Autoregressive Integrated Adaptive Neural Networks Classifier for EEG-P300 Signal Classification


 

 

Mechatronics, Electrical Power, and Vehicular Technology 04 (2013) 1-8 
 

Mechatronics, Electrical Power, and 
Vehicular Technology 

 
e-ISSN:2088-6985 
p-ISSN: 2087-3379 

Accreditation Number: 432/Akred-LIPI/P2MI-LIPI/04/2012 

 

 

www.mevjournal.com 
 

© 2013 RCEPM - LIPI All rights reserved 
doi: 10.14203/j.mev.2013.v4.1-8 

AUTOREGRESSIVE INTEGRATED ADAPTIVE NEURAL NETWORKS 
CLASSIFIER FOR EEG-P300 SIGNAL CLASSIFICATION 

 
Demi Soetraprawata*, Arjon Turnip 

Technical Implementation Unit for Instrumentation Development Division – LIPI 
Kompleks LIPI Gd. 30, Jalan Sangkuriang Bandung, 40135, Indonesia 

 
Received 09 October 2012; received in revised form 22 February 2013; accepted 27 February 2013 

Published online 30 July 2013 
 

Abstract 
Brain Computer Interface has a potency to be applied in mechatronics apparatus and vehicles in the future. Compared to the 

other techniques, EEG is the most preferred for BCI designs. In this paper, a new adaptive neural network classifier of different 
mental activities from EEG-based P300 signals is proposed. To overcome the over-training that is caused by noisy and non-
stationary data, the EEG signals are filtered and extracted using autoregressive models before passed to the adaptive neural 
networks classifier. To test the improvement in the EEG classification performance with the proposed method, comparative 
experiments were conducted using Bayesian Linear Discriminant Analysis. The experiment results show that the all subjects 
achieve a classification accuracy of 100%. 

 
Keywords: brain computer interface, feature extraction, classification accuracy, autoregressive, adaptive neural networks, EEG-

based P300, transfer rate. 

 
I. INTRODUCTION 

A Brain Computer Interface (BCI) is a device 
that allows users to communicate with the world 
without utilizing voluntary muscle activity. BCI 
systems utilize what is known about brain signals 
to detect the message that a user chose to 
communicate. These systems rely on the finding 
that the brain reacts differently to different 
stimuli, based on the level of attention that is 
given to the stimulus and the specific processing 
that is triggered by the stimulus. Therefore brain 
activity must be monitored with various 
techniques. Among these techniques, EEG is the 
most preferred for BCI designs, because of its 
non-invasive, cost effectiveness, easy 
implementation, and best temporal resolution [1, 
2]. 

EEGs are usually analyzed in two ways: (i) as 
free running EEG; (ii) as events related potentials 
(ERPs) (i.e., P300, slow cortical potentials 
(SCPs), readiness potentials (RPs), and steady 
state visual evoked potentials (SSVEPs)) [3]. 
Around 1964, Chapman and Bragdon as well as 
Sutton et al., are independently discovered a 
wave peaking at approximately 300 ms after task-

relevant stimuli [4]. This component is known as 
the P300. While the P300 is evoked by many 
types of paradigms, the most common factors 
that influence it are stimulus frequency and task 
relevance [5]. The presence, magnitude, 
topography and time of the response signalsare 
often used as metrics of cognitive function in 
decision making processes. The P300 has been 
shown to be fairly stable in locked-in patients, re-
appearing even after severe brain’s stem injuries. 
Farwell and Donchin (1988) first showed that this 
signal may be successfully used in a BCI [6]. 
Using a broad cognitive signal like the P300 has 
the benefit of enabling control through a variety 
of modalities, as the P300 enables discrete 
control in response to both auditory and visual 
stimuli. As it is a cognitive component, the P300 
has been known to change in response to 
subject’s fatigue [5]. 

One of the most important task in designing a 
BCI is in extracting relevant features from the 
EEG signals, which is naturally noisy and 
stochastic. In order to avoid the averaging 
processes and to remove the artifacts, which are 
computational complexity, poor generalization, 
and needs a large number of trainings to achieve 
a desired accuracy and a communication rate, * Corresponding Author. Tel: +62-22-2503053 

E-mail: {demi001, arjo001}@ lipi.go.id 

http://dx.doi.org/10.14203/j.mev.2013.v4.1-8


D. Soetraprawata and A. Turnip / Mechatronics, Electrical Power, and Vehicular Technology 04 (2013) 1-8 

 

2 
 

therefore a new adaptive neural network 
classifier (ANNC) of different mental activities 
are proposed. To overcome the over-training 
caused by noisy and non-stationary data, the 
features of the EEG-based P300 signals are 
extracted using autoregressive (AR) method 
before passed to the proposed classifier algorithm. 
In order to examine the performance 
improvements of the proposed classification 
method, comparative experiments were 
conducted using Bayesian Linear Discriminant 
Analysis (BLDA). 

