Brain–Computer Interfaces - Index of

316 Y. Li et al.
3.3.2 Autoregressive Model Coefficients
An autoregressive model is the model of the current value of the time series from
previous values. The principle behind autoregressive modeling is to extract certain
statistics such as the variance of the data for modeling the time series. Hence, the
coefficients of an AR model can be used as features of brain signals. Given k channels
of brain signal s1(t), ··· , sk(t), the brain signals can be modeled with p the
model order as follows
si(t) = ai1si(t − 1) +···+aipsi(t − p) + ɛi(t), (10)
where i = 1, ··· , k. ai1, ··· , aip are the coefficients of the AR model, and ɛi is
a zero-mean white noise process. The reader is referred to [31] for the process of
computing the coefficients of the AR model.
Given N trials of data, the feature vector of the nth trial can be constructed as
, ··· , a(n)
1p , ··· , a(n)
k1 , ··· , a(n)
kp , σ 2 n1 ··· , σ 2 nk ]T , where n represents the Nth trial,
[a (n)
11
n = 1, ··· , N. This is a simple method for feature extraction based on the AR
model. However, there exist other more advanced methods. For example, a feature
extraction method based on multivariate AR model is presented in [31], where a
sum-square error method is used to determine the order P of the AR model. An
adaptive AR model is used for feature extraction, of which the coefficients are
time-varying in [32], and also Chapter “Adaptive Methods in BCI Research–An
Introductory Tutorial” in this volume.
4 Feature Selection
The number of channels recorded by a BCI system may be large. The number of features
extracted from each individual channel can be large too. In the instance of 128
channels and features derived from an AR model with order 6, the number of features
in total, i.e. the dimension of the feature space, would be 6 times 128. This is a
fairly large amount of features. Although it can be assumed that data recorded from
a large number of channels contain more information, it is likely that some of it is
redundant or even irrelevant with respect to the classification process. Further, there
are at least two reasons why the number of features should not be too large. First,
the computational complexity may become too large to fulfill the real-time requirements
of a BCI. Second, an increase of the dimension of the feature space may
cause a decrease of the performance of the BCI system. This is because the pattern
recognition methods used in BCI systems are set up (trained) using training data,
and the BCI system will be affected much by those redundant or even irrelevant
dimensions of the feature space. Therefore, BCIs often select a subset of features
for further processing. This strategy is called feature or variable selection. Using
feature selection, the dimension of the feature space can be effectively reduced.
Feature selection may also be useful in BCI research. When using new mental tasks
or new BCI paradigms, it may not be always clear which channel locations and
which features are the most suitable. In such cases, feature selection can be helpful.