International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 01, January 2019, pp. 690–698, Article ID: IJMET_10_01_070
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INSIGHT TO MUTUAL INFORMATION AND
MATRIX FACTORIZATION WITH LINEAR
NEURAL NETWORKS FOR EPILEPSY
CLASSIFICATION FROM EEG SIGNALS
Harikumar Rajaguru and Sunil Kumar Prabhakar
Department of ECE, Bannari Amman Institute of Technology
Sathyamangalam, India
ABSTRACT
As rich spatiotemporal dynamics are exhibited in the human brain, it is quite
complicated in nature. Sudden electrical disturbance of the brain occurs in a temporary
manner and it causes epileptic seizures. Seizures may be sometimes confused with other
events and sometimes it may even go unnoticed. Prediction of occurrence of an epileptic
seizure is quite difficult and it is very difficult to understand the course of action. To
analyze this widespread disorder of the brain, Electroencephalography (EEG) is used.
It is indeed one of the best techniques to probe the activity of the brain and it is highly
useful to diagnose the neurological disease. Tons of information is obtained by the EEG
monitoring system and analyzing it visually is quite difficult. Therefore, the
dimensionality of the EEG data is reduced with the help of dimensionality reduction
techniques like Mutual Information (MI) and Matrix Factorization (MF). The values
reduced through dimensionality reduction are then classified with the help of Linear
Layer Networks for the classification of epilepsy from EEG Signals. Results show that
when MI is used to reduce the dimensionality and classified with Linear Layer Networks
an average classification accuracy of 96.60% is obtained. When MF is employed with
Linear Layer Networks an average classification accuracy of 97.47% is obtained.
Keywords: EEG, Seizure, MI, MF, Epilepsy O.
Cite this Article: Harikumar Rajaguru and Sunil Kumar Prabhakar, Insight to Mutual
Information and Matrix Factorization with Linear Neural Networks for Epilepsy
Classification from EEG Signals International Journal of Mechanical Engineering and
Technology, 10(01), 2019, pp. 690-698.
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Harikumar Rajaguru and Sunil Kumar Prabhakar
1. INTRODUCTION
A set of brain disorders which are chronic in nature and characterized by recurrent seizures is
called as epilepsy [1]. The basic diagnostic test for epilepsy is done with the help of EEG [2].
EEG provides an incessant measure of the function of the cortex and has an amazing spatio
temporal resolution. For a lot of clinical purposes and reasons, various efforts are spent on
interpreting the EEG signals. For interpreting EEG signals, the gold standard in present clinical
practice is through visual scanning and inspection which is quite tedious [3]. Shortage in the
supply of experienced electroencephalographers is a big problem and so there is a need for the
automated systems which helps in the detailed interpretation of the EEG signals [4]. Some of
the significant and most relevant works discussed in literature regarding EEG signal processing
and epilepsy classification from EEG signals are discussed as follows.
The permutation entropy of scalp EEG in order to investigate epilepsy was given by
Ferlazzo et al [5]. The aggregation operators along with the fuzzy techniques for the epilepsy
classification from EEG signals using cerebral blood flow was done by Harikumar and Kumar
[6]. An automated detection system to detect the epileptic seizures was designed by Swami et
al with the help of Support Vector Machine (SVM) Classifier [7]. A Modified Sparse
Representation Classifier and Naïve Bayesian Classifier were developed by Rajaguru and
Prabhakar for the classification of epilepsy from EEG signals [8]. A chaos based nonlinear
analysis of epileptic seizures was developed by Sahu et al [9]. From a wavelet thresholding
point of view, the different frequency behaviors of EEG signals in epileptic patients were
analyzed by Harikumar and Kumar [10]. The diagnosis of epilepsy with the help of combined
doffing oscillator was done by Gandhi et al [11]. The dimensionality reduction techniques were
classified by utilizing the Genetic Algorithms for classifying epilepsy from EEG signals by
Prabhakar and Rajaguru [12]. The time-frequency analysis was done in a detailed manner for
detection of epileptic seizures by Tzallas et al [13]. The classification of epilepsy risk levels
using various distance measures was done by Prabhakar and Rajaguru [14]. The methodologies
like Bayesian Linear Discriminant Analysis (BLDA), Hybrid Artificial Bee Colony with
Particle Swarm Optimization (ABC-PSO), Sparse Principal Component Analysis (S-PCA), and
Soft Decision Trees Classifiers was utilized by Rajaguru and Prabhakar for classifying the
epilepsy risk levels from EEG signals [15],[16]. In this MF and MI are used as dimensionality
reduction techniques and it is later classified with the help of Linear Layer Networks.
The organization of the paper is described as follows. In section 2, the materials and
methods are discussed followed by the application of linear layer networks as post classifiers
for classification of epilepsy from EEG signals in section 3. Section 4 provides the results and
discussion. Section 5 gives the conclusion. The pictorial description of the work is shown in
Figure 1.
