Tensor reduction error analysis - Applications to video compression and classification

Tensor based dimensionality reduction has recently been extensively studied for computer vision applications. To our knowledge, however, there exist no rigorous error analysis on these methods. Here we provide the first error analysis of these methods and provide error bound results similar to Eckart-Young Theorem which plays critical role in the development and application of singular value decomposition (SVD). Beside performance guarantee, these error bounds are useful for subspace size determination according to the required video/image reconstruction error. Furthermore, video surveillance/retrieval, 3D/4D medical image analysis, and other computer vision applications require particular reduction in spatio-temporal space, but not along data index dimension. This motivates a D-1 tensor reduction. Standard method such as high order SVD (HOSVD) compress data in all index dimensions and thus can not perform the classification and pattern recognition tasks. We provide algorithm and error bound analysis of the D-1 factorization for spatio-temporal data dimensionality. Experiments on video sequences demonstrate our approach outperforms the previous dimensionality deduction methods for spatiotemporal data.