Classification via semi-Riemannian spaces

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Classification via semi-Riemannian spaces
In this paper, we develop a geometric framework for linear or nonlinear discriminant subspace learning and classification. In our framework, the structures of classes are conceptualized as a semi-Riemannian manifold which is considered as a submanifold embedded in an ambient semiRiemannian space. The class structures of original samples can be characterized and deformed by local metrics of the semi-Riemannian space. Semi-Riemannian metrics are uniquely determined by the smoothing of discrete functions and the nullity of the semi-Riemannian space. Based on the geometrization of class structures, optimizing class structures in the feature space is equivalent to maximizing the quadratic quantities of metric tensors in the semiRiemannian space. Thus supervised discriminant subspace learning reduces to unsupervised semi-Riemannian manifold learning. Based on the proposed framework, a novel algorithm, dubbed as Semi-Riemannian Discriminant Analysis (SRDA), is presented for subspace-based cl...
Deli Zhao, Zhouchen Lin, Xiaoou Tang
Added 19 Oct 2010
Updated 19 Oct 2010
Type Conference
Year 2008
Where CVPR
Authors Deli Zhao, Zhouchen Lin, Xiaoou Tang
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