Dictionary Learning and Sparse Coding for Third-order Super-symmetric Tensors

TL;DR

This paper introduces a method for approximating third-order super-symmetric tensors using sparse coding and dictionary learning, enabling efficient tensor compression and improved data aggregation for computer vision tasks.

Contribution

It presents a novel approach to tensor approximation via sparse conic combinations of symmetric positive semi-definite atoms, enhancing compression and performance.

Findings

Tensor approximation reduces data size significantly.

Sparse coefficients improve data aggregation.

Method outperforms state-of-the-art on vision tasks.

Abstract

Super-symmetric tensors - a higher-order extension of scatter matrices - are becoming increasingly popular in machine learning and computer vision for modelling data statistics, co-occurrences, or even as visual descriptors. However, the size of these tensors are exponential in the data dimensionality, which is a significant concern. In this paper, we study third-order super-symmetric tensor descriptors in the context of dictionary learning and sparse coding. Our goal is to approximate these tensors as sparse conic combinations of atoms from a learned dictionary, where each atom is a symmetric positive semi-definite matrix. Apart from the significant benefits to tensor compression that this framework provides, our experiments demonstrate that the sparse coefficients produced by the scheme lead to better aggregation of high-dimensional data, and showcases superior performance on two common computer vision tasks compared to the state-of-the-art.