# Matrix Product State for Higher-Order Tensor Compression and Classification

arXiv: https://arxiv.org/abs/1609.04541 · HTML: https://mlsanity.com/paper/1609.04541/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2016.

## Built on by (most cited first, 6 of 6)

- [Generative modeling with projected entangled-pair states](https://mlsanity.com/paper/2202.08177/) (2022)
- [A Matrix Product State Model for Simultaneous Classification and Generation](https://mlsanity.com/paper/2406.17441/) (2024)
- [Fast Hypergraph Regularized Nonnegative Tensor Ring Factorization Based on Low-Rank Approximation](https://mlsanity.com/paper/2109.02314/) (2021)
- [Tensor PCA from basis in tensor space](https://mlsanity.com/paper/2305.02803/) (2023)
- [Decomposition of linear tensor transformations](https://mlsanity.com/paper/2309.07819/) (2023)
- [Subspace Kernel Learning on Tensor Sequences](https://mlsanity.com/paper/2603.19546/) (2026)

## Abstract (arXiv)

This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and compression quality. Regardless of tensor order, MPS compresses tensors to matrices of moderate dimension which can be used for classification. Mainly based on a successive sequence of singular value decompositions (SVD), MPS is quite simple to implement and arrives at the global optimal matrix, bypassing local alternating optimization, which is not only computationally expensive but cannot yield the global solution. Benchmark results show that MPS can achieve better classification performance with favorable computation cost compared to other tensor compression methods.