SINGLE TRAIL P300 CLASSIFICATION VIA PROBABILISTIC

FUZZY CLASSIFIER AND GENETIC ALGORITHM

Amirhossein Jafarian

1,2

Mohammadhassan Moradi

, Vahid Abootalebi

2,3

and Mostafa Jafarian

Center of Digital Signal Processing,

Cardiff University, Weals, U.K.

Center of Excellence in Biomedical Engineering, Amirkabir University, Tehran, Iran

Department of Electrical Engineering, Yazd University, Yazd, Iran

School of Engineering, University of Manchester, Manchester, U.K.

Keywords: Probabilistic fuzzy classifier (PFC), P300, Genetic Algorithm (GA), Linear Discriminate Analysis (LDA),

Fuzzy classifier.

Abstract: P300 is an endogenous brain response to meaningful stimuli in oddball paradigm. Here the aim is to

estimate whether this component exists in the recorded electroencephalogram (EEG) segment. A

Probabilistic Fuzzy Classifier (PFC) followed by Genetic Algorithm (GA) has been developed in this paper.

The main motivation of using PFC is that it not merely has the advantages of fuzzy systems, but also can

exploit the stochastic properties of the underlying data. Moreover, by selecting the best set of time-

frequency features utilizing GA the classification accuracy is enhanced. A comparison between the

performance of the classifier and those based on stochastic properties of the data, like LDA (Linear

Discriminate Analysis) and conventional fuzzy classifier verifies the superior performance of using this

system.

1 INTRODUCTION

Event related potentials (ERPs) are the brain

responses to the various brain stimulation and are

widely used in cognition processing (Kropotov,

2007). An endogenous ERP, which has been most

studied, is P300 widely used in brain computer

interfacing (BCI), emotion analysis, neurological

disorders research, etc. (Meyer and Lopes Da Silva,

2000). This can often be seen in response to

uncommon meaningful stimuli, mostly “oddball”

(Meyer and Lopes Da Silva, 2000). P300 arises from

response rarely a meaningful visual, audio, and

somatosensory stimulations and by cognition

processing, e.g. when recognizing meaningful word

among other ones flashing infrequently on a

computer screen. P300 is a positive-going wave with

a scalp amplitude distribution in which it is the

largest parietally (at Pz) and the smallest frontally

(Fz), taking intermediate values centrally, over Cz

(Fz, Cz, and Pz are scalp sites along the midline of

the head) (Meyer and Lopes Da Silva, 2000). P300

has a latency of 300–1000 ms from stimulus onset

(Kropotov, 2007), (Abootalebi et al., 2009). The

amplitude of P300 at a given recording site is

inversely proportional to the rareness of

presentation; in practice, presentation probabilities

of less than 0.3 are considered (Kropotov, 2007),

(Abootalebi et al., 2009). The meaningfulness of the

stimulus is also extremely influential in determining

the magnitude of P300.

Non-stationary characteristics of EEG signals,

poor signal-to-noise ratio (SNR), changes in both

latency, width, and amplitude, and finally frequency

of occurrence of P300, make P300 detection by

averaging very inaccurate. Single trial estimation of

P300 is therefore becoming popular and many

frameworks have been established for

representation, extraction and classification of single

trail P300 component (Meyer and Lopes Da Silva,

2000), (Kropotov, 2007).

The contribution of this paper is to use a hybrid

fuzzy and probabilistic information modelling

algorithm, called probabilistic fuzzy system to detect

P300. Such a system is used in different kinds of real

world problems including human control strategy

modelling (Meghdadi and Akbarzadeh, 2001),

human uncertainty modelling (Meghdadi and

Akbarzadeh, 2001), considering financial time series

such as in (Van den Berg and Kaymak, 2002),

174

Jafarian A., Moradi M., Abootalebi V. and Jafarian M..

SINGLE TRAIL P300 CLASSIFICATION VIA PROBABILISTIC FUZZY CLASSIFIER AND GENETIC ALGORITHM.

DOI: 10.5220/0003706901740179

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2012), pages 174-179

ISBN: 978-989-8425-89-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

robotics (Liu and Li

, 2005), and image and video

segmentation and tracking (Zhou and Zhang, 2005).

Besides, a wavelet transform (WT) has been

employed for extraction of time-frequency features

from the EEG due to its advantage in non-stationary

signal characterization (Abootalebi et al., 2009).

