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.

本文介绍了如何利用研究超对称张量在字典学习和稀疏编码中的应用，将其近似为来自学习字典的对称半正定矩阵成的稀疏锥组合。此方法可以更好地聚合高维数据，在一些计算机视觉任务上展现了优越表现。