Fast Embedding for JOFC Using the Raw Stress Criterion. Issue 4 (2nd October 2017)

• Record Type: Journal Article
• Authors: Lyzinski, Vince; Park, Youngser; Priebe, Carey E.; Trosset, Michael
• Is Part Of: Journal of computational and graphical statistics. Volume 26:Issue 4(2017)
• Page Start: 786
• Page End: 802
• Publication Date: 2017-10-02
• Subjects: Distance geometry -- Distance matrices -- Manifold matching -- Multidimensional scaling; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2017.1321551
• Languages: English
• ISSNs: 1061-8600

Abstract

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 article, 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.