Lorentzian discriminant projection and its applications

Authors:
Risheng Liu;Zhixun Su;Zhouchen Lin;Xiaoyu Hou
Affiliations:
Dalian University of Technology, Dalian, China;Dalian University of Technology, Dalian, China;Microsoft Research Asia, Beijing, China;Dalian University of Technology, Dalian, China
Venue:
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part III
Year:
2009

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Abstract

This paper develops a supervised dimensionality reduction method, Lorentzian Discriminant Projection (LDP), for discriminant analysis 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 The experimental results on benchmark databases demonstrate the effectiveness of our proposed method.