wave before the QRS complex represents sinus rhythm. of P waves may suggest atrial fibrillation, junction rhythm or ventricular rhythm. The is the largest voltage deflection of approximately 10–20 mV but may vary in size depending on age, and gender. The voltage amplitude of QRS complex may also give information about the cardiac epresents ventricular repolarization. sents the results obtained using Levenberg Marquardt Back Back Propagation Neural Network Design Analysis Results ‘TRAINLM’ Training Algorithm 10 Time ( in Sec) 0:00:02 Epochs ( Max: 30) 6 MSE (0.0001) 0.00753 Gradient 0.110 Passed Hidden neurons, representing the number of neurons in the Hidden layer. Mean Squared Error the error goal being fixed at 0.0001 and hence here the Levenberg Marquardt Back propagation training algorithm. logy (IJECET), ISSN 0976 – © IAEME before the QRS complex represents sinus rhythm. Absence rhythm. The QRS complex 20 mV but may vary in size depending on age, and gender. The voltage amplitude of QRS complex may also give information about the cardiac Levenberg Marquardt Back Back Propagation Neural Network Design Analysis Results Mean Squared Error the error goal being fixed at 0.0001 and hence here the difference MSE-
  • 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME 22 The following images are analysis plots for this work, each representing different properties about the network. Figure 2: Training Process Results In the above figure 2, less number of epochs means that network is a good learner and it learns in small repetitions. Less time means network achieving goal easily and in short span of time. Performance indicates final Mean Square Error (MSE) achieved in which lower value corresponds to higher network accuracy. Figure 3: Mean Squared Error ( MSE) Plot In Figure 3, the Mean Squared Error (MSE) Plot shows achieved error value. Lower value depicts less probability of false predictions. Hence, our network achieved quite low error probability.
  • 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME 23 Figure 4: Gradient & Validation Check Plots In Figure 4, Lower value of Gradient plot shows that network is learning upto large extent representing fine adjustments in weights and biases making the network more accurate and reliable avoiding any false predictions. Validation plot represents the point where network learned sufficiently and has passed the validation. The magnitude of the gradient and the number of validation checks are used to terminate the training. The gradient will become very small as the training reaches a minimum of the performance. The number of validation checks represents the number of successive iterations that the validation performance fails to decrease. 6. CONCLUSION This network gives quite low value of MSE and is near 0.00753 in just 6 epochs. Levenberg Marquardt Algorithm proves to be fastest method for training moderate sized neural networks. The network based on Back Propagation Neural network algorithm with trainlm training algorithm was best for case of normal beat analysis giving an accuracy of about 99.9% as well as low memory requirement. Hence this method was preferred for normal beat analysis. By this work we conclude that by using MATLAB based Neural network design [6]; such networks can be made with capability to understand different class of inputs which are fed to be analyzed. Though the objective of this research was not to use MATLAB or Neural Networks and these were used to get higher accuracy for analysis of ECG which is more useful for the mankind. The results obtained with other methods are compared with our results [4][5][7][8][10]. Table 2 shows the comparison of results.
  • 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 19-24 © IAEME 24 Table 2: Comparison of Results METHOD % OF CORRECT CLASSIFICATION Multilayer Perceptron (MLP) 98.87 Hybrid Neuro- Fuzzy System (HFNS) 98.68 Principal Component Analysis (PCA) 98.73 Weightless 99.63 Our Method 99.9 These networks are not tested with the current real patients record but it will give the same high accuracy, the network being trained and tested with sufficient number of inputs. In this research paper, all arrhythmias are not classified by their name, they are just tested as normal or abnormal. The classification needs to be done as the next step of the research. REFERENCES [1] A. R. Gomes e Silva, H.M. de Oliveira, R.D. Lins., “Converting ECG and other paper legated biomedical maps into digital signals,” XXV Simposio Brasileiro de Telecomunicacoes, Setembro 3-6, Recife –PE, Brasil. [2] Ayub and Saini / International Journal of Engineering, Science and Technology, Vol. 3, No. 3, 2011, pp. 41-4. [3] Brown G., 2006, MIT-BIH Arrhythmia database, MIT. [4] Chickh M. A.N. Belgacem, F. Bereksi-Reguig, 2002, Neural classifier to classify ectopic beats. Acte des IX emes rencontre de la Societe Francophone de Classification, Toulouse, le 16-18. [5] Chow H.S,. Moody G. B., and Mark R.G.1993, Detection of ventricular ectopic beats using neural networks, Computers in Cardiology, pp 659-662. [6] Demuth Horward, Beale Mark, Hagan Martin, 2008, MATLAB Neural Network Toolbox, MATHWORKS INC., MATLAB Version R2008b, October. [7] Gao D, Kinouchi Y, Ito K, Zhao X, 2003, Neural Networks for Event extraction from Time Series, A back propagation Algorithm Approach, Future generation , Computer System. [8] Nadal J. and Bosson M.C.,1993, Classification of cardiac arrhythmias based on principal component analysis and feedforward neural networks, Computers m Cardiology, pp 341- 344. [9] Rafael C. Gonzalez and Richard E. Woods,, “Digital Image Processing (3rd Edition)”, Prentice Hall, 2008. [10] Thomson D. C., Soraghan J. J, and Durrani T.S, 1993, An artificial neural-network based SVT/VT classification system, Computers in Cardiology,(pp 333-336. [11] Zurada, 1999, Introduction to Artificial Neural Systems, West Publishing House. [12] Shivajirao M. Jadhav, Sanjay L. Nalbalwar and Ashok A. Ghatol, “Performance Evaluation of Multilayer Perceptron Neural Network Based Cardiac Arrhythmia Classifier”, International Journal of Computer Engineering & Technology (IJCET), Volume 3, Issue 2, 2012, pp. 1 - 11, ISSN Print: 0976 – 6367, ISSN Online: 0976 – 6375.