# Tensor Decompositions via Two-Mode Higher-Order SVD (HOSVD)

arXiv: https://arxiv.org/abs/1612.03839 · HTML: https://mlsanity.com/paper/1612.03839/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2016.

## Built on by (most cited first, 2 of 2)

- [Tensor Principal Component Analysis in High Dimensional CP Models](https://mlsanity.com/paper/2108.04428/) (2021)
- [Causal Discovery in Knowledge Graphs by Exploiting Asymmetric Properties of Non-Gaussian Distributions](https://mlsanity.com/paper/2106.01043/) (2021)

## Abstract (arXiv)

Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlike the classical higher-order singular value decomposition which unfolds a tensor along a single mode, we consider unfoldings along two modes and use rank-1 constraints to characterize the underlying components. This tensor decomposition method provably handles a greater level of noise compared to previous methods and achieves a high estimation accuracy. Numerical results demonstrate that our algorithm is robust to various noise distributions and that it performs especially favorably as the order increases.