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An Insight to Mutual Information and Matrix Factorization with Linear Neural Networks for
Epilepsy Classification from EEG Signals
Figure 1 Proposed Flow of Work
2. DATA SET AND DIMENSIONALITY REDUCTION TECHNIQUES
The EEG data analyzed here is for totally 20 patients which are obtained from the Neurology
Department of the Sri Ramakrishna Hospital, Coimbatore. The EEG data is obtained in
European Data Format (EDF). The 16 channel electrodes are kept on the scalp of the epileptic
patients according to the standard 10-20 International system and the recordings of EEG are
done. The recordings of the EEG are done for more than 55 minutes and the EEG recordings
are split into epochs for easy analysis and computation. Each epoch of a single channel has
approximately 400 values and so for all the epochs of the 16 channels of the total 20 patients,
the values are too high and so to reduce the overall dimensionality of the EEG signals,
dimensionality reduction techniques such as Mutual Information and Matrix Factorization is
utilized.
2.1. Mutual Information
Given wa  dom(a) and wb  dom(b) , the probability parameters are denoted as follows:
p ( wa ) : the probability of a which takes the value wa
p(wa , wb ) : the joint probability of a which takes the value wa and b takes the value wb .
p (wb wa ) = p ( wa , wb ) p( wa )
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Harikumar Rajaguru and Sunil Kumar Prabhakar
Entropy and Mutual Information are very closely related [17]. In information theory, one
of the central notices is entropy which helps to assess the uncertainty in a particular random
variable. The entropy of a random variable a denoted as H (a) is defined as
H (a) = −
 p(w ) log p(w )
wa dom ( a )
a
a
The information which one random variable tells about another random variable is
described with the help of MI. The MI of 2 random variables a and b denoted as I (a, b) is
defined as
I=


wa dom ( a ) wb dom ( b )
p( wa , wb ) log
p( wa , wb )
p( wa ) p( wb )
The important information that b tells about a is the reduction in uncertainty about a due
to the knowledge of b and vice-versa. If the value of I (a, b) is greater, then more information
will be shared by a and b about each other.
2.2. Matrix Factorization
It is a famous computational method utilized for reducing the dimensionality of the data [18].
This technique has also been used widely in the fields of chemical spectral analysis, data
mining, image processing, formulation of new drugs and so on. It is by means of factorizing the
data matrix into a sparse, low rank and non-negative matrix. It is widely called as Positive
Matrix Factorization. Assume L to be a non-negative matrix with a dimension c  d . The nonmatrix factorization decomposes the matrix into a sparse, low rank and non-negative factors so
that the approximation of the original data is modeled as
L = KQ
where K and Q have non-negative elements.
K is of a particular dimension c  r and is termed as the basis matrix because its row
contains a set of basis vectors. Q is of a particular dimension r  d , and is termed as the weight
matrix because its row has coefficient sequences. For the factorization, the rank r is chosen so
that (c + d )r  cd . To the columns of L , the columns of Q are always in one-to-one
correspondence. Therefore, the result (KQ) in easily interpreted as weighted sum of every basis
vector in K . The weight represents the corresponding columns of Q . The resulting additive
properties obtained from the non-negative constraints of negative matrix factorization results
in a specific basis vector that represents the local component of the standard original data.
3. POST CLASSIFICATION WITH LINEAR LAYER NEURAL
NETWORK
The dimensionally reduced values are then fed inside the Linear Neural Networks to classify
the risk of epilepsy from EEG signals. A linear neural network is an affine mapping technique
[19]. The training of this network can be done in two ways, firstly with the least squares
methodology or secondly using the Widrow-Hoff algorithm. Least squares can be implemented
using the pseudo inverse and Widrow-Hoff algorithm is nothing but a simple approximate
gradient descent present on the least squares error. In time series, the application includes
prediction and removal of noise, where initially the time series is embedded to k and so this
linear layer networks is predominantly used in the analysis of signal community.
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An Insight to Mutual Information and Matrix Factorization with Linear Neural Networks for
Epilepsy Classification from EEG Signals
The linear neural node has a schematic form where the data flows generally from left to
right. The real numbers z1 ,..., z n to the input layers is presented initially. The w1k corresponds
to a specific weight. A weighted edge means it is multiplied by w1k and generally it corresponds
to the edge which travels from node k to node i . After a particular mode Q , the total sum of the
incoming signals is considered and then added to a particular value d . The resting state of the
cell is taken as 'd ' and finally the result is passed along the axon. The end result is expressed
as
z  (w11 z1 + w12 z 2 + ....,+ w1n z n + d )
which can be visualized as an n -dimensional plane. So only a linear neural node is
specifically considered as an affine map. Similarly, multiple computational nodes are combined
together in order to get a linear neural network. The affine problem is represented as Fz + g = t
)
))
)
and is quite equivalent to solve a linear nature problem Fz = t , where F is m n and g is m 1
, where the total number of nodes in the input layer is given as 'n' and the total number of nodes
in the output layer is given as 'm' . To best determine both the respective biases and weights that
best match a given input-output set, training a linear network is perfectly done. Training
corresponds to a particular computation of a pseudo inverse when all the data is available.
