| The dissimilarity representation is a vital component of modern statistical analysis. By examining all pairs of dissimilarities between the elements of an observed data set, one can leverage the more than 50-year history of statistical pattern recognition on high- and infinite-dimensional spaces, spaces that exhibit non-Euclidean geometry, and spaces that defy analysis by traditional means. However, for most data sets observed in spaces like these, there are many dissimilarities that could be successfully applied. A critical question facing the researcher is: how should one choose which dissimilarity to use in these circumstances, and, if there are many that perform well, can they be combined to optimize inferential performance? We will begin to address these questions by applying a variety of methods from matrix analysis, factor analysis, optimization, combinatorics, and statistics. |
