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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Lorentzian Discriminant Projection and Its Applications
verfasst von : Risheng Liu, Zhixun Su, Zhouchen Lin, Xiaoyu Hou
Erschienen in: Computer Vision – ACCV 2009
Verlag: Springer Berlin Heidelberg
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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.