Classification of Normal and Epileptic Seizure EEG Signals Based on Empirical Mode Decomposition - Complex System Modelling and Control Through Intelligent Soft Computations - page 373

q

ðl

b ¼ 1 7321

X þ l Y D Þ

ð 19 Þ

:

The ellipse area can be computed from the parameters a and b as:

A ellipse ¼ p ab ð 20 Þ

:

2.4 Least Square Support Vector Machine

Classi finding out the particular category of data to which the

new upcoming observed sample can belong. The decision is made on the basis of
the observed samples of data whose category is already known, these sets of
observed samples are known as training sets. Support vector machine (SVM) is a
machine learning technique used to classify samples belongs to different classes.
SVM is a very useful tool for pattern classi

cation is a problem of

cation problem (Cortes and Vapnik
1995 ). SVM is trained to search for an optimal separating hyperplane that can
provide superior generalization, particularly when dimension of input data is large.
Hyper planes are determined to create decision boundaries between two different
classes of data in SVM. The effectiveness of the features in classifying normal and
epileptic seizure EEG signals has been evaluated using a least square support vector
machine (LS-SVM) a least square version of SVM (Suykens and Vandewalle
1999 ).
Consider a training set of N data points

ð x i ; y i Þ , i ¼ 1

; ... ;

N, where x i is input

data and y i ¼ þ 1, class label for two different classes. The SVM approach

aims at constructing a discriminant function of the form:

1or −

T g

f ð x Þ ¼ sign x ð x Þþ b ð 21 Þ

where, is the d-dimensional weight vector and b is a bias, and g(x) is a mapping

function that maps x into d-dimensional space. The goal of SVM algorithm is to
identify optimum separating hyper plane which is able to maximize the distance
from either class to the hyperplane. This problem of optimization can be formulated
as a quadratic programming problem considering inequality constraints (Suykens
and Vandewalle 1999 ). The LS-SVM is the least square variant of SVM for clas-
si

x

cation of two class problem. The statement of the problem can be written as in
following way:

x þ 2 X

N

1
2 x

T

e i

Minimize J ðx ; b ; e Þ ¼ ð 22 Þ

i¼1