Classification of continuous multi-way data via dissimilarity representation

For many pattern recognition applications, objects are represented by high-dimensional feature vectors, as the result of measurements that are taken from them. Such is the case of spectral data, which is commonly represented by sampling, as a set of individual observations, ignoring the continuous nature of the original data. However, for a considerable number of applications like chemometrics, psychometrics, neuroinformatics, a more appropriate structure to represent data would be a three-way or multi-way array. This type of data should be analyzed with multi-way methods, and this is how researchers from the related fields, moved from multivariate analysis to multi-way analysis. The work reported in this thesis is concerned with the representation and classification of spectral, or in general, continuous multi-way data, such that their continuous nature (structure) is used in their analysis. Although multi-way analysis is not a new research area, classification algorithms for data with this structure and the idea of taking into account the nature of data in their analyses are rather poorly developed. This thesis shows the importance of taking into account the structure/nature of data, in this case continuous multi-way e.g. spectral data, for their discrimination. The first part of our research is dedicated to the study of alternative representations for 1D spectral data, such that their functional nature can be taken into account in their analysis. A representation based on using dissimilarities of an object to other objects as features is studied. In the second part of this study, we show that this dissimilarity representation is also very suitable for multi-way data classification. Particularly, it is useful to incorporate knowledge on the original features/application into the dissimilarities between objects. The dissimilarity representation is also a powerful approach to cope with the small sample size data sets, i.e. few objects in relation to the amount of features, which is very common in spectral data sets. It is further shown that for spectral data, the dissimilarity representation gives flexibility to concentrate on characteristics of spectra, such as the peaks in the signal. By selecting the most discriminative peaks on each feature direction of the array, noisy and redundant information can be discarded. This procedure reduces the cost of the computation of dissimilarities and may improve the accuracy of classifiers. The last part of the thesis studies how to deal with missing values in the context of dissimilarity-based classifiers, as this problem can occur frequently in multi-way data applications. We analyze how the data can be reconstructed before computing dissimilarities. Alternatively, we propose a modification of the dissimilarity measure that takes into account the shape information (CMS), in which dissimilarities are based on the available data only. Both approaches have shown to work well for relatively small amounts of missing values (up to 10%). For some imputation strategies, however, classifiers performed relatively well even for large amounts of missing data (70%). This thesis contributes to the classification of multi-way data. It is shown that including information about the problem at hand in the representation of multi-way data improves the performance of classifiers. As such, it is a new basis for further applications and research in other topics related to multi-way data