# Matrix Product State for Feature Extraction of Higher-Order Tensors

arXiv: https://arxiv.org/abs/1503.00516 · HTML: https://mlsanity.com/paper/1503.00516/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2015.

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

- [An end-to-end trainable hybrid classical-quantum classifier](https://mlsanity.com/paper/2102.02416/) (2021)
- [Generative modeling with projected entangled-pair states](https://mlsanity.com/paper/2202.08177/) (2022)
- [Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States](https://mlsanity.com/paper/2106.08334/) (2021)
- [Effective Tensor Completion via Element-wise Weighted Low-rank Tensor Train with Overlapping Ket Augmentation](https://mlsanity.com/paper/2109.05736/) (2021)
- [More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees](https://mlsanity.com/paper/2110.07631/) (2021)
- [Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation](https://mlsanity.com/paper/2105.14250/) (2021)

## Abstract (arXiv)

This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to the so-called core tensor of maximum order three which can be used for classification. Mainly based on a successive sequence of singular value decompositions (SVD), MPS is quite simple to implement without any recursive procedure needed for optimizing local tensors. Thus, it leads to substantial computational savings compared to other tensor feature extraction methods such as higher-order orthogonal iteration (HOOI) underlying the Tucker decomposition (TD). Benchmark results show that MPS can reduce significantly the feature space of data while achieving better classification performance compared to HOOI.