A New Linear Discriminant Analysis Method to Address the Over-Reducing Problem

• Published in: Pattern Recognition and Machine Intelligence pp. 65 - 72
• Main Authors: Wan, Huan, Guo, Gongde, Wang, Hui, Wei, Xin
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Binary classification; Dimensionality reduction; LDA for over-reducing problem; Linear discriminant analysis
• ISBN: 3319199404; 9783319199405
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-19941-2_7

Linear discriminant analysis (LDA) is an effective and efficient linear dimensionality reduction and feature extraction method. It has been used in a broad range of pattern recognition tasks including face recognition, document recognition and image retrieval. When applied to fewer-class classification tasks (such as binary classification), however, LDA suffers from the over-reducing problem – insufficient number of features are extracted for describing the class boundaries. This is due to the fact that LDA results in a fixed number of reduced features, which is one less the number of classes. As a result, the classification performance will suffer, especially when the classification data space has high dimensionality. To cope with the problem we propose a new LDA variant, orLDA (i.e., LDA for over-reducing problem), which promotes the use of individual data instances instead of summary data alone in generating the transformation matrix. As a result orLDA will obtain a number of features that is independent of the number of classes. Extensive experiments show that orLDA has better performance than the original LDA and two LDA variants – uncorrelated LDA and orthogonal LDA.