Moreover, GA, as a powerful tool in optimization, is

utilized to select the best set of wavelet coefficients

to enhance the classification accuracy.

The paper is organized as follow: in section 2 we

describe the methods of data acquisition and their

time domain analysis; in section 3 the feature

extraction procedure is discussed, design of the PFC

and GA is explored in section 4, and the results of

applying this method and its comparison to other

classifiers is given in section 5, and finally section 6

concludes the paper. Acquisition

2 DATA ACQUISITION

AND PREPROCESSING

Ten men participated in this study. They were

undergraduate or postgraduate students (20 to 28

years old) and all had normal or corrected to normal

vision.

2.1 Acquisition and Pre-processing

The EEG was recorded using Ag/Ag-CL electrodes

placed at Fz, Cz and Pz sites. All sites were

referenced to linked mastoids. In this paper, the

analysis from Pz will be reported. The

electrooculogram (EOG) was recorded from above

and below the right eye electrodes while the subjects

were grounded on forehead. Brain electrical

activities were amplified and digitized at a rate of

256 samples per second. Prior to processing the data

were digitally filtered in the 0.3-30 Hz range. In

order to construct oddball paradigm the volunteers

were asked to choose five numbers one of which had

distinguished meaning to them (e.g. their birthday).

Then, a string of length 150 was produced by these 5

numbers for each record. In each string, each set of

numbers was presented randomly for 30 times. The

numbers were shown by a monitor in front of each

person. Occasionally each number was demonstrated

for 2 seconds. Then, the monitor remained blank for

one second. Each person asked to count how many

times his target was seen.

After filtering the signals, each continuous

record was divided into single trials given the

stimulus presentation times. The length of each trial

was 1000ms, consisting of 256 samples of the

signal. EOG data were examined for blink artifact by

visual inspection and the trials with blink artifacts

were removed. Then, the pattern recognition method

including feature extraction, feature selection and

classification were applied to the signals and their

detection rates were assessed. In the following study

only the data at Pz site are considered. Figure1

shows the ensemble average of the different stimuli

for a subject in Pz site.

Figure 1: Average of different stimulus in Pz channel of a

subject. Stimuli 3 are the target stimuli while the other is

non-target.

Figure1 clearly demonstrates that the amplitude of

average response to the target stimuli in our

experiments is above the other stimuli for typical

subject.

3 FEATURE EXTRACTION

After the EEG was recorded, to evaluate the

performance of the classifier, wavelet features were

extracted from all the signals. The WT may be used

to optimally represent the EEG/ERP non-stationary

signals in time-frequency domain (Abootalebi et al.,

2009). The wavelets precisely represent the point of

occurrence of a transient event in a neuroelectric

waveform in both time and frequency. In this study,

such a multi-resolution decomposition is performed

by applying a decimated discrete WT. Quadratic B-

Spline functions were used here as mother wavelets

due to their similarity with the evoked responses

(Abootalebi et al., 2006). The filter coefficients

associated with quadratic B-Splines are shown in

Table 1.

In the Table1 the first column corresponds to the

high pass filter G used to obtain the frequency

details and the second column belongs to the low

pass filter H used to obtain the successive

approximations. The third and fourth columns are

SINGLE TRAIL P300 CLASSIFICATION VIA PROBABILISTIC FUZZY CLASSIFIER AND GENETIC ALGORITHM

175

the inverse filter coefficients used for reconstructing

the signal (Basar and Schurmann, 2001).

Table 1: Quadratic B-Spline wavelets filter coefficients

(Abootalebi, et all, 2009); (Basar, Schurmann, 2001).

In order to obtain the features all EEG data were

decomposed into five-octaves bands using the WT.

Six sets of coefficients (including residual scale)

within the following frequency bands were obtained;

0–4 Hz, 4–8 Hz, 8–16 Hz, 16–32 Hz, 32–64 Hz and

64–128 Hz. The coefficients in each set are related

to sequential time bands between 0 and 1000 ms.

The coefficients within 30– 128 Hz and 0–0.3 Hz

ranges were not applicable because these bands

originally excluded by the filtering of the signal.

Other coefficients however represent the signal

information in four frequency bands: A, 0.3–4 Hz;

B, 4–8 Hz; C, 8–16 Hz; and D, 16–30 Hz.