The contributions of this paper are as follow: 
a. Enhancements and strengthens the EEG signal 

according to the small amplitude of the EEG-
based P300 which is naturally noisy and 
stochastic. 

b. Driving the tracking error converges to a 
small value around zero while the closed-loop 
stability is guaranteed. 

c. The introduction of the AR method and the 
application of the proposed classifier improve 
the classification accuracy and the transfer 
rate of a BCI even when the subjects are in a 
fatigue condition. 
The structure of the paper is as follows. In 

Section 2, the EEG data set and pre-processing 
are described. Feature extraction and 
classification using AR method and adaptive 
neural networks, respectively, are explained in 
Section 3. Results and discussions are presented 
in Section 4. Conclusions are drawn in Section 5. 

 
II. DATA SET AND EEG PRE-

PROCESSING 
In order to examine the performance 

improvement of the proposed EEG classification 
method, the EEG based P300 data used in this 
paper was obtained previously by Hoffmann et al. 
(2008) who used the following procedure [5]. 
The data have been recorded according to the 10-
20 standards from the 32 electrode configurations. 
In this study, however, only the signals from the 
eight electrodes configuration were used. Each 
recorded signal has a length of 820 samples with 
a sampling rate of 2,048 Hz. A six-choice signal 
paradigm was tested using a population of five 
disable and four able bodied subjects. The 
subjects were asked to count silently the number 
of times a prescribed image flashed on a screen. 
Four seconds after a warning tone, six different 
images (a television, a telephone, a lamp, a door, 
a window, and a radio) were flashed in a random 
order. Each flash of an image lasted for 100 ms, 
and for the following 300 ms no image was 
flashed (i.e., the inter-stimulus interval was 400 
ms). Each subject completed four recording 

sessions. Each of the sessions consisted of six 
runs with one run for each of the six images. The 
duration of one run was approximately one 
minute and the duration of one session, including 
setup of electrodes and short breaks between runs, 
was approximately 30 minutes. One session 
comprised on average 810 trials, and the entire 
data for one subject was taken from an average of 
3,240 trials.  

Our goal is to discriminate all possible 
combinations of the pairs of mental activities 
from each other using the corresponding EEG 
signals. The EEG signals are processed in 
segments (EEG-trials) in which the BCI attempts 
to recognize the mental activities.  

Before the classification and validation are 
performed, several pre-processing operations 
including filtering, and down sampling were 
applied to the data. A 6th order forward-
backward Butterworth band pass filter with cut 
off frequencies of one Hz and 12 Hz was used to 
filter the data. The EEG was down sampled from 
2,048 Hz to 32 Hz by selecting each 64th sample 
from the band pass-filtered data. 
 
III. FEATURE EXTRACTION AND 

CLASSIFICATION 
A. Feature Extraction 

In this section, the feature extraction which is 
focused on the estimation of statistical 
measurements from the perturbation free EEG-
trials delivered by the pre-processing module, is 
explored. The features computed on a given 
EEG-trial are grouped into a vector called feature 
vector that is sent to the pattern recognition 
module which evaluates the likelihoods that the 
EEG-trial was produced during the execution of 
the mental activities.  

The autoregressive (AR) method is built on 
the hypotheses of stationarity, ergodicity, absence 
of coupling between the univariate components, 
and existence of a linear prediction model [7]. 
Let 𝒀𝒀  be an 𝑁𝑁𝑒𝑒 dimensional multivariable 
stochastic EEG signal of length sN , composed of 
randomvectors: { 𝒀𝒀(𝑘𝑘) = (𝑦𝑦1 (𝑘𝑘) … 𝑦𝑦𝑁𝑁𝑒𝑒 (𝑘𝑘))

𝑇𝑇| �𝑘𝑘 =
0, … , 𝑁𝑁𝑠𝑠 − 1 } �where 𝑦𝑦1 , … , 𝑦𝑦𝑁𝑁𝑒𝑒 are the univariate 
components of 𝒀𝒀 . The AR model can be 
generated by a linear prediction model of the 
form [7]: 

 
𝒀𝒀(𝑘𝑘) = −∑ 𝑨𝑨(𝑘𝑘, 𝑖𝑖)𝒀𝒀(𝑘𝑘 − 𝑖𝑖) + 𝑒𝑒1 (𝑘𝑘)

