We propose a novel algorithm, called ℓ1 filtering, for exactly solving PCP with an complexity, where m×n is the size of data matrix and r is the rank of the matrix to recover, which is supposed to be much smaller than m and n.

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 semi-Riemannian space.

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