If consider that SFS matrix is a set of features f1 (x)....fi (x) where
x is excitation-emission coordinate, the applicable dissimilarity
measure for SFS objects space is weighted Minkowski metric. The
dimension of SFS feature space is high (25 40 = 1000) thus the
selected metric is exposed to the detrimental effects of curse of
the dimensionality, a term introduced by Bellman in 1961 (Beyer,
Goldstein, Ramakrishnan, & Shaft, 1999).
It is proposed to use feature extraction method to extract the
relevant information from SFS data and thereby suppress dimensionality
effect.
It is assumed that for the selected dataset of juice products the
needed information is carried in the variance of the features.
Thereby Principal Component Analysis (PCA) was selected as
method to extract the relevant features from data. The linear transformation
employed by PCA method is based on preserving the
most variance in the data using reduced to a minimum number
of dimensions. Using linear transformation the high-dimensional
data is embedded in low dimensional Principal Component (PC)
space where the new uncorrelated features have the best represent
of entire data (Shlens, 2009). As will be shown later two first PCs
with highest variance provide robust classification of juice product
type and also have clear interpretation within the bounds of SFS
terms.