Complexity of Dissimilarity Based Pattern Classes

If the proper dissimilarity measures are provided, some sets of objects, e.g. curves or blobs, may be better described by using representation sets instead of features. The dissimilarity matrix of such a set is the base for further analysis. The question arises how from a given dissimilarity matrix can be judged whether the size of the training set is sufficient to describe the peculiarities of the set. In this paper the problem is defined, some approaches are discussed and illustrated by the analysis of dissimilarity matrices defined by the modified Hausdorff distances between sets of handwritten digits.