A generalizable framework for low-rank tensor completion with numerical priors

TL;DR

This paper introduces GCDTC, a novel framework for low-rank tensor completion that incorporates numerical priors, significantly improving accuracy over existing methods, especially in non-negative tensor completion tasks.

Contribution

The paper presents GCDTC, the first generalizable framework that systematically integrates numerical priors into low-rank tensor completion algorithms.

Findings

GCDTC outperforms existing methods in non-negative tensor completion.

SPTC, an instantiation of GCDTC, achieves state-of-the-art results.

Open-source code is provided for reproducibility.

Abstract

Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically considered exploiting the numerical priors of tensor elements. Ignoring numerical priors causes loss of important information regarding the data, and therefore prevents the algorithms from reaching optimal accuracy. Despite the existence of some individual works which consider ad hoc numerical priors for specific tasks, no generalizable frameworks for incorporating numerical priors have appeared. We present the Generalized CP Decomposition Tensor Completion (GCDTC) framework, the first generalizable framework for low-rank tensor completion that takes numerical priors of the data into account. We test GCDTC by further proposing the Smooth Poisson Tensor Completion (SPTC) algorithm, an instantiation of the GCDTC framework, whose performance exceeds current state-of-the-arts by considerable margins in the task of non-negative tensor completion, exemplifying GCDTC's effectiveness. Our code is open-source.