JULIA: Joint Multi-linear and Nonlinear Identification for Tensor Completion

TL;DR

JULIA is a novel tensor completion framework that combines multi-linear and nonlinear models, enabling more accurate and efficient imputation of missing data in large-scale tensors by leveraging flexible model selection and an optimized alternating approach.

Contribution

The paper introduces JULIA, a unified framework that integrates multi-linear and nonlinear tensor completion models, improving accuracy and efficiency over existing methods.

Findings

JULIA outperforms existing tensor completion algorithms on six real datasets.

JULIA achieves up to 55% lower root mean-squared-error.

JULIA reduces computational complexity by 67% in large-scale scenarios.

Abstract

Tensor completion aims at imputing missing entries from a partially observed tensor. Existing tensor completion methods often assume either multi-linear or nonlinear relationships between latent components. However, real-world tensors have much more complex patterns where both multi-linear and nonlinear relationships may coexist. In such cases, the existing methods are insufficient to describe the data structure. This paper proposes a Joint mUlti-linear and nonLinear IdentificAtion (JULIA) framework for large-scale tensor completion. JULIA unifies the multi-linear and nonlinear tensor completion models with several advantages over the existing methods: 1) Flexible model selection, i.e., it fits a tensor by assigning its values as a combination of multi-linear and nonlinear components; 2) Compatible with existing nonlinear tensor completion methods; 3) Efficient training based on a well-designed alternating optimization approach. Experiments on six real large-scale tensors demonstrate that JULIA outperforms many existing tensor completion algorithms. Furthermore, JULIA can improve the performance of a class of nonlinear tensor completion methods. The results show that in some large-scale tensor completion scenarios, baseline methods with JULIA are able to obtain up to 55% lower root mean-squared-error and save 67% computational complexity.