Brendan Ames, University of Alabama will give a talk on "Alternating Direction Methods for Dimension Reduction, Classification, and Feature Selection", on Thursday 13 August 15:00-17:00, in the bldg. 303 room 136.
Abstract: Linear Discriminant Analysis (LDA) is a classical technique for dimensionality reduction in supervised classification which relies on projecting the given training data to a lower dimensional space where items in the same class are projected closer to each other than those in other classes. This process is typically performed using a simple change of variables and the solution of the resultant eigenproblem. Unfortunately, this approach fails in the high-dimensional setting where the data being processed contains fewer observations than features; in this case, we cannot perform the change of variables necessary to obtain this projection. In this talk, we present a modification, based on l1-regularization and the alternating direction method of multipliers, for performing LDA in this high-dimensional setting. Moreover, we describe how this approach can be extended to solve penalized eigenproblems in general, including those arising from Sparse Principal Component Analysis, and illustrate the efficacy of our approach on a variety of problems drawn from time-series classification.
Everybody is welcome!