Dissimilarity representation on functional spectral data for classification

In chemometrics, spectral data are typically represented by vectors of features in spite of the fact that they are usually plotted as functions of e.g. wavelengths and concentrations. In the representation, this functional information is thereby not reflected. Consequently, some characteristics of the data that can be essential for discrimination between samples of different classes or any other analysis are ignored. Examples are the continuity between measured points and the shape of curves. In the Functional Data Analysis (FDA) approach, the functional characteristics of spectra are taken into account by approximating the data by real valued functions, e.g. splines. Another solution is the Dissimilarity Representation (DR), in which classifiers are trained in a space built by dissimilarities with training examples or prototypes of each class. Functional information may be incorporated in the definition of the dissimilarity measure. In this paper we compare the feature-based representation of chemical spectral data with three other representations: FDA, DR defined on raw data and DR defined on FDA descriptions. We analyze the classification results of these four representations for five data sets of different types, by using different classifiers. We demonstrate the importance of reflecting the functional characteristics of chemical spectral data in their representation, and we show when the presented approaches are more suitable.