title: Linear discriminant analysis based on L1-norm maximization.
abstract: Linear discriminant analysis (LDA) is a well-known dimensionality reduction technique, which is widely used for many purposes. However, conventional LDA is sensitive to outliers because its objective function is based on the distance criterion using L2-norm. This paper proposes a simple but effective robust LDA version based on L1-norm maximization, which learns a set of local optimal projection vectors by maximizing the ratio of the L1-norm-based between-class dispersion and the L1-norm-based within-class dispersion. The proposed method is theoretically proved to be feasible and robust to outliers while overcoming the singular problem of the within-class scatter matrix for conventional LDA. Experiments on artificial datasets, standard classification datasets and three popular image databases demonstrate the efficacy of the proposed method.
authors.affiliation: Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 610031, China. fujin-zhong@163.com
authors.forename: Fujin
authors.initials: F
authors.lastname: Zhong
authors.forename: Jiashu
authors.initials: J
authors.lastname: Zhang
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016002:Discriminant Analysis; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016014:Linear Models; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity