# JULIA: Joint Multi-linear and Nonlinear Identification for Tensor Completion

arXiv: https://arxiv.org/abs/2202.00071 · HTML: https://mlsanity.com/paper/2202.00071/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 31 Jan 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Spatiotemporal Tensor Completion for Improved Urban Traffic Imputation](https://mlsanity.com/paper/2103.08323/) (2021)
- [Tensor Completion from Regular Sub-Nyquist Samples](https://mlsanity.com/paper/1903.00435/) (2019)
- [Differential Privacy for Stackelberg Games](https://mlsanity.com/paper/2002.00944/) (2020)
- [NePTuNe: Neural Powered Tucker Network for Knowledge Graph Completion](https://mlsanity.com/paper/2104.07824/) (2021)
- [Multi-version Tensor Completion for Time-delayed Spatio-temporal Data](https://mlsanity.com/paper/2105.05326/) (2021)
- [TeX-Graph: Coupled tensor-matrix knowledge-graph embedding for COVID-19 drug repurposing](https://mlsanity.com/paper/2010.11367/) (2020)

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

- [Triple Simplex Matrix Completion for Expense Forecasting](https://mlsanity.com/paper/2310.15275/) (2023)

## Abstract (arXiv)

Tensor completion aims at imputing missing entries from a partially observed tensor. Existing tensor completion methods often assume either multi-linear or nonlinear relationships between latent components. However, real-world tensors have much more complex patterns where both multi-linear and nonlinear relationships may coexist. In such cases, the existing methods are insufficient to describe the data structure. This paper proposes a Joint mUlti-linear and nonLinear IdentificAtion (JULIA) framework for large-scale tensor completion. JULIA unifies the multi-linear and nonlinear tensor completion models with several advantages over the existing methods: 1) Flexible model selection, i.e., it fits a tensor by assigning its values as a combination of multi-linear and nonlinear components; 2) Compatible with existing nonlinear tensor completion methods; 3) Efficient training based on a well-designed alternating optimization approach. Experiments on six real large-scale tensors demonstrate that JULIA outperforms many existing tensor completion algorithms. Furthermore, JULIA can improve the performance of a class of nonlinear tensor completion methods. The results show that in some large-scale tensor completion scenarios, baseline methods with JULIA are able to obtain up to 55% lower root mean-squared-error and save 67% computational complexity.