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Indexed by:Journal Papers

Date of Publication:2010-10-01

Journal:PATTERN RECOGNITION

Included Journals:SCIE、EI、Scopus

Volume:43

Issue:10

Page Number:3298-3306

ISSN No.:0031-3203

Key Words:Feature extraction; Dimensionality reduction; Lorentzian geometry; Metric learning; Discriminant analysis

Abstract: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.