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When Fisher meets Fukunaga-Koontz: A New Look at Linear Discriminants

10 years 2 months ago
When Fisher meets Fukunaga-Koontz: A New Look at Linear Discriminants
The Fisher Linear Discriminant (FLD) is commonly used in pattern recognition. It finds a linear subspace that maximally separates class patterns according to Fisher's Criterion. Several methods of computing the FLD have been proposed in the literature, most of which require the calculation of the so-called scatter matrices. In this paper, we bring a fresh perspective to FLD via the Fukunaga-Koontz Transform (FKT). We do this by decomposing the whole data space into four subspaces, and show where Fisher's Criterion is maximally satisfied. We prove the relationship between FLD and FKT analytically, and propose a method of computing the most discriminative subspace. This method is based on the QR decomposition, which works even when the scatter matrices are singular, or too large to be formed. Our method is general and may be applied to different pattern recognition problems. We validate our method by experimenting on synthetic and real data.
Sheng Zhang, Terence Sim
Added 12 Oct 2009
Updated 28 Oct 2009
Type Conference
Year 2006
Where CVPR
Authors Sheng Zhang, Terence Sim
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