𝑄𝑄
𝑖𝑖=1 , (1) 

 
where 𝑄𝑄  is the model order, the 𝑨𝑨(𝑘𝑘, 𝑖𝑖) are 
𝑁𝑁𝑒𝑒𝑥𝑥𝑁𝑁𝑠𝑠 matrices (𝑁𝑁𝑒𝑒 Ne  denoting the number of 
electrodes and Ns  denotes the number of 
temporal samples per EEG channel), and 𝑒𝑒1 (𝑘𝑘) is 



D. Soetraprawata and A. Turnip / Mechatronics, Electrical Power, and Vehicular Technology 04 (2013) 1-8 

 

3 

the prediction error with a zero mean random 
vector. Since the coupling between the channels 
is ignored, equation (1) can be split into linear 
prediction models corresponding to each 
univariate component. Thus, the n-th univariate 
component of 𝒀𝒀can be written in the form: 

 
𝑦𝑦𝑛𝑛 (𝑘𝑘) = −∑ 𝑎𝑎𝑛𝑛 (𝑘𝑘, 𝑖𝑖)𝑦𝑦𝑛𝑛 (𝑘𝑘 − 𝑖𝑖) + 𝑒𝑒n (𝑘𝑘)

𝑄𝑄𝑛𝑛
𝑖𝑖=1 , (2) 

 
where the 𝑎𝑎𝑛𝑛 (𝑘𝑘, 𝑖𝑖)  are the AR coefficients and 
𝑄𝑄𝑛𝑛  is the AR order corresponding to 𝑦𝑦𝑛𝑛 , and 𝑒𝑒n  is 
the n-th prediction error process. The indexes n 
and k are used to reference the electrode and time 
index, respectively. Furthermore, as stationarity 
and ergodicity are assumed, then the AR model 
for the n-th channel becomes: 

 
𝑦𝑦𝑛𝑛 (𝑘𝑘) = −∑ 𝑎𝑎𝑛𝑛 (𝑖𝑖)𝑦𝑦𝑛𝑛 (𝑘𝑘 − 𝑖𝑖) + 𝑒𝑒n (𝑘𝑘)

𝑄𝑄𝑛𝑛
𝑖𝑖=1 . (3) 

 
The coefficients 𝑎𝑎𝑛𝑛 (1), … , 𝑎𝑎𝑛𝑛 (𝑄𝑄𝑛𝑛 )  can be 

determined by minimizing the averaged squared 
prediction error: 

 
𝜀𝜀(𝑄𝑄𝑛𝑛 )   =

1
𝑁𝑁𝑠𝑠
∑ 𝑒𝑒𝑛𝑛2 (𝑘𝑘)
𝑁𝑁𝑠𝑠−1
𝑘𝑘=0   

= 1
𝑁𝑁𝑠𝑠
∑ �𝑦𝑦𝑛𝑛 (𝑘𝑘) + ∑ 𝑎𝑎𝑛𝑛 (𝑖𝑖)𝑦𝑦(𝑘𝑘 − 𝑖𝑖)

𝑄𝑄𝑛𝑛
𝑖𝑖=1 �

𝟐𝟐𝑁𝑁𝑠𝑠−1
𝑘𝑘=0  (4) 

 
In this relation, the samples prior to 𝑦𝑦𝑛𝑛 (0)  are 
assumed to be zero. 

 
B. Adaptive Neural Networks Classifier 

Artificial neural networks have been proposed 
in the fields of information and neural sciences 
following research into the mechanisms and 
structures of the brain. This has led to the 
development of new computational models for 
solving complex problems such as pattern 
recognition, rapid information processing, 
learning and adaptation, classification, 
identification and modelling, speech, vision and 
control systems [8-14]. 

In this paper, we are only concerned with the 
adaptive classifier problem of EEG-based P300 
represented by nonlinear discrete-time systems 
which can be transformed in state space 
description [15] as follow: 

 
𝑥𝑥1 (𝑘𝑘 + 1) = 𝑥𝑥2 (𝑘𝑘),
𝑥𝑥2 (𝑘𝑘 + 1) = 𝑥𝑥3 (𝑘𝑘),
⋮
𝑥𝑥𝑛𝑛 (𝑘𝑘 + 1) = 𝑓𝑓(𝑥𝑥(𝑘𝑘)) + 𝑔𝑔�𝑥𝑥(𝑘𝑘)�𝑢𝑢(𝑘𝑘),
𝑦𝑦𝑘𝑘 = 𝑥𝑥1 (𝑘𝑘),

