Fidelity-Commensurability Tradeoff in Joint Embedding of Disparate Dissimilarities

TL;DR

This paper explores a joint embedding method for disparate dissimilarities that balances fidelity and commensurability, optimizing statistical power in match detection tasks.

Contribution

It introduces a weighted multidimensional scaling approach to explicitly control the fidelity-commensurability tradeoff in joint embeddings.

Findings

Optimal weights differ from equal weighting for best inference performance.

Weighted embedding significantly improves statistical power in match detection.

Explicit tradeoff control enhances joint embedding effectiveness.

Abstract

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