# Efficient Structure-preserving Support Tensor Train Machine

arXiv: https://arxiv.org/abs/2002.05079 · HTML: https://mlsanity.com/paper/2002.05079/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2020.

## Built on by (most cited first, 3 of 3)

- [Stochastic tensor space feature theory with applications to robust machine learning](https://mlsanity.com/paper/2110.01729/) (2021)
- [A weighted subspace exponential kernel for support tensor machines](https://mlsanity.com/paper/2302.08134/) (2023)
- [Low Rank Support Quaternion Matrix Machine](https://mlsanity.com/paper/2512.08327/) (2025)

## Abstract (arXiv)

An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor classification methods. In the presence of small amounts of training data, kernel methods offer an attractive choice as they provide the possibility for a nonlinear decision boundary. We develop the Tensor Train Multi-way Multi-level Kernel (TT-MMK), which combines the simplicity of the Canonical Polyadic decomposition, the classification power of the Dual Structure-preserving Support Vector Machine, and the reliability of the Tensor Train (TT) approximation. We show by experiments that the TT-MMK method is usually more reliable computationally, less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification when benchmarked against other state-of-the-art techniques.