Tensor learning and automated rank selection for regression-based video classification

The logistic regression is a widely used method for multimedia classification. However, when it is applied to high-order data such as video sequences, traditional vector-based logistic regression often incurs loss of space-time structural information. The tensor extension method based on CP (CANDECOMP/PARAFAC) decomposition is powerful for capturing the multilinear latent information. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank. To effectively exploit underlying space-time structural in video sequences, we propose a tensor-based logistic regression learning algorithm, in which the weight parameter are regarded to be a tensor, calculated after the CP tensor decomposition. We introduce a regularization term, L(2,1)-norm, into the logistic tensor regression, and automatically select the CP rank, making it adaptive to the input videos for improved weight tensor and thus classification performances. Extensive experimental results in comparison with five state-of-the-art regression methods support that our proposed algorithm achieves the best classification performances, providing a good potential for a range of applications towards computerized video classifications via tensor-based video descriptions.