 (5) 

 
where 𝑥𝑥(𝑘𝑘) = [𝑥𝑥1 (𝑘𝑘), 𝑥𝑥2 (𝑘𝑘), … , 𝑥𝑥𝑛𝑛 (𝑘𝑘)]𝑇𝑇 ∈ 𝑅𝑅𝑛𝑛 ,
𝑢𝑢(𝑘𝑘) ∈ 𝑅𝑅 ,  𝑦𝑦(𝑘𝑘) ∈ 𝑅𝑅  are the state variables, 
system input and output, respectively; 

𝑓𝑓(𝑥𝑥(𝑘𝑘)) and 𝑔𝑔�𝑥𝑥(𝑘𝑘)�  are unknown which may 
not be linearly parameterized. The classifier 
system attempts to make the plant output 
𝑦𝑦𝑑𝑑 (𝑘𝑘)match the target output asymptotically, so 
that lim𝑡𝑡→∞‖𝑦𝑦𝑑𝑑 (𝑘𝑘) − 𝑦𝑦𝑘𝑘‖ ≤ 𝜀𝜀 for some specified 
constant 𝜀𝜀 ≥ 0 . If 𝑓𝑓(𝑥𝑥(𝑘𝑘))  and 𝑔𝑔�𝑥𝑥(𝑘𝑘)� are 
known, the following classifier can be used, and 
the system would exactly track the target output 
𝑦𝑦𝑑𝑑 (𝑘𝑘). 

 
𝑢𝑢(𝑘𝑘) = 𝑔𝑔−1�𝑥𝑥(𝑘𝑘)��𝑦𝑦𝑑𝑑 (𝑘𝑘) − 𝑓𝑓(𝑥𝑥(𝑘𝑘))� (6) 
 
Since 𝑓𝑓(𝑥𝑥(𝑘𝑘))  and 𝑔𝑔�𝑥𝑥(𝑘𝑘)�  are unknown, 

neural networks can be used to learn to 
approximate these functions and generate suitable 
classifiers. Although the function 𝑔𝑔�𝑥𝑥(𝑘𝑘)� is not 
known, it can be assumed that its sign is known 
along system trajectories and that there exist two 
constants 𝑔𝑔0 , 𝑔𝑔1 > 0 such that 𝑔𝑔0 ≤ �𝑔𝑔�𝑥𝑥(𝑘𝑘)�� ≤
𝑔𝑔1 , ∀𝑥𝑥 ∈ Ω ∈ 𝑅𝑅𝑛𝑛  with compact subset Ω  
containing the origin. This assumption implies 
that the function 𝑔𝑔�𝑥𝑥(𝑘𝑘)�  is strictly either 
positive or negative. From this point forward 
therefore, without losing generality, we shall 
assume 𝑔𝑔�𝑥𝑥(𝑘𝑘)� > 0.  

Neural networks are general modelling tools 
that can approximate any continuous or discrete 
nonlinear function to any desired accuracy over a 
compact set [9-11, 16, 17]. In this work, a new 
adaptive neural network classifier is developed 
for nonlinear system (5) using high order neural 
networks. Therefore the mental activities 
according to the given stimuli could be extracted 
and classified with high accuracy. It should be 
noted that although the new states 𝑥𝑥2 , 𝑥𝑥3 , . . . , 𝑥𝑥𝑛𝑛  
are not available in practice, we can predict them 
as will be detailed in the following discussion. 
Let 𝑥𝑥𝑑𝑑 = [𝑦𝑦𝑑𝑑 (𝑘𝑘), 𝑦𝑦𝑑𝑑 (𝑘𝑘 + 1), … , 𝑦𝑦𝑑𝑑 (𝑘𝑘 + 𝑛𝑛 −
1)]𝑇𝑇 the target system states. Define error 
𝑒𝑒(𝑘𝑘) = 𝑥𝑥(𝑘𝑘) − 𝑥𝑥𝑑𝑑 (𝑘𝑘). The equation of  𝑒𝑒(𝑘𝑘) can 
be written as: 

 
𝑒𝑒1 (𝑘𝑘 + 1) = 𝑒𝑒2 (𝑘𝑘),
𝑒𝑒2 (𝑘𝑘 + 1) = 𝑒𝑒3 (𝑘𝑘),
⋮
𝑒𝑒𝑛𝑛 (𝑘𝑘 + 1) = 𝑓𝑓�𝑥𝑥(𝑘𝑘)� + 𝑔𝑔�𝑥𝑥(𝑘𝑘)�𝑢𝑢(𝑘𝑘)
                       −𝑦𝑦𝑑𝑑 (𝑘𝑘 + 𝑛𝑛).

