Maximum margin criterion with tensor representation

In this paper, we propose tensor based Maximum Margin Criterion algorithm (TMMC) for supervised dimensionality reduction. In TMMC, an image object is encoded as an nth-order tensor, and its 2-D representation is directly treated as matrix. Meanwhile, the k-mode optimization approach is exploited to iteratively learn multiple interrelated discriminative subspaces for dimensionality reduction of the higher order tensor. TMMC generalizes the traditional MMC based on vector data to the one based on matrix and tensor data, which completes the MMC family in terms of data representation. The results of experiments conducted on four databases show that the accurate recognition rate of TMMC is better than that of the method of Concurrent Subspaces Analysis (CSA), and is comparable with the method of Multilinear Discriminant Analysis (MDA). The experimental results also show that the accurate recognition rate of the tensor/matrix-based methods may not always be better than that of vector-based methods. Reasonable discussions about this phenomenon have been given in this paper.