Figure.3shows the decomposition and reconstruction

of a single trial ERP into five octaves, using the

quadratic B-Spline wavelet. Here, 8 coefficients of

band A, 8 coefficients of band B and 16 coefficients

of band C were obtained for the post-stimulus epoch

(Abootalebi et al., 2009).

4 PROBABILISTIC FUZZY

CLASSIFIER AND GENETIC

ALGORITHM FOR ERP

CLASSIFICATION

4.1 Probabilistic Fuzzy Classifier

The objective of a PFC is to assign a class label from

{}

cccy ,...,,

to each of the feature vectors

],...,[

21 n

xxxx =

. The PFC “if-then” rule can be

written as follow

() () ( )

, ..., , , :

,22,211,1 nniniii

xAisxandxAisxxAisxifR

Then,

cy =

with

()

cyRcP =

..., ,|

with

()

RcP |

Where R

represents the i

rule

()

Ri ,...,1=

in the

the probabilistic fuzzy classifier;

nii

,1,

,...,

are

the Gaussian membership functions i.e.

()

⎟

⎠

⎞

⎜

⎝

⎛

−

−=

exp

jijk

where

ji,

and

,ji

represent

mean and variance for each feature, respectively.

()

rcP |

()

Ck ,...,2,1=

denotes the probability of the

rule representing class. General frameworks to

construct PFC are as follows (Liu and Li, 2005);

(Van den Berg and Kaymak, 2002).

i) Divide the input space into fuzzy cells using the

training data.

ii) Allocate probability distribution to each cell and

estimate its un-known parameters for each class of

data, by using training data and its class labels (0 for

the signals that do not have P300 and 1 for the rest).

iii) Test the performance of the classifier by fusion

expectation maximization for all the cells to find the

most probable solution (Liu and Li, 2005).

Figure 2: Typical single trail ERP decomposition. The

Horizontal axes are amplitude of wavelet transform and

Vertical axes is time.

Dividing the input space to fuzzy cells may be

carried out via fuzzy clustering (Liu and Li, 2005).

For this, we used FCM (fuzzy c-means). After the

cells have been created, a supervised fuzzy

clustering has been employed to model each of class

distribution in each cell which is the implementation

of step ii (Liu and Li, 2005). In other words, for a

given N observations (in a typical cell) from the

training data set

{}

yxX ,=

, the objective of

supervised fuzzy clustering is to partition X into C

clusters, where

Nk ,...,1=

and,

{}

ccy ,...,

∈

(

Van

den Berg, 2002).

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

176

The fuzzy partitioning is represented by the

membership matrix

[

]

where

ki,

denotes

the membership of k

observation belonging to the

cluster. The clustering is based on minimization

of the following objective function

()

∑∑

ikki

RxDJ

Where m is the fuzziness index and

()

ikki

RxD ,

is a

distance measure. Selection of m has some influence

on the final partitioning and predicting results (Van

den Berg and Kaymak, 2002). For

1=m

, the fuzzy

clustering is a hard clustering of the data and for

∞→m

, the partition tends to maximal fuzziness. In

order to estimate the parameters of the if-then fuzzy

rules described above from the obtained fuzzy

clusters the product of Gaussian probability

distribution as geometrical distance criteria; and also

the class label to represent the density of classes of a

data; and defined as bellow (Van den Berg,

Kaymak, 2002)

()

() ( )

)|.(

jii

ikki

RcyPArP

RxD

∏

(1)

Where

()

is the a priori probability of the ith

cluster. Therefore, the supervised clustering is

carried out by minimizing the objective function J

iteratively according to the well-established

parameter estimation in the Gath-Geva clustering

(Hoppner, et all, 1999) can be given as follow

i) Initialize the fuzzy partitioning matrix by using

FCM.

[

]

ii) Calculate the centres and standard deviation of

the Gaussian membership Functions,

()

∑

−

jijk

,,,1

νμ

iii) Estimate the consequent probability parameters,

()

RjCircP

kic

≤≤≤≤=

∑

1,1,)|(

iv) Compute the a priori probability of the cluster,

()

∑

kii

v) Update the partition matrix

()

[]

()

[]

()

NkandRi

,rx/D

,rxD

jkj,k

iki,k

≤≤≤≤=

∑

−

1 1 ,

12/

ki,

vi) If

<−

−

||||

1ll

stop, where

,...,2,1=l

denotes

the iteration number and is a small positive

constant.

vii) Else go to (ii) and repeat the process.