 (7) 

 
In order to develop the output feedback 

classifier clearly, define the following new 
variables 𝑦𝑦�(𝑘𝑘) = [𝑦𝑦𝑘𝑘−𝑛𝑛+1 , … , 𝑦𝑦𝑘𝑘−1 , 𝑦𝑦𝑘𝑘 ]𝑇𝑇,
𝑢𝑢�𝑘𝑘−1 (𝑘𝑘) = [𝑢𝑢𝑘𝑘−1 , … , 𝑢𝑢𝑘𝑘−𝑛𝑛+1 ]𝑇𝑇 , and 𝑧𝑧̅(𝑘𝑘) =
�𝑦𝑦�𝑇𝑇(𝑘𝑘), 𝑢𝑢�𝑘𝑘−1

𝑇𝑇 (𝑘𝑘) �
𝑇𝑇
∈ Ω𝑧𝑧̅ ⊂𝑅𝑅2𝑛𝑛−1 .  According to 

the definition of the new states, 𝑦𝑦�(𝑘𝑘) =



D. Soetraprawata and A. Turnip / Mechatronics, Electrical Power, and Vehicular Technology 04 (2013) 1-8 

 

4 
 

[𝑥𝑥1 (𝑘𝑘 − 𝑛𝑛 + 1), … , 𝑥𝑥1 (𝑘𝑘 − 1), 𝑥𝑥1 (𝑘𝑘)]𝑇𝑇 and from 
Eq. (5), the following equation is obtained. 

 
𝑦𝑦𝑘𝑘+1 = 𝑥𝑥2 (𝑘𝑘) = 𝑥𝑥3 (𝑘𝑘 − 1) = ⋯  
          = 𝑥𝑥𝑛𝑛 (𝑘𝑘 − 𝑛𝑛 + 2)  
          = 𝑓𝑓�𝑦𝑦�(𝑘𝑘)� + 𝑔𝑔�𝑦𝑦�(𝑘𝑘)�𝑢𝑢𝑘𝑘−𝑛𝑛+1  
          = 𝜙𝜙2�𝑧𝑧̅(𝑘𝑘)�, (8) 
 

which𝑥𝑥2 (𝑘𝑘)  is a function of 𝑦𝑦(𝑘𝑘)  and 𝑢𝑢𝑘𝑘−𝑛𝑛+1 . 
From (5), similarly the following equation is 
obtained. 
 

𝑦𝑦𝑘𝑘+2 = 𝑓𝑓�𝑦𝑦�(𝑘𝑘 + 1)� + 𝑔𝑔�𝑦𝑦�(𝑘𝑘 + 1)�𝑢𝑢𝑘𝑘−𝑛𝑛+2
          = 𝜙𝜙3��̅�𝑧(𝑘𝑘)�,
⋮
𝑦𝑦𝑘𝑘+𝑛𝑛−1 = 𝑓𝑓�𝑦𝑦�(𝑘𝑘 + 𝑛𝑛 − 2)� + 𝑔𝑔�𝑦𝑦�(𝑘𝑘 + 𝑛𝑛 − 2)�𝑢𝑢𝑘𝑘−1
               = 𝜙𝜙𝑛𝑛�𝑧𝑧̅(𝑘𝑘)�

(9) 

 
It proves that  𝑥𝑥𝑛𝑛 (𝑘𝑘)  is a function of 𝑧𝑧̅(𝑘𝑘) . 

Substituting the predicted states into the last 
equation in (5), we obtain: 

 
𝑦𝑦𝑘𝑘+𝑛𝑛 = 𝑥𝑥𝑛𝑛 (𝑘𝑘 + 1)  
          = 𝑓𝑓�𝑧𝑧̅(𝑘𝑘)� + 𝑔𝑔�𝑧𝑧̅(𝑘𝑘)�𝑢𝑢(𝑘𝑘) (10) 
 

where 
𝑓𝑓�𝑧𝑧�(𝑘𝑘)� = 𝑓𝑓��𝑥𝑥1(𝑘𝑘),𝜙𝜙2�𝑧𝑧�(𝑘𝑘)�, … , 𝜙𝜙𝑛𝑛�𝑧𝑧�(𝑘𝑘)��

𝑇𝑇
�, (11) 

𝑔𝑔�𝑧𝑧�(𝑘𝑘)� = 𝑔𝑔��𝑥𝑥1(𝑘𝑘), 𝜙𝜙2�𝑧𝑧�(𝑘𝑘)�, … , 𝜙𝜙𝑛𝑛�𝑧𝑧�(𝑘𝑘)��
𝑇𝑇
�. (12) 

