A weighted subspace exponential kernel for support tensor machines
This work addresses the problem of unclear feature exploitation in tensor kernels for researchers in machine learning, though it appears incremental as it builds on existing Tucker decomposition approaches.
The paper tackles the challenge of kernel classification for high-dimensional tensor data by proposing a novel weighted subspace exponential kernel based on Tucker decomposition with re-weighted singular values. The method achieves higher test accuracy than the state-of-the-art tensor train kernel and significantly reduces computational time on real-world datasets.
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.