S. K. XIE ET AL.

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ljkilj ilki

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. 2) Calculate for each Fourier

frequency

for each test signal

j

of group

l

the sample

mean of

, denoted by

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2

1()

l

n

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n

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=

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,

i.e

.

with respect to all the training signals

k

of the group

l

, for

. 3) Calculate the sample variance

of

with respect to

. 4) A test signal

j

is classi-

fiedinto a group

l

if

is the smallest value of

{

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2.3. Experimental Data

We consider the publicly available data [ 7] that h ave five

sets, denoted as Set A, B, C, D, and E, respectively. Sets

A and B consist of the data segments taken from the sur-

face of EEG recordings of five healthy volunteers. Data

in Sets C, D and E come from patients suffering from

epilepsy. Set E contains only seizure activity. Each data

set (i.e., from A to E) contains 100 single-channel EEG

signals, each with a total of 4097 sample points. The

classification of the normal type and the type with epi-

leptic seizure activities has been widely studied for the

considered data sets (i.e., Sets A, B, C, D and E) and a

high accuracy of these classifications have been achieved.

However, in this paper, we focus on the multi-class clas-

sification problem.

3. Results

3.1. Two-Class Classificat ion

Before we address the three-class classification problem

(i.e., the classification problem of the normal, inter-ictal

and seizure classes), first, we split randomly the data of

each of the Sets A, B, C, D and E, respectively, into the

training data set and the test data set of 50 signals each.

Next, we study if the test data of each data Set A, B, C, D,

and E can be successfully classified as of the type of the

respective training data set using the statistical similarity

test. To carry out this test, the confidence band of each

average of the Fourier power sp ectra of the pre-processed

training data set of each Set A, B, C, D and E is calcu-

lated. Next, the computed statistical similarity value of

CI test is compared to a pre-defined statistical similarity

level to enable a classification decision of each test signal.

If the computed statistical similarity value is higher than

the pre-defined level, then the pre-processed test signal is

classified as of the type of the respective training data.

Finally, we count the total number of the correct classi-

fications. Table 1 shows the results of the accuracy of

the two-class classification problem when different levels

of the statistical similarity tests are considered for each

pre-processed data set. For the statistical similarity level

of 0.8 we obtain an accuracy o f classification of 50 out of

50 test signals selected from Set A and an accuracy

Table 1. The number of correct classifications (displayed in

the right columns) out of 50 EEG test signals with respect to

different pre-defined statistical similarity levels (listed in

the left column) for 5 different data sets (i.e., sets A, B, C, D

and E) for two-class classification problem.

Statistical

similarity level Set A Set B Set C Set D Set E

0.95 33 12 34 40 37

0.90 45 19 41 44 46

0.85 48 29 41 45 49

0.80 50 37 41 45 49

of classification of 49 ou t of 50 test signals se lected from

Set E. However, the results in Table 1 show that the ap-

plied CIC method with statistical similarity level of 0.8

does not successfully classify the test data selected from

Set B into a group of the respective training data set.

3.2. Three-Class Classification

For the three-class classification problem, first, we split

randomly the data of each of the Sets A, B, C, D and E,

respectively, into the training data set and the test data set

of 50 signal s each. Inste ad of only co ns ideri ng t he data of

Sets A and E separa tely and ignoring the data of the Sets

C, B and D, we combine together data from different sets

(e.g., from Set C and Set D). The above described CI

based classification method and the proposed EC method

need to be modified in order to be applied to the above

three-class classification problem. The modifications of

the classification methods are needed because we do not

classify the test signals into all three possible groups. A

test signal from the normal group is classified as either a

normal or an inter-Ictal signal and a test signal from the

inter-Ictal group is classified as either a normal, or an

inter-Ictal, or an Ictal signal. The results of accuracy of

the three-classs classification, based on the CIC method

and the EC method, are reported in Table 2 and Figu re 1.

The three-class classification achieves 100% accuracy

when the proposed EC method, using only a few PCs

(i.e., 4 or 5), is applied to the training and test signals.

The CIC method used in three-class classification suc-

cessfully classifies the test data of the inter-Ictal group

and the seizure group into the inter-Ictal group and the

Ictal group, respectively, but it does not classify suc-

cessfully test data of the normal group.

Our study shows that the accuracy of classification of

the normal group test data depend on the selected feature

dimensions for both classification methods. When more

features are retained, the classification accuracy of the

normal group is decreased regardless which method is

used, i.e . the CIC method or the EC method (see Figure

1). However, for our three-class classification problem,

the EC method is more robust than the CIC method in