Semi-supervised tensor learning for image classification

In this paper, we propose a new tensor-based representation algorithm for image classification. The algorithm is realized by learning the parameter tensor for image tensors. One novelty is that the parameter tensor is learned according to the Tucker tensor decomposition as the multiplication of a core tensor with a group of matrices for each order, which endows that the algorithm preserved the spatial information of image. We further extend the proposed tensor algorithm to a semi-supervised framework, in order to utilize both labeled and unlabeled images. The objective function can be solved by using the alternative optimization method, where at each iteration, we solve the typical ridge regression problem to obtain the closed form solution of the parameter along the corresponding order. Experimental results of gray and color image datasets show that our method outperforms several classification approaches. In particular, we find that our method can implement a high-quality classification performance when only few labeled training samples are provided.