# Image classification using local tensor singular value decompositions

arXiv: https://arxiv.org/abs/1706.09693 · HTML: https://mlsanity.com/paper/1706.09693/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2017.

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

- [A Tensor SVD-based Classification Algorithm Applied to fMRI Data](https://mlsanity.com/paper/2111.00587/) (2021)
- [T-ADAF: Adaptive Data Augmentation Framework for Image Classification Network based on Tensor T-product Operator](https://mlsanity.com/paper/2306.04240/) (2023)
- [sparseGeoHOPCA: A Geometric Solution to Sparse Higher-Order PCA Without Covariance Estimation](https://mlsanity.com/paper/2506.08670/) (2025)

## Abstract (arXiv)

From linear classifiers to neural networks, image classification has been a widely explored topic in mathematics, and many algorithms have proven to be effective classifiers. However, the most accurate classifiers typically have significantly high storage costs, or require complicated procedures that may be computationally expensive. We present a novel (nonlinear) classification approach using truncation of local tensor singular value decompositions (tSVD) that robustly offers accurate results, while maintaining manageable storage costs. Our approach takes advantage of the optimality of the representation under the tensor algebra described to determine to which class an image belongs. We extend our approach to a method that can determine specific pairwise match scores, which could be useful in, for example, object recognition problems where pose/position are different. We demonstrate the promise of our new techniques on the MNIST data set.