# Tensor Completion Algorithms in Big Data Analytics

arXiv: https://arxiv.org/abs/1711.10105 · HTML: https://mlsanity.com/paper/1711.10105/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2017.

## Built on by (most cited first, 30 of 48)

- [Implicit Regularization in Tensor Factorization](https://mlsanity.com/paper/2102.09972/) (2021)
- [Provable Tensor-Train Format Tensor Completion by Riemannian Optimization](https://mlsanity.com/paper/2108.12163/) (2021)
- [SlimmeRF: Slimmable Radiance Fields](https://mlsanity.com/paper/2312.10034/) (2023)
- [Robust Factorization of Real-world Tensor Streams with Patterns, Missing Values, and Outliers](https://mlsanity.com/paper/2102.08466/) (2021)
- [Implicit Regularization in Deep Tensor Factorization](https://mlsanity.com/paper/2105.01346/) (2021)
- [Covariate-assisted Sparse Tensor Completion](https://mlsanity.com/paper/2103.06428/) (2021)
- [MTC: Multiresolution Tensor Completion from Partial and Coarse Observations](https://mlsanity.com/paper/2106.07135/) (2021)
- [Nonnegative Tensor Completion via Integer Optimization](https://mlsanity.com/paper/2111.04580/) (2021)
- [Network-wide Freeway Traffic Estimation Using Sparse Sensor Data: A Dirichlet Graph Auto-Encoder Approach](https://mlsanity.com/paper/2503.15845/) (2025)
- [Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Data](https://mlsanity.com/paper/2106.10422/) (2021)
- [Implicit Regularization with Polynomial Growth in Deep Tensor Factorization](https://mlsanity.com/paper/2207.08942/) (2022)
- [Data Augmentation for Sparse Multidimensional Learning Performance Data Using Generative AI](https://mlsanity.com/paper/2409.15631/) (2024)
- [Protecting Big Data Privacy Using Randomized Tensor Network Decomposition and Dispersed Tensor Computation](https://mlsanity.com/paper/2101.04194/) (2021)
- [TTML: tensor trains for general supervised machine learning](https://mlsanity.com/paper/2203.04352/) (2022)
- [Spatiotemporal Regularized Tucker Decomposition Approach for Traffic Data Imputation](https://mlsanity.com/paper/2305.06563/) (2023)
- [Tensor completion using geodesics on Segre manifolds](https://mlsanity.com/paper/2108.00735/) (2021)
- [Low-rank Tensor Learning with Nonconvex Overlapped Nuclear Norm Regularization](https://mlsanity.com/paper/2205.03059/) (2022)
- [Accelerated Nonnegative Tensor Completion via Integer Programming](https://mlsanity.com/paper/2211.15770/) (2022)
- [A generalizable framework for low-rank tensor completion with numerical priors](https://mlsanity.com/paper/2302.05881/) (2023)
- [Image Reconstruction using Superpixel Clustering and Tensor Completion](https://mlsanity.com/paper/2305.09564/) (2023)
- [Knowledge Graph Completion by Intermediate Variables Regularization](https://mlsanity.com/paper/2506.02749/) (2025)
- [Tensor Train Completion from Fiberwise Observations Along a Single Mode](https://mlsanity.com/paper/2509.18149/) (2025)
- [Robust Low-Rank Tensor Completion based on M-product with Weighted Correlated Total Variation and Sparse Regularization](https://mlsanity.com/paper/2604.13525/) (2026)
- [Applying Differential Privacy to Tensor Completion](https://mlsanity.com/paper/2110.00539/) (2021)
- ["Sparse + Low-Rank'' Tensor Completion Approach for Recovering Images and Videos](https://mlsanity.com/paper/2110.09298/) (2021)
- [Tensor PCA from basis in tensor space](https://mlsanity.com/paper/2305.02803/) (2023)
- [Scalable and Robust Tensor Ring Decomposition for Large-scale Data](https://mlsanity.com/paper/2305.09044/) (2023)
- [Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra](https://mlsanity.com/paper/2308.02621/) (2023)
- [Tensor Completion via Integer Optimization](https://mlsanity.com/paper/2402.05141/) (2024)
- [A PID-Controlled Non-Negative Tensor Factorization Model for Analyzing Missing Data in NILM](https://mlsanity.com/paper/2403.07012/) (2024)

## Abstract (arXiv)

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data analytics characterized by diverse variety, large volume, and high velocity. We characterize these advances from four perspectives: general tensor completion algorithms, tensor completion with auxiliary information (variety), scalable tensor completion algorithms (volume), and dynamic tensor completion algorithms (velocity). Further, we identify several tensor completion applications on real-world data-driven problems and present some common experimental frameworks popularized in the literature. Our goal is to summarize these popular methods and introduce them to researchers and practitioners for promoting future research and applications. We conclude with a discussion of key challenges and promising research directions in this community for future exploration.