Chemometric Methods for Biomedical Raman Spectroscopy and Imaging - Emerging Raman Applications and Techniques in Biomedical and Pharmaceutical Fields - page 176

related to categorizing substances into classes that reflect function. With the
emergence of large-scale data recording (including imaging), high-throughput
experimental designs, and increasing computational power, this categorization
is increasingly being conducted using automated numerical algorithms. The
richness and availability of myriad data allow vibrational spectroscopists to
both use methods from and actively contribute to the development of chemo-
metrics [2]. The primary focus here is on describing the general methods a
practicing spectroscopist may use for biomedical data processing and their
relative merits. We also present an illustrative case study from our laborato-
ries to emphasize an integrated approach to designing experiments, recording
data, obtaining results, and verifying their statistical validity.
Chemometrics relates chemical measurements of a material to its func-
tional state using mathematical and statistical methods. Hence, in our view,
it encompasses the domain of using numerical methods to improve data qual-
ity (both the signal-to-noise ratio and resolution), classification of informa-
tion from the data (both supervised and unsupervised methods), and the
appropriate display of information (both visualization of information content
and its statistical validity). For problems especially focused on classification,
the first category of methods is usually termed as pre-processing while the
last is usually termed as post-processing. In this chapter, we organize the
method descriptions within these broad sub-sections. Due to limited space,
we do not provide many details of methods but will point to key references.
We also do not discuss aspects of data acquisition physics, for example, for
tomography or nonlinear spectroscopy that are needed to obtain the data.
Last, since the data handling methods for IR and Raman spectroscopy are
rather similar, we provide examples from either domain without significant
distinction.
The vibrational spectrum is a quantitative measure of a sample's molecu-
lar composition. Hence, classical chemometric methods, especially regression
based, have focused on exact mapping between identity and sample com-
position. Typically, these methods include a training (calibration) step and
a prediction (validation) step in which exact compositions of molecules are
known and predicted. Fundamentally, the methods involve some form of re-
gression [3] for identity mapping with different optimization conditions and
constraints, using optimized spectral sections [4, 5]. The basic process in clas-
sical chemometrics [6] is illustrated in Fig. 8.1. Consider that measurements
are performed on a sample. The “sample” may be a protein, tablet, person,
or some other extract. Many data may be expressed for the sample, including
identity (class) of the sample, concentrations, or spectra. The measured quan-
tities are generally termed as variables. When K variables are measured for
S samples, the resulting data can be reconstituted in terms of a matrix of size
S K (Fig. 8.1). The fundamental focus of classical chemometrics approaches

is to decompose the matrix into significantly smaller matrices of size S

×

× M

and M × K that contain all relevant information about the sample as well as a

matrix S × K that is predominantly noise. The principal rationale is that the