GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completion

TL;DR

This paper introduces GOCPT, a unified framework for online tensor factorization that handles complex evolving patterns, missing data, and element changes, outperforming existing methods in accuracy and efficiency.

Contribution

The paper proposes GOCPT, a novel generalized online tensor factorization framework capable of modeling complex dynamic tensor scenarios, including mode growth and element updates.

Findings

GOCPT improves fitness by up to 2.8% on Covid data.

GOCPT achieves 9.2% better fitness on a proprietary dataset.

GOCPTE offers up to 1.2% fitness gain with 20% faster computation.

Abstract

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.