361. New results on the multi-dimensional linear discriminant analysis problem
Invited abstract in session TA-1: Plenary II - Amir Beck, stream Plenaries.
Thursday, 8:45 - 9:35Room: M:A
Authors (first author is the speaker)
| 1. | Amir Beck
|
| School of Mathematical Sciences, Tel-Aviv University |
Abstract
Fisher linear discriminant analysis (LDA) is a well-known technique for dimensionality reduction and classification. The method was first formulated in 1936 by Fisher. We present three different formulations of the multi-dimensional problem and show why two of them are equivalent. We then prove a rate of convergence of the form $O(q^{k^2}))$ for solving the third model. Finally, we consider the max-min LDA problem in which the objective function seeks to maximize the minimum separation among all distances between all classes. We show how this problem can be reduced into a quadratic programming problem with nonconvex polyhedral constraints and describe an effective branch and bound method for its solution. Joint work with Raz Sharon.
Keywords
- Linear and nonlinear optimization
Status: accepted
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