title: Complexity-reduced implementations of complete and null-space-based linear discriminant analysis.
abstract: Dimensionality reduction has become an important data preprocessing step in a lot of applications. Linear discriminant analysis (LDA) is one of the most well-known dimensionality reduction methods. However, the classical LDA cannot be used directly in the small sample size (SSS) problem where the within-class scatter matrix is singular. In the past, many generalized LDA methods has been reported to address the SSS problem. Among these methods, complete linear discriminant analysis (CLDA) and null-space-based LDA (NLDA) provide good performances. The existing implementations of CLDA are computationally expensive. In this paper, we propose a new and fast implementation of CLDA. Our proposed implementation of CLDA, which is the most efficient one, is equivalent to the existing implementations of CLDA in theory. Since CLDA is an extension of null-space-based LDA (NLDA), our implementation of CLDA also provides a fast implementation of NLDA. Experiments on some real-world data sets demonstrate the effectiveness of our proposed new CLDA and NLDA algorithms.
authors.affiliation: School of Information Science and Engineering, Southeast University, Nanjing 210096, China. luguifu_jsj@163.com
authors.forename: Gui-Fu
authors.initials: GF
authors.lastname: Lu
authors.forename: Wenming
authors.initials: W
authors.lastname: Zheng
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016002:Discriminant Analysis; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D010363:Pattern Recognition, Automated / Q000379:methods
keywords: Complete linear discriminant analysis; Dimensionality reduction; Feature extraction; Null-space-based linear discriminant analysis; Small sample size problem