Biomedical Engineering Reference
In-Depth Information
Window Length and Model Order Selections
The important considerations for determining window length for segmentation are
the balance between (1) acquiring a suffi cient number of data points and (2) main-
taining local stationarity. The window length should be small enough to allow treat-
ing the data as stationary yet large enough to allow estimation of VAR coeffi cients.
The general rule is that the number of parameters should be <10 % of the data
samples, i.e., to fi t a VAR model with model order
p
on data of
k
dimensions (
k
ICs
selected from ICA), the following relation needs to be satisfi ed:
w
10 × (
k
2
×
p
/
n
),
where
w
and
n
represent the window length and the number of trials, respectively.
Model order, which is related to the length of the signal in the past that is relevant
to the current observation, is another key parameter that needs to be determined. If
the chosen model is too low, the VAR model cannot capture dynamic relations in the
data and the frequency resolution will be impaired. The most popular approach for
model order selection is based on the Akaike information criterion (AIC) (Akaike
1974
) and/or the Bayesian information criterion (BIC) (Schwarz
1978
). A detailed
comparison of different information criteria can be found in (Lütkepohl
2005
).
≥
Spectral Functional Connectivity Measures
Functional connectivity, which is defi ned as the temporal correlation between
spatially remote neurophysiological events (Friston et al.
1993
), is one way to
characterize interaction or functional integration between brain regions.
Coherency, which is the spectral analogue of the cross correlation, and its deriva-
tives, such as coherence and partial coherence, are common spectral VAR-based
functional connectivity measures (Brillinger
2001
). Their incapability to access
causality or directionality between or among signals is one of the main drawbacks
of functional connectivity measures; this can be overcome by using effective con-
nectivity measures.
Spectral Effective Connectivity Measures
Most of the spectral effective connectivity measures are based on the concept of
Granger causality (GC): if one can predict signal
X
better by incorporating past
information from signal
Y
than by using only information from its own past, then
signal
Y
is causal for signal
X
(Wiener
1956
; Granger
1969
). Brief overviews of
effective connectivity measures for multichannel data can be found in (Delorme
et al.
2011
; Blinowska
2011
).
In contrast to functional connectivity measures, effective connectivity measures
capture asymmetric causal dependencies between signals, which can reveal direc-
tional information fl ow between brain regions. Effective connectivity measures can
be classifi ed into two types, according to the number of signals included in the
VAR estimation: bivariate or multivariate. Bivariate measures estimate VAR
