Image Representation and Learning With Graph-Laplacian Tucker Tensor Decomposition

Tucker tensor decomposition (TD) is widely used for image representation, reconstruction, and learning tasks. Compared to principal component analysis (PCA) models, tensor models retain more 2-D characteristics of images whereas PCA models linearize images. However, traditional TD involves attribute information only and thus does not consider the pairwise similarity information between images. In this paper, we propose a graph-Laplacian tucker tensor decomposition (GLTD) which explores both attributes and pairwise similarity information simultaneously. Generally, GLTD has three main benefits: 1) GLTD reconstruction shows clear robustness against image occlusions/outliers. We provide analysis to show that Laplacian regularization is mainly responsible to this robustness via an out-of-sample GLTD model. To the best of our knowledge, this Laplacian regularization induced robustness of TD has not been studied or emphasized before; 2) GLTD representation performs more regularity, which improves both unsupervised and supervised learning results; and 3) an effective algorithm is derived to solve GLTD problem. Although GLTD is a noncovex problem, the proposed algorithm is shown experimentally to provide a stable/unique solution starting from different random initializations. Experimental results on image reconstruction, data clustering, and classification tasks show the benefits of GLTD.