 
Define a tracking error as 𝑒𝑒𝑦𝑦 (𝑘𝑘) = 𝑦𝑦𝑘𝑘 −

𝑦𝑦𝑑𝑑 (𝑘𝑘). The tracking error dynamics are given by: 
 
𝑒𝑒𝑘𝑘 (k + n) = −𝑦𝑦𝑑𝑑 (𝑘𝑘 + 𝑛𝑛) + 𝑓𝑓�𝑧𝑧̅(𝑘𝑘)�  
                        +𝑔𝑔�𝑧𝑧̅(𝑘𝑘)�𝑢𝑢(𝑘𝑘). (13) 
 
Supposing that the nonlinear functions 

𝑓𝑓�𝑧𝑧̅(𝑘𝑘)� and 𝑔𝑔�𝑧𝑧̅(𝑘𝑘)�are known exactly, then a 
desired classifier, such that the output 𝑦𝑦𝑘𝑘 follows 
the target trajectory 𝑦𝑦𝑑𝑑 (𝑘𝑘), is written as follow: 

 
𝑢𝑢∗(𝑘𝑘) = − 1

𝑔𝑔�𝑧𝑧̅(𝑘𝑘)�
�𝑓𝑓��̅�𝑧(𝑘𝑘)�� − 𝑦𝑦𝑑𝑑 (𝑘𝑘 + 𝑛𝑛). (14) 

 
Substituting the desired classifier equation 

(14) into error dynamics equation (13), i.e., 
𝑢𝑢(𝑘𝑘) = 𝑢𝑢∗(𝑘𝑘), then the error dynamics goes to 
zero is obtained. This means that after n steps, we 
have 𝑒𝑒𝑦𝑦 (𝑘𝑘) = 0 . Therefore, 𝑢𝑢∗(𝑘𝑘)  is a n-step 
dead-beat classifier. Moreover, the desired 
classifier 𝑢𝑢∗(𝑘𝑘) can be expressed as: 

 
𝑢𝑢∗(𝑘𝑘) = 𝑢𝑢�∗�𝑧𝑧̅(𝑘𝑘)�, (15) 
 

where 𝑧𝑧̅(𝑘𝑘) = [𝑧𝑧̅𝑇𝑇(𝑘𝑘), 𝑦𝑦𝑑𝑑 (𝑘𝑘 + 𝑛𝑛)]𝑇𝑇 ∈ Ω𝑧𝑧̅ ⊂ 𝑅𝑅2𝑛𝑛  
with component set zΩ  is defined as 

 
Ω𝑧𝑧̅ = ��(𝑦𝑦�(𝑘𝑘), 𝑢𝑢𝑘𝑘−1 (𝑘𝑘), 𝑦𝑦𝑑𝑑 )|𝑢𝑢�𝑘𝑘−1 (𝑘𝑘) ∈

Ω𝑢𝑢,𝑦𝑦𝑘𝑘,𝑦𝑦𝑑𝑑∈Ω𝑦𝑦. (16) 
 
When the nonlinear functions 𝑓𝑓�𝑧𝑧̅(𝑘𝑘)�  and 

𝑔𝑔�𝑧𝑧̅(𝑘𝑘)� are unknown, the nonlinearity 𝑢𝑢∗(𝑘𝑘) is 
not available. In the following, high order neural 
networks (HONNs) is introduced to construct the 
unknown nonlinear functions 𝑓𝑓�𝑧𝑧̅(𝑘𝑘)�  and 
𝑔𝑔�𝑧𝑧̅(𝑘𝑘)� for approximating the desired feedback 
signal 𝑢𝑢∗(𝑘𝑘) . Under certain conditions, it has 
been proven that neural networks has function 
approximation abilities and has been frequently 
used as function approximators, which include 
linearly and nonlinearly parameterized networks. 
Consider the following HONNs [16, 18]:  

 
𝜑𝜑(𝑊𝑊, 𝑧𝑧) = 𝑊𝑊𝑇𝑇𝑆𝑆(𝑧𝑧), 𝑊𝑊and 𝑆𝑆(𝑧𝑧) ∈ 𝑅𝑅𝑙𝑙 , (17) 
𝑆𝑆(𝑧𝑧) = [𝑠𝑠1 (𝑧𝑧), 𝑠𝑠2 (𝑧𝑧), … , 𝑠𝑠𝑙𝑙(𝑧𝑧)]𝑇𝑇, (18) 
𝑠𝑠𝑖𝑖(𝑧𝑧) = ∏ �𝑠𝑠(𝑧𝑧𝑗𝑗 )�

