Multiple channels (multivariate) signals - Practical Biomedical Signal Analysis Using MATLAB - page 94

such as electroencephalograms or local field potentials (LFP). This problem will be
further discussed in Sect. 4.1. In this context it is worth mentioning that some linear
methods, e.g., DTF, work quite well also for non-linear time series [Winterhalder
et al., 2005].
In the above quoted reference comparison of linear techniques inferring directed
interactions in multivariate systems was carried out. Partial phase spectrum (PC) and
three methods based on Granger causality: GCI, DTF and PDC, were tested in re-
spect to specificity in absence of influences, correct estimation of direction, direct
versus indirect transmissions, non-linearity of data, and influences varying in time.
All methods performed mostly well with some exceptions. PC failed in the most
important aspect—estimation of direction. It was due to the large errors in phase es-
timation for particular frequencies and the inability to detect reciprocal interactions.
GCI failed in the presence of non-linearities. DTF did not distinguish direct from
cascade flows, but when such distinction is important dDTF may be used. PDC for
signals with a non-linear component gave correct results only for very high model
orders, which makes the method hardly applicable for strongly non-linear signals be-
cause of limitations connected with the number of parameters of MVAR mentioned
in Sect. 3.3.2.3.2.
More important drawbacks of PDC were pointed out by [Schelter et al., 2009],
namely:
i) PDC is decreased when multiple signals are emitted from a given source,
ii) PDC is not scale-invariant, since it depends on the units of measurement of the
source and target processes,
iii) PDC does not allow conclusions on the absolute strength of the coupling.
The authors proposed the renormalization of PDC similar to the one used in the
definition of DTF, which helped in alleviation of the above problems.
Point iii) is illustrated in Figure 3.5. In a situation when activity is emitted in sev-
eral directions PDC shows weaker flows than in the situation when the same activity
is emitted in one direction only. Another feature of PDC is a weak dependence on
frequency. The PDC spectrum is practically flat, whereas DTF spectrum (especially
for non-normalized DTF) reflects the spectral characteristics of the signal. An exam-
ple of application of DTF and PDC to experimental data (EEG) will be given in Sect.
4.1.6.2.2.
We can conclude that the methods estimating direction which perform best are
the linear multivariate methods based on the Granger causality concept, and in the
frequency domain the methods or choice are DTF (or dDTF) and renormalized PDC.