Fast Embedding for JOFC Using the Raw Stress Criterion

TL;DR

This paper introduces a fast and efficient method for JOFC manifold embedding by exploiting its structure to accelerate Guttman transforms, enabling scalable in-sample and out-of-sample embeddings on real and simulated data.

Contribution

It presents an exact and efficient computation of Guttman transforms for JOFC, significantly speeding up the embedding process.

Findings

Achieved substantial speed-up in JOFC embedding process.

Demonstrated scalability on real and simulated datasets.

Improved efficiency without sacrificing embedding quality.

Abstract

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.