统计与管理学院2015年学术报告第54期
【主 题】Two-stage Regularized Linear Discriminant Analysis for 2-D Data
【报告人】赵建华
云南财经大学统计系
【时 间】 2015年12月3日（星期四）10:00－11:00
【地 点】 上海财经大学统计与管理学院大楼1208室
【语 言】 英文
【摘 要】Fisher linear discriminant analysis (LDA) involves within-class and between class covariance matrices. For 2 D data such as images, regularized LDA (RLDA) can improve LDA due to the regularized eigenvalues of the estimated within-class matrix. However, it fails to consider the eigenvectors and the estimated between class matrix. To improve these two matrices simultaneously, we propose in this paper a new two-stage method for 2-D data, namely a bi-directional LDA (BLDA) in the first stage and the RLDA in the second stage, where both BLDA and RLDA are based on the Fisher criterion that tackles correlation. BLDA performs the LDA under special separable covariance constraints that incorporate the row and column correlations inherent in 2-D data. The main novelty is that we propose a simple but effective statistical test to determine the subspace dimensionality in the first stage. As a result, the first stage reduces the dimensionality substantially while keeping the significant discriminant information in the data. This enables the second stage to perform RLDA in a much lower dimensional subspace and thus improves the two estimated matrices simultaneously. Experiments on a number of 2-D synthetic and real-world data sets show that BLDA$+$RLDA outperforms several closely related competitors.
【邀请人】柏杨
