# GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completion

arXiv: https://arxiv.org/abs/2205.03749 · HTML: https://mlsanity.com/paper/2205.03749/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 8 May 2022.

## Builds on (most cited first, 8 of 8)

- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors](https://mlsanity.com/paper/1404.4667/) (2014)
- [Grassmannian Optimization for Online Tensor Completion and Tracking with the t-SVD](https://mlsanity.com/paper/2001.11419/) (2020)
- [Fast online low-rank tensor subspace tracking by CP decomposition using recursive least squares from incomplete observations](https://mlsanity.com/paper/1709.10276/) (2017)
- [MTC: Multiresolution Tensor Completion from Partial and Coarse Observations](https://mlsanity.com/paper/2106.07135/) (2021)
- [Inductive Framework for Multi-Aspect Streaming Tensor Completion with Side Information](https://mlsanity.com/paper/1802.06371/) (2018)
- [Multi-version Tensor Completion for Time-delayed Spatio-temporal Data](https://mlsanity.com/paper/2105.05326/) (2021)
- [Streaming Generalized Canonical Polyadic Tensor Decompositions](https://mlsanity.com/paper/2110.14514/) (2021)

## Abstract (arXiv)

Low-rank tensor factorization or completion is well-studied and applied in various online settings, such as online tensor factorization (where the temporal mode grows) and online tensor completion (where incomplete slices arrive gradually). However, in many real-world settings, tensors may have more complex evolving patterns: (i) one or more modes can grow; (ii) missing entries may be filled; (iii) existing tensor elements can change. Existing methods cannot support such complex scenarios. To fill the gap, this paper proposes a Generalized Online Canonical Polyadic (CP) Tensor factorization and completion framework (named GOCPT) for this general setting, where we maintain the CP structure of such dynamic tensors during the evolution. We show that existing online tensor factorization and completion setups can be unified under the GOCPT framework. Furthermore, we propose a variant, named GOCPTE, to deal with cases where historical tensor elements are unavailable (e.g., privacy protection), which achieves similar fitness as GOCPT but with much less computational cost. Experimental results demonstrate that our GOCPT can improve fitness by up to 2:8% on the JHU Covid data and 9:2% on a proprietary patient claim dataset over baselines. Our variant GOCPTE shows up to 1:2% and 5:5% fitness improvement on two datasets with about 20% speedup compared to the best model.