期刊
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
卷 40, 期 1, 页码 92-105出版社
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2017.2666148
关键词
Discriminant analysis; dimensionality reduction; fluid dynamics; Gauss principle of least constraint; Gaussian processes
资金
- NSRI
- BK21Plus [MITIP-10048320]
- AFOSR
- OFRN-C4ISR
- NSF [IIS EAGER 1550757]
- BMRR
- Soft Robot ERC
- U.S. NSF
- ONR
- ARL
- DOT
- DARPA
- [IITP-R0126-16-1072]
- [KEIT-10060086]
- [KEIT-10044009]
Classical discriminant analysis attempts to discover a low-dimensional subspace where class label information is maximally preserved under projection. Canonical methods for estimating the subspace optimize an information-theoretic criterion that measures the separation between the class-conditional distributions. Unfortunately, direct optimization of the information-theoretic criteria is generally non-convex and intractable in high-dimensional spaces. In this work, we propose a novel, tractable algorithm for discriminant analysis that considers the class-conditional densities as interacting fluids in the high-dimensional embedding space. We use the Bhattacharyya criterion as a potential function that generates forces between the interacting fluids, and derive a computationally tractable method for finding the low-dimensional subspace that optimally constrains the resulting fluid flow. We show that this model properly reduces to the optimal solution for homoscedastic data as well as for heteroscedastic Gaussian distributions with equal means. We also extend this model to discover optimal filters for discriminating Gaussian processes and provide experimental results and comparisons on a number of datasets.
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