Global plus local: A complete framework for feature extraction and recognition

Linear discriminant analysis (LDA) is one of the most popular supervised feature extraction techniques used in machine learning and pattern classification. However, LDA only captures global geometrical structure information of the data and ignores the geometrical structure information of local data points. Though many articles have been published to address this issue, most of them are incomplete in the sense that only part of the local information is used. We show here that there are total three kinds of local information, namely, local similarity information, local intra-class pattern variation, and local inter-class pattern variation. We first propose a new method called enhanced within-class LDA (EWLDA) algorithm to incorporate the local similarity information, and then propose a complete framework called complete global–local LDA (CGLDA) algorithm to incorporate all these three kinds of local information. Experimental results on two image databases demonstrate the effectiveness of our algorithms.