A1034
Title: Linear discriminant regularized regression
Authors: Xin Bing - University of Toronto (Canada) [presenting]
Abstract: Linear discriminant analysis (LDA) is an important classification approach. Its simple linear form makes it easy to interpret, and it is capable of handling multi-class responses. It is closely related to other classical multivariate statistical techniques, such as Fisher's discriminant analysis, canonical correlation analysis and linear regression. Its connection to multivariate response regression is strengthened by characterizing the explicit relationship between the discriminant directions and the regression coefficient matrix. This key characterization leads to a new regression-based multi-class classification procedure that is flexible enough to deploy any existing structured, regularized, and even non-parametric regression methods. Moreover, the new formulation is generically easy to analyze compared to existing regression-based LDA procedures. In particular, complete theoretical guarantees are provided for using the widely used $\ell_1$-regularization that has not yet been fully analyzed in the LDA context. The theoretical findings are corroborated by extensive simulation studies and real data analysis.
