文档介绍：Least Squares Linear Discriminant Analysis Jieping Ye jieping.******@ Department puter Science and Engineering, Arizona State University, Tempe, AZ 85287 USA Abstract Linear Discriminant Analysis (LDA) is a well-known method for dimensionality reduc- tion and classi?cation. LDA in the binary- class case has been shown to be equiva- lent to linear regression with the class label as the output. This implies that LDA for binary-class classi?cations can be formulated as a least squares problem. Previous stud- ies have shown certain relationship between multivariate linear regression and LDA for the multi-class case. Many of these studies show that multivariate linear regression with a speci?c class indicator matrix as the out- put can be applied as a preprocessing step for LDA. However, directly casting LDA as a least squares problem is challenging for the multi-class case. In this paper, a novel for- mulation for multivariate linear regression is proposed. The equivalence relationship be- tween the proposed least squares formulation and LDA for multi-class classi?cations is rig- orously established under a mild condition, which is shown empirically to hold in many applications involving high-dimensional data. Several LDA extensions based on the equiv- alence relationship are discussed. 1. Introduction Linear Discriminant Analysis (LDA) is a well-known method for dimensionality