𝑑𝑑𝑗𝑗 (𝑖𝑖)
𝑗𝑗∈𝑙𝑙𝑖𝑖 , 𝑖𝑖 = 1,2, … , 𝑙𝑙  , (19) 

 
where 𝑧𝑧 = [𝑧𝑧1 , 𝑧𝑧2 , … , 𝑧𝑧𝑚𝑚 ]𝑇𝑇 ∈ Ω𝑧𝑧 ⊂ 𝑅𝑅𝑚𝑚 ; the 
positive integer 𝑙𝑙 indicates the node number of 
neural network; 𝑑𝑑𝑗𝑗 (𝑖𝑖) indicates the non-negative 
integers; 𝑊𝑊  is an adjustable synoptic weight 
vectors; and 𝑠𝑠(𝑧𝑧𝑗𝑗 )  is chosen as a hyperbolic 
tangent function. 

 

𝑠𝑠(𝑧𝑧𝑗𝑗 ) =
𝑒𝑒𝑧𝑧𝑗𝑗 − 𝑒𝑒−𝑧𝑧𝑗𝑗

𝑒𝑒𝑧𝑧𝑗𝑗 + 𝑒𝑒−𝑧𝑧𝑗𝑗
 (20) 

 
According to Girosi and Poggio (1989) [19], 

there exist ideal weight 𝑊𝑊∗such that the function 
𝜑𝜑(𝑧𝑧)  can be approximated by an ideal neural 
network on a compact set Ω𝑧𝑧 ⊂ 𝑅𝑅𝑚𝑚 : 

 
𝜑𝜑(𝑧𝑧) = 𝑊𝑊∗𝑇𝑇𝑆𝑆(𝑧𝑧) + 𝜀𝜀𝑧𝑧, (21) 
 

where 𝜀𝜀𝑧𝑧 is called the neural network 
approximation error. It is representing the 
minimum possible deviation of the ideal 
approximator 𝑊𝑊∗𝑇𝑇𝑆𝑆(𝑧𝑧) from the unknown 
function 𝜑𝜑(𝑧𝑧).  In general, the ideal neural 
network weight 𝑊𝑊∗ is not known and needs to be 
estimated. In this paper, there exist an integer 𝑙𝑙∗ 
and an ideal constant weight vector 𝑊𝑊∗, such that 
for all 𝑙𝑙 ≥ 𝑙𝑙∗,  

 
𝑢𝑢�∗(𝑧𝑧̅(𝑘𝑘)) = 𝑊𝑊∗𝑇𝑇𝑆𝑆(𝑧𝑧̅(𝑘𝑘)) + 𝜀𝜀𝑧𝑧̅, ∀𝑧𝑧̅ ∈ Ω𝑧𝑧̅, (22) 
 

where 𝜀𝜀𝑧𝑧̅  is the neural network estimation error 
satisfying |𝜀𝜀𝑧𝑧̅| < 𝜀𝜀0 . Based on Lyapunov 
technique, it has been proven in Ge et al., 2003 
[17] that the adaptive classifier law and the 
updating law can be chosen as: 



D. Soetraprawata and A. Turnip / Mechatronics, Electrical Power, and Vehicular Technology 04 (2013) 1-8 

 

5 

 
𝑢𝑢(𝑘𝑘) = 𝑊𝑊� 𝑇𝑇𝑆𝑆(𝑧𝑧̅(𝑘𝑘)), (23) 
𝑊𝑊� (𝑘𝑘 + 1) = 𝑊𝑊� (𝑘𝑘1 ) + Γ[𝑆𝑆�𝑧𝑧̅(𝑘𝑘1 )�(𝑦𝑦𝑘𝑘+1  
                         −𝑦𝑦𝑑𝑑 (𝑘𝑘 + 1)) + 𝜌𝜌𝑊𝑊� (𝑘𝑘)], (24) 
 

where 𝑘𝑘1 = 𝑘𝑘 − 𝑛𝑛 + 1 , diagonal gain matrix 
Γ > 0, and 𝜌𝜌 > 0. Therefore, the tracking error 
converges to a small neighborhood of zero by 
increasing the approximation accuracy of the 
neural networks and the closed-loop stability is 
guaranteed.  

Figure 1 shows the structure of the pre-
processing, feature extraction, and the ANNC 
algorithm. In Figure 1, )(tx  indicates a non-pre 
processed (raw) EEG signal; )(kx  indicates a 
filtered signal; )(ky  indicates an extracted 
signals in which the artifact was removed;  

)(kyd  and ky  indicate a target and classified 
signal, respectively. 

