Dictionary Learning and Sparse Coding for Third-order Super-symmetric Tensors
This work addresses tensor compression and data aggregation challenges in computer vision, offering an incremental improvement over existing techniques.
The paper tackled the problem of exponential size in third-order super-symmetric tensors by developing a dictionary learning and sparse coding framework to approximate them as sparse conic combinations of atoms, resulting in better data aggregation and superior performance on two computer vision tasks compared to state-of-the-art methods.
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.