Metric and non-metric proximity transformations at linear costs

Abstract: Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these data are given as pairwise (dis-)similarities only. The few available methods for such data focus widely on similarities and do not scale to large data sets. Kernel methods are very effective for metric similarity matrices, also at large scale, but costly transformations are necessary starting with non-metric (dis-) similarities. We propose an integrative combination of Nystroem approximation, potential double centering and eigenvalue correction to obtain valid kernel matrices at linear costs in the number of samples. By the proposed approach effective kernel approaches, become accessible. Experiments with several larger (dis-)similarity data sets show that the proposed method achieves much better runtime performance than the standard strategy while keeping competitive model accuracy. The main contribution is an efficient and accurate technique, to convert (potentially non-metric) large scale dissimilarity matrices into approximated positive semi-definite kernel matrices at linear costs.