Biomedical Engineering Reference
In-Depth Information
ability to use prior information about the sample are two drawbacks added
to those mentioned above. In controlled systems, however, for example where
a small class of pure materials or limited numbers of constituents without
chance of significant contamination are available, PCA is exceptionally useful
for classification and identification. Several recent examples are available from
studies on protein optical activity [53], recognition of atherosclerotic plaques
[54], polymer mixtures [55], fiber types [56], narcotics [57], chemical histol-
ogy [58], cellular transformations [59-61]. Finally, our logic for assigning PCA
to the pre-processing stage is the emergence of many sophisticated classifica-
tion studies that do not employ simple spectral measures but employ PCA
loadings and vectors as inputs for more sophisticated classification techniques
discussed in the next sections [62-65].
PCA is also a powerful adjunct to classical regression techniques [66]. One
major drawback of multivariate linear regression (MLR) techniques is their
sensitivity to collinear data [67], which is sometimes masked by noise. Hence,
approaches like step-wise linear regression have been suggested to discard vari-
ables. An alternative is to employ PCA and conduct regression on components
that are, by definition, orthogonal. Further, principal components regression
(PCR) is less sensitive to measurement noise. The blind nature of variance,
however, does not guarantee that the first
m
selected features are indeed most
relevant to the scientific question. Hence, all components need to be extracted
and evaluated in the prediction model. Partial least-squares regression [67, 68]
(PLSR) and related formulations [69-71] can be used to address this drawback
[72]. The algorithm extracts components that are relevant to both dependent
and independent variables in the regression in decreasing order of relevance.
Hence, an incrementally larger model can be compared to a smaller model to
choose the more useful one. Implicit in these strategies is the fact that the cor-
related signal in the first few components is akin to signal averaging spectra
in the data set. Hence, noise reduction is implicit in PCA-based regression.
Other classification schemes will have to explicitly use larger spectral features
or, for example, constrained regularization methods [73] to be comparable.
Similarly, other algorithms can be used to eliminate sample variances due
to preparation and process artifacts [74], but PCA-based methods retain the
noise reduction benefits from all data points very well. A major consequence
of this property and orthogonality is that classifications are often highly ac-
curate and facile, contributing to the popularity of PCA-based methods [75].
Similarly, PCA-based discriminant analysis has been used to obtain highly ac-
curate classifications that are at least as good as more sophisticated, nonlinear
methods [76].
8.2.6 High-Performance Algorithms
While we have discussed pre-processing steps in a sequential manner, newer
approaches are capable of integrating all the steps into single transforma-
tion approaches. For example, applications of wavelet transforms [77] can
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