FAST ALGORITHMS FOR THE GENERALIZED FOLEY-SAMMON DISCRIMINANT ANALYSIS

doi:10.1137/080720863

CORC > 上海财经大学 > 上海财经大学

	FAST ALGORITHMS FOR THE GENERALIZED FOLEY-SAMMON DISCRIMINANT ANALYSIS
	Zhang, Lei-Hong 2; Liao, Li-Zhi 1; Ng, Michael K.1
刊名	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
	2010
卷号	31 期号:4 页码:1584-1605
关键词	dimension reduction linear discriminant analysis regularization Foley-Sammon transform global convergence quadratic convergence
ISSN号	0895-4798
DOI	10.1137/080720863
英文摘要	Linear discriminant analysis (LDA) is one of the most popular approaches for feature extraction and dimension reduction to overcome the curse of the dimensionality of the high-dimensional data in many applications of data mining, machine learning, and bioinformatics. In this paper, we made two main contributions to an important LDA scheme, the generalized Foley-Sammon transform (GFST) [Foley and Sammon, IEEE Trans. Comput., 24 (1975), pp. 281-289; Guo et al., Pattern Recognition Lett., 24 (2003), pp. 147-158] or a trace ratio model [Wang et al., Proceedings of the International Conference on Computer Vision and Pattern Recognition, 2007, pp. 1-8] and its regularized GFST (RGFST), which handles the undersampled problem that involves small samples size n, but with high number of features N (N > n) and arises frequently in many modern applications. Our first main result is to establish an equivalent reduced model for the RGFST which effectively improves the computational overhead. The iteration method proposed by Wang et al. is applied to solve the GFST or the reduced RGFST. It has been proven by Wang et al. that this iteration converges globally and fast convergence was observed numerically, but there is no theoretical analysis on the convergence rate thus far. Our second main contribution completes this important and missing piece by proving the quadratic convergence even under two kinds of inexact computations. Practical implementations, including computational complexity and storage requirements, are also discussed. Our experimental results on several real world data sets indicate the efficiency of the algorithm and the advantages of the GFST model in classification.
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000279347600004
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/2925]
专题	上海财经大学
通讯作者	Liao, Li-Zhi
作者单位	1.Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China; 2.Shanghai Univ Finance & Econ, Dept Appl Math, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Lei-Hong,Liao, Li-Zhi,Ng, Michael K.. FAST ALGORITHMS FOR THE GENERALIZED FOLEY-SAMMON DISCRIMINANT ANALYSIS[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2010,31(4):1584-1605.
APA	Zhang, Lei-Hong,Liao, Li-Zhi,&Ng, Michael K..(2010).FAST ALGORITHMS FOR THE GENERALIZED FOLEY-SAMMON DISCRIMINANT ANALYSIS.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,31(4),1584-1605.
MLA	Zhang, Lei-Hong,et al."FAST ALGORITHMS FOR THE GENERALIZED FOLEY-SAMMON DISCRIMINANT ANALYSIS".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 31.4(2010):1584-1605.