 
IV. RESULT AND DISCUSSION 

In this study, a new method using adaptive 
neural networks for the classification of the EEG-
based P300 signals is proposed. This method is 
supported by the AR model to extract the features 

and reduce the artifact that is contained within 
the EEG signals. The methods mentioned above 
were applied to the training of eight subjects who 
participated in four training sessions with six runs 
for each session. Figure 2 and 3 are the pre-
processed EEG-based P300 signals using 
Butterworth band pass filter and after applying 
the AR method as feature extractor and artifacts 
remover, respectively. Although we can notice 
some improvement, at Figure 3, it is still difficult 
to classify the signals with respect to the P300 
component. Thus, a new adaptive neural 
networks classifier is proposed. 

The tracking error graph with and without 
applying the AR model approach is shown in 
Figure 4. The curves show that a level of 
accuracy is attained after about 250 iterations by 
applying the AR model approach. On the other 
hand, the same level of accuracy is attained after 
1,800 iterations if the proposed feature extraction 
method is not applied. It means the introduction 
of the AR method is relevant to accelerate the 
training processes. 

The tracking error converges to a small value 
around zero while the closed-loop stability is 
guaranteed. Furthermore, the tracking error with 
the AR model was converging in faster. 
According to [17], the data set for subject five 
were not included in the simulation since the 
subject misunderstood the instructions given 
before the experiment. Comparative plots of the 

 
 

Figure 1. Structure of feature extraction and classification 
algorithms 
 

 

 
 
Figure 2. Pre-processed EEG signals using the         
Butterworth band pass filter 

 
Figure 3. Extracted EEG signals using the AR model 

 

 
 
Figure 4. Network’s performance according tomean squares 
errors 



D. Soetraprawata and A. Turnip / Mechatronics, Electrical Power, and Vehicular Technology 04 (2013) 1-8 

 

6 
 

classification accuracies and transfer rates 
(obtained with BLDA, ANNC, and the 
combination of the AR model and ANNC 
methods and averaged over four sessions) for the 
disable-bodied subjects (subjects 1 – 4) and able-
bodied subjects (subjects 6 – 9) are shown in 
Figure 5 and 6, respectively.  

All of the subjects (with the combination of 
the AR model and ANNC methods), except for 
subjects 6 and 9, achieved an average 
classification accuracy of 100% after five blocks 
of stimulus presentations were averaged (i.e., 14 
second). However, subjects 6 and 9, compared 
with BLDA, still achieved an average 
classification accuracy of 100% after nine and ten 

 
 
Figure 5. Comparison of classification accuracy and transfer rate plots obtained with BLDA, ANNC, and the combination of the 
AR model and ANNC for disable-bodied  subjects 
 

 
 
Figure 6. Comparison of classification accuracy and transfer rate plots obtained with BLDA, ANNC, and the combination of the 
AR model and ANNC for able-bodied subjects 

 

 

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D. Soetraprawata and A. Turnip / Mechatronics, Electrical Power, and Vehicular Technology 04 (2013) 1-8 

 

7 

blocks of stimulus presentations were averaged, 
respectively. This results give a significant 
improvement compared with the results presented 
in [17] in which subject 6 and subject 9 were not 
achieved an average classification accuracy of 
100%. It means the introduction of the AR 
method and the application of the proposed 
classifier enables the BCI to extract and classify 
the information in terms of the classification 
accuracy from a fatigue subject. Thus, fatigue as 
one of the reasons for the poorer performance of 
subject 9, as mentioned in Hoffmann et al. [5], 
can be solved using the proposed method. 

 
V. CONCLUSIONS 

The results presented in this study show that 
corresponding to the classification accuracy, the 
data indicates that a P300-based BCI system can 
communicates at the rate of 31.2 bits/min and 
36.7 bits/min for the disable-bodied and able-
bodied subjects, respectively. The classification 
and transfer rate accuracies obtained based 
ANNC with the AR models approach are found 
to be far superior in comparison with the BLDA 
approach and therefore better suited for BCI 
applications. 

 
ACKNOWLEDGEMENT 

This work is a part of thematics project 
research funded by UPT BPI LIPI (DIPA NO. 
3425.01.011) budgetting year of 2012. The 
authors would like to thank the Deputy 
Chairmant for Scientific Services Dr. Fatimah 
Zulfah S. Padmadinata for supporting to publish 
this paper. 

 
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	Feature Extraction
	Adaptive Neural Networks Classifier