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JMLR
2010

Fluid Dynamics Models for Low Rank Discriminant Analysis

11 years 1 days ago
Fluid Dynamics Models for Low Rank Discriminant Analysis
We consider the problem of reducing the dimensionality of labeled data for classification. Unfortunately, the optimal approach of finding the low-dimensional projection with minimal Bayes classification error is intractable, so most standard algorithms optimize a tractable heuristic function in the projected subspace. Here, we investigate a physics-based model where we consider the labeled data as interacting fluid distributions. We derive the forces arising in the fluids from information theoretic potential functions, and consider appropriate low rank constraints on the resulting acceleration and velocity flow fields. We show how to apply the Gauss principle of least constraint in fluids to obtain tractable solutions for low rank projections. Our fluid dynamic approach is demonstrated to better approximate the Bayes optimal solution on Gaussian systems, including infinite dimensional Gaussian processes.
Yung-Kyun Noh, Byoung-Tak Zhang, Daniel D. Lee
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where JMLR
Authors Yung-Kyun Noh, Byoung-Tak Zhang, Daniel D. Lee
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