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Abstract: Human experts constitute pattern classes of natural objects based on their observed appearance. Automatic systems for pattern recognition may be designed on a structural description derived from sensor observations. Alternatively, training sets of examples can be used in statistical learning procedures. They are most powerful for vectorial object representations. Unfortunately, structural descriptions do not match well with vectorial representations. Consequently it is difficult to combine the structural and statistical approaches to pattern recognition. Structural descriptions may be used to compare objects. This leads to a set of pairwise dissimilarities from which vectors can be derived for the purpose of statistical learning. The resulting dissimilarity representation bridges thereby the structural and statistical approaches. The dissimilarity space is one of the possible spaces resulting from this representation. It is very general and easy to implement. This paper gives a historical review and discusses the properties of the dissimilarity space approaches illustrated by a set of examples on real world datasets. [Copyright &y& Elsevier]

Abstract: A conventional way to discriminate between objects represented by dissimilarities is the nearest neighbor method. A more efficient and sometimes a more accurate solution is offered by other dissimilarity-based classifiers. They construct a decision rule based on the entire training set, but they need just a small set of prototypes, the so-called representation set, as a reference for classifying new objects. Such alternative approaches may be especially advantageous for non-Euclidean or even non-metric dissimilarities. The choice of a proper representation set for dissimilarity-based classifiers is not yet fully investigated. It appears that a random selection may work well. In this paper, a number of experiments has been conducted on various metric and non-metric dissimilarity representations and prototype selection methods. Several procedures, like traditional feature selection methods (here effectively searching for prototypes), mode seeking and linear programming are compared to the random selection. In general, we find out that systematic approaches lead to better results than the random selection, especially for a small number of prototypes. Although there is no single winner as it depends on data characteristics, the k-centres works well, in general. For two-class problems, an important observation is that our dissimilarity-based discrimination functions relying on significantly reduced prototype sets (3–10% of the training objects) offer a similar or much better classification accuracy than the best k-NN rule on the entire training set. This may be reached for multi-class data as well, however such problems are more difficult. [Copyright &y& Elsevier]

In this paper, a classification task on dissimilarity representations is considered. A traditional way to discriminate between objects represented by dissimilarities is the nearest neighbor method. It suffers, however, from a number of limitations, i.e., high computational complexity, a potential loss of accuracy when a small set of prototypes is used and sensitivity to noise. To overcome these shortcomings, we propose to use a normal density-based classifier constructed on the same representation. We show that such a classifier, based on a weighted combination of dissimilarities, can significantly improve the nearest neighbor rule with respect to the recognition accuracy and computational effort. [Copyright &y& Elsevier]