# Multi-version Tensor Completion for Time-delayed Spatio-temporal Data

arXiv: https://arxiv.org/abs/2105.05326 · HTML: https://mlsanity.com/paper/2105.05326/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 11 May 2021.

## Builds on (most cited first, 7 of 7)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [On Tensor Completion via Nuclear Norm Minimization](https://mlsanity.com/paper/1405.1773/) (2014)
- [Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors](https://mlsanity.com/paper/1404.4667/) (2014)
- [Computing Large-Scale Matrix and Tensor Decomposition with Structured Factors: A Unified Nonconvex Optimization Perspective](https://mlsanity.com/paper/2006.08183/) (2020)
- [STELAR: Spatio-temporal Tensor Factorization with Latent Epidemiological Regularization](https://mlsanity.com/paper/2012.04747/) (2020)
- [Streaming Probabilistic Deep Tensor Factorization](https://mlsanity.com/paper/2007.07367/) (2020)

## Built on by (most cited first, 3 of 3)

- [JULIA: Joint Multi-linear and Nonlinear Identification for Tensor Completion](https://mlsanity.com/paper/2202.00071/) (2022)
- [GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completion](https://mlsanity.com/paper/2205.03749/) (2022)
- [Robust Predictions with Ambiguous Time Delays: A Bootstrap Strategy](https://mlsanity.com/paper/2408.12801/) (2024)

## Abstract (arXiv)

Real-world spatio-temporal data is often incomplete or inaccurate due to various data loading delays. For example, a location-disease-time tensor of case counts can have multiple delayed updates of recent temporal slices for some locations or diseases. Recovering such missing or noisy (under-reported) elements of the input tensor can be viewed as a generalized tensor completion problem. Existing tensor completion methods usually assume that i) missing elements are randomly distributed and ii) noise for each tensor element is i.i.d. zero-mean. Both assumptions can be violated for spatio-temporal tensor data. We often observe multiple versions of the input tensor with different under-reporting noise levels. The amount of noise can be time- or location-dependent as more updates are progressively introduced to the tensor. We model such dynamic data as a multi-version tensor with an extra tensor mode capturing the data updates. We propose a low-rank tensor model to predict the updates over time. We demonstrate that our method can accurately predict the ground-truth values of many real-world tensors. We obtain up to 27.2% lower root mean-squared-error compared to the best baseline method. Finally, we extend our method to track the tensor data over time, leading to significant computational savings.