Abstract

For matched data from disparate sources (objects observed under different conditions), optimality of information fusion must be defined with respect to the inference task at hand. Defining the task as matched/unmatched hypothesis testing for dissimilarity observations, the forthcoming Manifold Matching paper by Priebe et al. presents an embedding method based on joint optimization of fidelity (preservation of within-condition dissimilarities between observations of an object) and commensurability (preservation of between-condition dissimilarities between observations). We investigate the tradeoff between fidelity and commensurability by varying weights in weighted embedding of an omnibus dissimilarity matrix. Optimal (defined with respect to the power of the test) weights for the optimization correspond to an optimal compromise between fidelity and commensurability. The two extremes of this tradeoff are commensurability optimization prioritized over fidelity optimization and vice versa. Results indicate optimal weights are different than equal weights for commensurability and fidelity and our weighted embedding scheme provides significant improvements in test power.