Title :
Fisher Discriminant Analysis With L1-Norm
Author :
Haixian Wang ; Xuesong Lu ; Zilan Hu ; Wenming Zheng
Author_Institution :
Key Lab. of Child Dev. & Learning Sci., Southeast Univ., Nanjing, China
Abstract :
Fisher linear discriminant analysis (LDA) is a classical subspace learning technique of extracting discriminative features for pattern recognition problems. The formulation of the Fisher criterion is based on the L2-norm, which makes LDA prone to being affected by the presence of outliers. In this paper, we propose a new method, termed LDA-L1, by maximizing the ratio of the between-class dispersion to the within-class dispersion using the L1-norm rather than the L2-norm. LDA-L1 is robust to outliers, and is solved by an iterative algorithm proposed. The algorithm is easy to be implemented and is theoretically shown to arrive at a locally maximal point. LDA-L1 does not suffer from the problems of small sample size and rank limit as existed in the conventional LDA. Experiment results of image recognition confirm the effectiveness of the proposed method.
Keywords :
feature extraction; image recognition; iterative methods; learning (artificial intelligence); Fisher discriminant analysis; L1-norm; L2-norm; LDA-L1; between-class dispersion; discriminative feature extraction; image recognition; iterative algorithm; pattern recognition problems; subspace learning technique; within-class dispersion; Dispersion; Feature extraction; Iterative methods; Linear programming; Principal component analysis; Robustness; Vectors; Dimensionality reduction; L1-norm; LDA-L1; linear discriminant analysis (LDA); robust modeling;
Journal_Title :
Cybernetics, IEEE Transactions on
DOI :
10.1109/TCYB.2013.2273355