Sparse Coding for Third-Order Super-Symmetric Tensor Descriptors with Application to Texture Recognition

Super-symmetric tensors - a higher-order extension of scatter matrices - are becoming increasingly popular in machine learning and computer vision for modeling data statistics, co-occurrences, or even as visual descriptors. They were shown recently to outperform second-order approaches, however, the size of these tensors are exponential in the data dimensionality, which is a significant concern. In this paper, we study third-order supersymmetric tensor descriptors in the context of dictionary learning and sparse coding. For this purpose, we propose a novel non-linear third-order texture descriptor. Our goal is to approximate these tensors as sparse conic combinations of atoms from a learned dictionary. Apart from the significant benefits to tensor compression that this framework offers, our experiments demonstrate that the sparse coefficients produced by this scheme lead to better aggregation of high-dimensional data and showcase superior performance on two common computer vision tasks compared to the state of the art.