# Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges

arXiv: https://arxiv.org/abs/2405.18412 · HTML: https://mlsanity.com/paper/2405.18412/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 104 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 30 of 58)

- [Escaping From Saddle Points --- Online Stochastic Gradient for Tensor Decomposition](https://mlsanity.com/paper/1503.02101/) (2015)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [A statistical model for tensor PCA](https://mlsanity.com/paper/1411.1076/) (2014)
- [On Iterative Hard Thresholding Methods for High-dimensional M-Estimation](https://mlsanity.com/paper/1410.5137/) (2014)
- [Tensor SVD: Statistical and Computational Limits](https://mlsanity.com/paper/1703.02724/) (2017)
- [An Optimal Statistical and Computational Framework for Generalized Tensor Estimation](https://mlsanity.com/paper/2002.11255/) (2020)
- [Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery](https://mlsanity.com/paper/1307.5870/) (2013)
- [Tensor principal component analysis via sum-of-squares proofs](https://mlsanity.com/paper/1507.03269/) (2015)
- [Nonconvex Low-Rank Tensor Completion from Noisy Data](https://mlsanity.com/paper/1911.04436/) (2019)
- [The landscape of the spiked tensor model](https://mlsanity.com/paper/1711.05424/) (2017)
- [On Tensor Completion via Nuclear Norm Minimization](https://mlsanity.com/paper/1405.1773/) (2014)
- [Provable Tensor Factorization with Missing Data](https://mlsanity.com/paper/1406.2784/) (2014)
- [Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decomposition](https://mlsanity.com/paper/2002.04457/) (2020)
- [Spectral algorithms for tensor completion](https://mlsanity.com/paper/1612.07866/) (2016)
- [On Polynomial Time Methods for Exact Low Rank Tensor Completion](https://mlsanity.com/paper/1702.06980/) (2017)
- [Community Detection for Hypergraph Networks via Regularized Tensor Power Iteration](https://mlsanity.com/paper/1909.06503/) (2019)
- [Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization](https://mlsanity.com/paper/2103.08895/) (2021)
- [Non-Convex Projected Gradient Descent for Generalized Low-Rank Tensor Regression](https://mlsanity.com/paper/1611.10349/) (2016)
- [Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entries](https://mlsanity.com/paper/1711.04934/) (2017)
- [Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit](https://mlsanity.com/paper/2012.09996/) (2020)
- [Polynomial-time Tensor Decompositions with Sum-of-Squares](https://mlsanity.com/paper/1610.01980/) (2016)
- [Guaranteed Non-Orthogonal Tensor Decomposition via Alternating Rank-1 Updates](https://mlsanity.com/paper/1402.5180/) (2014)
- [Factor Models for High-Dimensional Tensor Time Series](https://mlsanity.com/paper/1905.07530/) (2019)
- [Autoregressive Models for Matrix-Valued Time Series](https://mlsanity.com/paper/1812.08916/) (2018)
- [Multiway clustering via tensor block models](https://mlsanity.com/paper/1906.03807/) (2019)
- [Provable Tensor-Train Format Tensor Completion by Riemannian Optimization](https://mlsanity.com/paper/2108.12163/) (2021)
- [Provable Sparse Tensor Decomposition](https://mlsanity.com/paper/1502.01425/) (2015)
- [Spectral Learning on Matrices and Tensors](https://mlsanity.com/paper/2004.07984/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Robust and Non-Iterative Tensor Decomposition Method with Automatic Thresholding](https://mlsanity.com/paper/2505.06203/) (2025)

## Abstract (arXiv)

Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity of such data provides vast new opportunities for modeling and analysis, but efficiently extracting information content from them, both statistically and computationally, presents unique and fundamental challenges. Addressing these challenges requires an interdisciplinary approach that brings together tools and insights from statistics, optimization and numerical linear algebra among other fields. Despite these hurdles, significant progress has been made in the last decade. This review seeks to examine some of the key advancements and identify common threads among them, under eight different statistical settings.