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论文类型：期刊论文

发表时间：2010-10-01

发表刊物：PATTERN RECOGNITION

收录刊物：SCIE、EI、Scopus

卷号：43

期号：10

页面范围：3298-3306

ISSN号：0031-3203

关键字：Feature extraction; Dimensionality reduction; Lorentzian geometry; Metric learning; Discriminant analysis

摘要：We develop a supervised dimensionality reduction method, called Lorentzian discriminant projection (LDP), for feature extraction and classification. Our method represents the structures of sample data by a manifold, which is furnished with a Lorentzian metric tensor. Different from classic discriminant analysis techniques, LDP uses distances from points to their within-class neighbors and global geometric centroid to model a new manifold to detect the intrinsic local and global geometric structures of data set. In this way, both the geometry of a group of classes and global data structures can be learnt from the Lorentzian metric tensor. Thus discriminant analysis in the original sample space reduces to metric learning on a Lorentzian manifold. We also establish the kernel, tensor and regularization extensions of LDP in this paper. The experimental results on benchmark databases demonstrate the effectiveness of our proposed method and the corresponding extensions. (C) 2010 Elsevier Ltd. All rights reserved.