Orthogonal vs. uncorrelated least squares discriminant analysis for feature extraction

Authors:
Feiping Nie;Shiming Xiang;Yun Liu;Chenping Hou;Changshui Zhang
Affiliations:
Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Automation, Tsinghua University, Beijing 100084, China;National Laboratory of Pattern Recognition (NLPR), Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China;School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore;Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Automation, Tsinghua University, Beijing 100084, China;Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Automation, Tsinghua University, Beijing 100084, China
Venue:
Pattern Recognition Letters
Year:
2012

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Abstract

In this paper, a new discriminant analysis for feature extraction is derived from the perspective of least squares regression. To obtain great discriminative power between classes, all the data points in each class are expected to be regressed to a single vector, and the basic task is to find a transformation matrix such that the squared regression error is minimized. To this end, two least squares discriminant analysis methods are developed under the orthogonal or the uncorrelated constraint. We show that the orthogonal least squares discriminant analysis is an extension to the null space linear discriminant analysis, and the uncorrelated least squares discriminant analysis is exactly equivalent to the traditional linear discriminant analysis. Comparative experiments show that the orthogonal one is more preferable for real world applications.