  Sparse coding (SC) is an unsupervised learning scheme that has received an
increasing amount of interests in recent years. However, conventional SC
vectorizes the input images, which destructs the intrinsic spatial structures
of the images. In this paper, we propose a novel graph regularized tensor
sparse coding (GTSC) for image representation. GTSC preserves the local
proximity of elementary structures in the image by adopting the newly proposed
tubal-tensor representation. Simultaneously, it considers the intrinsic
geometric properties by imposing graph regularization that has been
successfully applied to uncover the geometric distribution for the image data.
Moreover, the returned sparse representations by GTSC have better physical
explanations as the key operation (i.e., circular convolution) in the
tubal-tensor model preserves the shifting invariance property. Experimental
results on image clustering demonstrate the effectiveness of the proposed
scheme.
