A weighted subspace exponential kernel for support tensor machines

TL;DR

This paper introduces a novel weighted Tucker-based kernel for support tensor machines that improves classification accuracy and reduces computational time by balancing tensor core and factor contributions.

Contribution

The paper proposes a new kernel based on Tucker decomposition with re-weighted singular values, enhancing feature extraction and computational efficiency in tensor classification.

Findings

Higher test accuracy than tensor train kernel

Robustness across different classification scenarios

Lower computational time compared to state-of-the-art methods

Abstract

High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been proposed. However, what decisive features of the tensors are exploited by these kernels is often unclear. In this paper we propose a novel kernel that is based on the Tucker decomposition. For this kernel the Tucker factors are computed based on re-weighting of the Tucker matrices with tuneable powers of singular values from the HOSVD decomposition. This provides a mechanism to balance the contribution of the Tucker core and factors of the data. We benchmark support tensor machines with this new kernel on several datasets. First we generate synthetic data where two classes differ in either Tucker factors or core, and compare our novel and previously existing kernels. We show robustness of the new kernel with respect to both classification scenarios. We further test the new method on real-world datasets. The proposed kernel has demonstrated a higher test accuracy than the state-of-the-art tensor train multi-way multi-level kernel, and a significantly lower computational time.