# Kernelized Support Tensor Train Machines

arXiv: https://arxiv.org/abs/2001.00360 · HTML: https://mlsanity.com/paper/2001.00360/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2020.

## Built on by (most cited first, 5 of 5)

- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Quantum-inspired Techniques in Tensor Networks for Industrial Contexts](https://mlsanity.com/paper/2404.11277/) (2024)
- [T'ecnicas Quantum-Inspired en Tensor Networks para Contextos Industriales](https://mlsanity.com/paper/2404.17645/) (2024)
- [Subspace Kernel Learning on Tensor Sequences](https://mlsanity.com/paper/2603.19546/) (2026)
- [Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning](https://mlsanity.com/paper/2610.06080/) (2026)

## Abstract (arXiv)

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we propose a tensor train (TT)-based kernel technique for the first time, and apply it to the conventional support vector machine (SVM) for image classification. Specifically, we propose a kernelized support tensor train machine that accepts tensorial input and preserves the intrinsic kernel property. The main contributions are threefold. First, we propose a TT-based feature mapping procedure that maintains the TT structure in the feature space. Second, we demonstrate two ways to construct the TT-based kernel function while considering consistency with the TT inner product and preservation of information. Third, we show that it is possible to apply different kernel functions on different data modes. In principle, our method tensorizes the standard SVM on its input structure and kernel mapping scheme. Extensive experiments are performed on real-world tensor data, which demonstrates the superiority of the proposed scheme under few-sample high-dimensional inputs.