# Tensor-based algorithms for image classification

arXiv: https://arxiv.org/abs/1910.02150 · HTML: https://mlsanity.com/paper/1910.02150/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2019.

## Built on by (most cited first, 7 of 7)

- [A block-sparse Tensor Train Format for sample-efficient high-dimensional Polynomial Regression](https://mlsanity.com/paper/2104.14255/) (2021)
- [Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning](https://mlsanity.com/paper/2507.21726/) (2025)
- [Fast Tucker Rank Reduction for Non-Negative Tensors Using Mean-Field Approximation](https://mlsanity.com/paper/2103.02898/) (2021)
- [Patch-based Medical Image Segmentation using Matrix Product State Tensor Networks](https://mlsanity.com/paper/2109.07138/) (2021)
- [Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data](https://mlsanity.com/paper/2309.03439/) (2023)
- [Natural Riemannian gradient for learning functional tensor networks](https://mlsanity.com/paper/2604.09263/) (2026)
- [Adapting Tensor Kernel Machines to Enable Efficient Transfer Learning for Seizure Detection](https://mlsanity.com/paper/2512.02626/) (2025)

## Abstract (arXiv)

The interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used for supervised learning problems and propose two novel approaches for image classification. One is a kernel-based reformulation of the previously introduced MANDy (multidimensional approximation of nonlinear dynamics), the other an alternating ridge regression in the tensor-train format. We apply both methods to the MNIST and fashion MNIST data set and show that the approaches are competitive with state-of-the-art neural network-based classifiers.