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

Shiran Yuan, Kaizhu Huang

TL;DR

The Generalized CP Decomposition Tensor Completion (GCDTC) framework is presented, the first generalizable framework for low-rank tensor completion that takes numerical priors of the data into account.

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.

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

TL;DR

The Generalized CP Decomposition Tensor Completion (GCDTC) framework is presented, the first generalizable framework for low-rank tensor completion that takes numerical priors of the data into account.

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.
Paper Structure (2 sections, 1 figure)

This paper contains 2 sections, 1 figure.

Table of Contents

  1. Introduction
  2. Contributions

Figures (1)

  • Figure 1: Graphical illustration of the proposed GCDTC framework. The main innovation of our work is the creation of a framework that allows numerical priors of the incomplete tensor to be taken into consideration during the process of completion. Most other LRTC methods, in comparison, are only innovative in their choice of Inter-Element Priors, and their methods of optimization also often do not allow for adaptability.