Noninvasive Cardiac Signal Analysis Using Data Decomposition Techniques - Modeling in Computational Biology and Biomedicine - page 108

Tabl e 3. 1 Comparative summary of the main features of PCA and ICA

Features PCA ICA

Source assumptions Uncorrelated (second-order

independent) Gaussian or
non-Gaussian sources
(principal components)

Independent (at orders higher than
two) non-Gaussian sources
(independent components)

Mixing matrix
assumptions

Full column rank with
orthogonal columns (scaled
principal directions)

Full column rank with arbitrary
structure

Statistics Second-order statistics

(covariance matrix)

Higher-order statistics (typically,
fourth-order cumulants)

Solutions Matrix decompositions (EVD,

SVD)

Iterative algorithms (e.g.,
RobustICA)

Computational cost Lower than ICA's Higher than PCA's

Additional features Optimal compression in the

MSE sense

Insensitive to additive Gaussian
noise

be difficult to analyze by the cardiologist, especially when different leads or
time intervals provide seemingly conflicting information. Yet, as we have seen
throughout the chapter, this diversity can effectively be exploited by signal process-
ing techniques decomposing the observed data into latent components or sources
that are often easier to interpret than the observed ECG. Such components yield
alternative representations of the original data according to specific features of
interest. While PCA explains the data in terms of second-order statistics (variance
and covariance) and results in uncorrelated sources, ICA can sometimes provide
deeper insights by searching for independence through the use of higher-order
statistics (cumulants). The main features of PCA and ICA are summarized in
Tab le 3.1 . These linear data decomposition techniques are capable of revealing
underlying structures of the ECG signal that remain otherwise hidden to the
naked eye. As a result, such methods prove useful in noninvasively detecting and
estimating cardiac electrophysiological phenomena of interest, such as TWA and
atrial activity during AF, thus aiding the cardiologist to make subsequent clinical
decisions. Indeed, an accurate TWA detection allows a more precise assessment of
the risks of sudden cardiac death, whereas a clean atrial activity signal simplifies the
estimation and improves the statistical significance of clinically pertinent parameters
such as dominant atrial frequency or atrial cycle length.
Although the chapter has focused on ECG signals, these decomposition tech-
niques have also shown their success in processing other biomedical data such
as functional magnetic resonance images, electroencephalograms and electromyo-
grams, to name but a few [ 27 ], [ 9 , Chap. 18]. Chapters 5 and 7 of this topic
apply PCA to cardiac imaging and brain signal analysis, respectively. Other linear
data decomposition approaches including nonnegative matrix factorization, sparse
component analysis and tensor factorizations have drawn intense research attention
in recent years [ 9 ], and so have nonlinear dimensionality reduction techniques [ 23 ]
(see also Chap. 7). Their application to ECG signal processing and other biomedical
problems is a promising avenue of ongoing research.