Visualizing pairwise similarity via Semidefinite Programming

Amir Globerson, Sam Roweis

Research output: Contribution to journalConference articlepeer-review

Abstract

We introduce a novel learning algorithm for binary pairwise similarity measurements on a set of objects. The algorithm delivers an embedding of the objects into a vector representation space that strictly respects the known similarities, in the sense that objects known to be similar are always closer in the embedding than those known to be dissimilar. Subject to this constraint, our method selects the mapping in which the variance of the embedded points is maximized. This has the effect of favoring embeddings with low effective dimensionality. The related optimization problem can be cast as a convex Semidefinite Program (SDP). We also present a parametric version of the problem, which can be used for embedding out of sample points. The parametric version uses kernels to obtain nonlinear maps, and can also be solved using an SDP. We apply the two algorithms to an image embedding problem, where it effectively captures the low dimensional structure corresponding to camera viewing parameters.

Original languageEnglish
Pages (from-to)139-146
Number of pages8
JournalJournal of Machine Learning Research
Volume2
StatePublished - 2007
Externally publishedYes
Event11th International Conference on Artificial Intelligence and Statistics, AISTATS 2007 - San Juan, Puerto Rico
Duration: 21 Mar 200724 Mar 2007

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