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.

翻译：以张量形式存在的高维数据对核分类方法构成挑战。为降低计算复杂度并提取信息性特征，基于低秩张量分解的核方法已被提出，然而这些核所利用的张量决定性特征往往不明确。本文提出一种基于Tucker分解的新型核函数。该核的Tucker因子通过采用HOSVD分解中奇异值的可调幂次对Tucker矩阵进行重新加权计算，从而提供平衡数据Tucker核与因子贡献的机制。我们在多个数据集上对采用该新型核的支持张量机进行基准测试。首先，我们生成两类在Tucker因子或核上存在差异的合成数据，并将本文提出的新型核与现有核进行对比，证明其在两种分类场景下的鲁棒性。进一步在真实数据集上进行测试，结果表明本文提出的核函数相较于当前最优的张量列多路多层级核具有更高的测试精度，同时计算时间显著降低。