Fast Embedding for JOFC Using the Raw Stress Criterion
This work addresses a computational bottleneck for researchers using JOFC in multi-modal data analysis, though it is incremental as it optimizes an existing method.
The paper tackled the computational inefficiency of the JOFC manifold matching method by exploiting its special structure to compute successive Guttman transforms exactly and efficiently, resulting in greatly sped up embeddings for both in-sample and out-of-sample cases, as demonstrated on real and simulated data.
The Joint Optimization of Fidelity and Commensurability (JOFC) manifold matching methodology embeds an omnibus dissimilarity matrix consisting of multiple dissimilarities on the same set of objects. One approach to this embedding optimizes the preservation of fidelity to each individual dissimilarity matrix together with commensurability of each given observation across modalities via iterative majorization of a raw stress error criterion by successive Guttman transforms. In this paper, we exploit the special structure inherent to JOFC to exactly and efficiently compute the successive Guttman transforms, and as a result we are able to greatly speed up the JOFC procedure for both in-sample and out-of-sample embedding. We demonstrate the scalability of our implementation on both real and simulated data examples.