After the unknown parameters of each cell are

estimated and the algorithm finally converged, the

final decision is made by finding the expectation

values of the posterior probability, which is the

realization of step iii.

The output of the fuzzy classifier is determined by

the label of the class that has the highest activation:

()

∑

∏

∑

∏

jji

rcPxA

kcy

maxarg*,

4.2 Genetic Algorithm based Feature

Selection

The In classification application, reduction in the

number of features becomes useful since this allows

reduction in the computational time and the design

complexity. Moreover, using feature selection

algorithm is mainly motivated by peaking

phenomenon often observed when the classifier is

trained with a limited set of training samples if the

number of features is increase, the classification rate

will decrease after the peak (Goldberg, 1989). In

this study, a technique that uses GA to select the

features for probabilistic fuzzy classification of ERP

signals is proposed. PFC accuracy is used for

evaluating the fitness function of the GA population.

The parameters used in the GA are listed in Table 2.

The proposed algorithm is based on the iteration of

the following steps until population convergence:

Step1: Generating initial GA population.

General initial populations with number of gens of

binary numbers (0 or 1 where bit 0 denotes

deactivation and bit 1 denotes activation of feature)

e.g.

• Population 1: 101 . . . . . 00111

• Population 2: 10111 . . . . 1111

…………………………………

• Population N: 111010 . . . 011,

Step2: Population fitness calculation based on PFC

performance based on ten-fold cross validation as it

SINGLE TRAIL P300 CLASSIFICATION VIA PROBABILISTIC FUZZY CLASSIFIER AND GENETIC ALGORITHM

177

will be described in the next section,

Step 3: Next generation GA population is generated.

Step 4: Evaluation of performance of the classifier

for P300 classification.

Table 2: GA Parameters.

Coding of Genes Binary Coding

Population size 15

No. of genes 32 (numbers of WT features)

Reproduction Tournament selection

Crossover Two point crossover

Crossover rate 0.5

Mutation Random mutation

Convergence Max 800 generation of population

convergence

Population convergence if 80% of population one

are similar

Vigilance parameter Varied from 0 to 1 in steps of 0.1

Mutation rate 0.01

4.3 Performance Measure

The performance of the obtained PFC and GA based

feature selection was measured by a ten-fold cross

validation. Each individual was left out once, whilst

the other nine were applied for construction of the

classifier which was subsequently validated for the

unseen cases in the left-out sub-set. In each

generation during the running of GA, the maximum

of fitness function calculated. After producing 800

generation, the best chromosome was obtained and

its correspondence feature set determined. The

results of PFC and PFC by using GA as feature

selection algorithm (PFC+GA) for the ERP data

have been depicted in Table 3. The m parameter has

also been selected manually for finding the best

result. The best features selected using the GA

algorithm for the best accuracy.

For comparing the results we also applied LDA

as pure statistical classifier and fuzzy classifier

described in (Roubos, et all, 2001). and GA for

feature selection for both of these classifiers

(LDA+GA and Fuzzy+GA). The framework for

calculation of the results was the same as before, i.e.

based on ten-folds cross validation, and were

depicted in Table 4.

Table 3: Classification results for the PFC with and

without using GA measured by 10 fold cross validation.

Classifier

Type

m Classification

Accuracy

PFC 1.9 79.5%

PFC+GA 1.6 83.3%

5 CONCLUSIONS

In this paper time-frequency features, PFC, and GA

have been utilized for classification of P300 signals.

In order to generate the ERP, oddball paradigm has

been employed. The accuracy of classification for

the PFC together with wavelet features was 79%,

which was better than that of the LDA (purely

statistical classifier), 75%, and higher than that of

fuzzy classifier, which was 77.1%. Moreover, by

using GA to select the best set of wavelet features

the accuracy of classification increased. The

comparison between these classifiers when, GA is

used as feature selector also verified the superior

performance of the PFC with 83% accuracy. The

results justify that combination of the probabilistic

and fuzzy approaches is very useful for classification

of ERP and outperforms other classifiers solely

based on fuzzy or statistical properties.

Table 4: Performance of LDA and Fuzzy classifier

measured by 10 fold cross validation.

Classifier

Type

Classification

Accuracy

LDA 75%

LDA+GA 78.3%

Fuzzy (Roubos, et all, 2001). 77.1%

Fuzzy+GA 80.2%

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