Convex support and Relevance Vector Machines for selective multimodal pattern recognition

We address the problem of featureless pattern recognition under the assumption that pair-wise comparison of objects is arbitrarily scored by real numbers. Such a linear embedding is much more general than the traditional kernel-based approach, which demands positive semi-definiteness of the matrix of object comparisons. This demand is frequently prohibitive and is further complicated if there exist a large number of comparison functions, i.e., multiple modalities of object representation. In these cases, the experimenter typically also has the problem of eliminating redundant modalities and objects. In the context of the general pair-wise comparison space this problem becomes mathematically analogous to that of wrapper-based feature selection. The resulting convex SVM-like training criterion is analogous to Tipping's Relevance Vector Machine, but essentially generalizes it via the presence of a structural parameter controlling the selectivity level.