Fidelity-Commensurability Tradeoff in Joint Embedding of Disparate Dissimilarities

摘要

In various data settings, it is necessary to compare observations fromdisparate data sources. We assume the data is in the dissimilarityrepresentation and investigate a joint embedding method that results in acommensurate representation of disparate dissimilarities. We further assumethat there are "matched" observations from different conditions which can beconsidered to be highly similar, for the sake of inference. The joint embeddingresults in the joint optimization of fidelity (preservation of within-conditiondissimilarities) and commensurability (preservation of between-conditiondissimilarities between matched observations). We show that the tradeoffbetween these two criteria can be made explicit using weighted raw stress asthe objective function for multidimensional scaling. In our investigations, weuse a weight parameter, $w$, to control the tradeoff, and choose matchdetection as the inference task. Our results show weights that are optimal(with respect to the inference task) are different than equal weights forcommensurability and fidelity and the proposed weighted embedding schemeprovides significant improvements in statistical power.