4. RESULTS AND DISCUSSION
When Mutual Information and Matrix Factorization are considered as dimensionality reduction
techniques and when it is classified with Linear Neural Networks classifier and based on the
parameters like Performance Index, Accuracy, Quality Values, Time Delay, Specificity and
Sensitivity the average results are computed in Tables 1 and 2. The mathematical formulae for
the Performance Index (PI), Sensitivity, Specificity and Accuracy are given as follows
 PC − MC − FA 
PI = 
  100
PC


where Perfect Classification is expressed by PC, Missed Classification is denoted by MC
and the False Alarm is expressed by FA. The Sensitivity, Specificity and Accuracy measures
are mathematically explained by the following
Sensitivity =
PC
 100
PC + FA
Specificity =
PC
 100
PC + MC
Sensitivity + Specificity
2
The Quality Value QV is mathematically defined as follows
Accuracy =
Qv =
C
( R fa + 0.2) * (Tdly * Pdct + 6 * Pmsd )
where C specifies the scaling constant, Rfa mentions the number of false alarm per set, Tdly
denotes the average delay of the onset classification in seconds, Pdct explains the percentage of
perfect classification and Pmsd specifies the percentage of perfect risk level missed.
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Harikumar Rajaguru and Sunil Kumar Prabhakar
The time delay is mathematically written as follows
MC 
 PC
Delay = 2 
+ 6
100 
 100
Several reasons justify the use of this formula.
i. QV monotonically increases where Rfa decreases. The lower the false alarm rate is better
the classifier performance
ii. The constant false alarm of 0.2 per set is added to Rfa in the QV formula. In our method,
the false alarm rate is low and usually ranges form 0 – 0.5. A rate higher than 0.5 is
unacceptable
iii. Tdly * Pdct + 6*Pmsd is actually the weighted average of the delay of onset classification
while Tdly in the average delay of onset classification is used as a delay for missed risk
level by the method. The weights for the average delay of classification or missed risk
level or the percentages of perfectly classified and missed risk levels consequently the
weighted average delay reflects the quality of a classifier with respect to the
classification delay.
iv.
As a result of (iii), QV is inversely proportional to the weighted average of the delay of
onset classification. This reflects the fact that the shorter the onset classification delays
the better the classifier.
v. Theoretically, the weighted delay, Tdly * Pdct + 6*Pmsd could be zero if no level is missed
(Pmsd is zero) and all classification delays Tdly are zero. However, this cannot happen
because Tdly can never be zero. In order to classify a perfect risk level with the shortest
possible delay, the classification window, this lasts 2.0 seconds. As a result, the
weighted delay Tdly * Pdct + 6*Pmsd cannot be very small.
A constant C is empirically set to 10 because this scale is the value of QV to an easy reading
range. The higher value of QV, the better the classifier among the different classifier, the
classifier with the highest QV should be the best.
Time
Table 1 Performance Analysis of MI with Linear Neural Networks
Parameters
Epoch 1
Epoch 2
Epoch 3
Average
PC (%)
94.08
93.54
94.38
94.00
MC (%)
6.66
4.37
4.37
5.13
FA (%)
0.41
2.08
1.24
1.24
PI (%)
91.67
92.89
93.88
92.81
Specificity (%)
93.33
95.6
95.63
94.86
Sensitivity (%)
99.38
97.31
98.35
98.35
Time Delay (sec)
2.26
2.13
2.15
2.18
Quality Values
21.98
21.57
22.12
21.89
Accuracy (%)
96.36
96.47
96.99
96.60
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An Insight to Mutual Information and Matrix Factorization with Linear Neural Networks for
Epilepsy Classification from EEG Signals
Table 2 Performance Analysis of MF with Linear Neural Networks
Parameters
Epoch 1
Epoch 2
Epoch 3
Average
PC (%)
96.25
95.84
95.84
95.97
MC (%)
2.49
1.45
1.66
1.87
FA (%)
1.24
2.70
2.49
2.14
PI (%)
96.08
95.65
95.65
95.79
Specificity (%)
97.50
98.54
98.33
98.12
Sensitivity (%)
98.15
95.99
96.30
96.11
Time Delay (sec)
2.07
2.00
2.02
2.03
Quality Values
22.78
22.07
22.14
22.33
Accuracy (%)
97.82
97.27
97.32
97.47
5. CONCLUSION
It is thus concluded that when Mutual Information is utilized as a dimensionality reduction
technique and when it is classified with Linear Neural Networks, an average classification
accuracy of 96.60% along with an average quality value of 21.89 is obtained. Similarly, when
Matrix Factorization is utilized as a dimensionality reduction technique and when it is classified
with Linear Neural Networks, a classification accuracy of 97.47% along with an average quality
value of 22.33 is obtained. Thus, the performance of the Matrix Factorization surpasses the
performance of the Mutual Information when classified with Linear Neural Networks. Future
works aim to work with different dimensionality reduction techniques and classify with Linear
Neural Networks to classify the epilepsy risk level from EEG signals.
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