Chemometric Methods for Biomedical Raman Spectroscopy and Imaging - Emerging Raman Applications and Techniques in Biomedical and Pharmaceutical Fields - page 177

K M K K

M

= +

X e

S S S

Fig. 8.1. A key idea in chemometrics is to record K variables (including spectral
data) for S samples to form a matrix S × K . The critical characteristics of both the
samples and the spectral data can then be understood using a smaller set of matrices
S × M and M × K while the unmodeled residual remains available for analysis as
the matrix e . While the reduced matrices provide insight into the system or process,
residual data can be used to understand errors or limitations of the model

recorded data are repeated measures of a small set of sample characteristics.
The small set defines almost entirely the sample as well as its characteristic
spectral properties.
A number of excellent references are available for classical techniques, in-
cluding those by Kowalski et al. [7, 8], Kramer [9], Brereton [10], compilations
[11, 12], and series of periodic reviews [13]. There are two somewhat related
problems in chemometrics that are relevant to spectral data. The first is to
predict molecular identifications in mixtures from a spectrum and the sec-
ond is to predict a class or label for a spectrum. While regression techniques
work well for molecular identifications, problems of biomedical interest of-
ten involve stochastically varying compositions and spatial distributions of

Data Acquisition

Pre-processing

Feature Selection

Classification

Supervised Unsupervised

Bayes
Classifier

Nearest
Neighbor

Decision
Trees

Genetic
Algorithms

ANN LDA K-means Hierarchical

Fig. 8.2. Overview of data processing steps and classification methods discussed in
this chapter