# Tensor Methods and Recommender Systems

arXiv: https://arxiv.org/abs/1603.06038 · HTML: https://mlsanity.com/paper/1603.06038/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2016.

## Built on by (most cited first, 24 of 24)

- [Long Random Matrices and Tensor Unfolding](https://mlsanity.com/paper/2110.10210/) (2021)
- [Guaranteed Nonconvex Factorization Approach for Tensor Train Recovery](https://mlsanity.com/paper/2401.02592/) (2024)
- [Low-Precision Hardware Architectures Meet Recommendation Model Inference at Scale](https://mlsanity.com/paper/2105.12676/) (2021)
- [Influence-guided Data Augmentation for Neural Tensor Completion](https://mlsanity.com/paper/2108.10248/) (2021)
- [Tensor-based Sequential Learning via Hankel Matrix Representation for Next Item Recommendations](https://mlsanity.com/paper/2212.05720/) (2022)
- [On High-dimensional and Low-rank Tensor Bandits](https://mlsanity.com/paper/2305.03884/) (2023)
- [A Scalable Factorization Approach for High-Order Structured Tensor Recovery](https://mlsanity.com/paper/2506.16032/) (2025)
- [A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation](https://mlsanity.com/paper/2402.03169/) (2024)
- [Sharp Analysis of Power Iteration for Tensor PCA](https://mlsanity.com/paper/2401.01047/) (2024)
- [Tensor completion using geodesics on Segre manifolds](https://mlsanity.com/paper/2108.00735/) (2021)
- [Error Analysis of Tensor-Train Cross Approximation](https://mlsanity.com/paper/2207.04327/) (2022)
- [Data Leakage via Access Patterns of Sparse Features in Deep Learning-based Recommendation Systems](https://mlsanity.com/paper/2212.06264/) (2022)
- [Image Reconstruction using Superpixel Clustering and Tensor Completion](https://mlsanity.com/paper/2305.09564/) (2023)
- [Higher-Order Transformers With Kronecker-Structured Attention](https://mlsanity.com/paper/2412.02919/) (2024)
- [Tensor-Tensor Products, Group Representations, and Semidefinite Programming](https://mlsanity.com/paper/2507.12729/) (2025)
- [Efficient Low-Tubal-Rank Tensor Estimation via Alternating Preconditioned Gradient Descent](https://mlsanity.com/paper/2512.07490/) (2025)
- [Consistent Collaborative Filtering via Tensor Decomposition](https://mlsanity.com/paper/2201.11936/) (2022)
- [Robust Bayesian Tensor Factorization with Zero-Inflated Poisson Model and Consensus Aggregation](https://mlsanity.com/paper/2308.08060/) (2023)
- [Dynamic Collaborative Filtering for Matrix- and Tensor-based Recommender Systems](https://mlsanity.com/paper/2312.10064/) (2023)
- [sparseGeoHOPCA: A Geometric Solution to Sparse Higher-Order PCA Without Covariance Estimation](https://mlsanity.com/paper/2506.08670/) (2025)
- [Personalized Product Search Ranking: A Multi-Task Learning Approach with Tabular and Non-Tabular Data](https://mlsanity.com/paper/2508.09636/) (2025)
- [Guaranteed Noisy CP Tensor Recovery via Riemannian Optimization on the Segre Manifold](https://mlsanity.com/paper/2510.00569/) (2025)
- [Recommending Composite Items Using Multi-Level Preference Information: A Joint Interaction Modeling Approach](https://mlsanity.com/paper/2601.19005/) (2026)
- [Quaternion Nonlinear Transform-Induced Nuclear Norm for Low-Rank Tensor Completion](https://mlsanity.com/paper/2605.01467/) (2026)

## Abstract (arXiv)

A substantial progress in development of new and efficient tensor factorization techniques has led to an extensive research of their applicability in recommender systems field. Tensor-based recommender models push the boundaries of traditional collaborative filtering techniques by taking into account a multifaceted nature of real environments, which allows to produce more accurate, situational (e.g. context-aware, criteria-driven) recommendations. Despite the promising results, tensor-based methods are poorly covered in existing recommender systems surveys. This survey aims to complement previous works and provide a comprehensive overview on the subject. To the best of our knowledge, this is the first attempt to consolidate studies from various application domains in an easily readable, digestible format, which helps to get a notion of the current state of the field. We also provide a high level discussion of the future perspectives and directions for further improvement of tensor-based recommendation systems.