Fourier Low-rank and Sparse Tensor for Efficient Tensor Completion

TL;DR

The paper introduces FLoST, a novel tensor completion model that leverages Fourier transforms to separately model low-frequency and high-frequency components, improving accuracy and efficiency in spatiotemporal data reconstruction.

Contribution

FLoST is a new tensor completion model that decomposes the temporal mode using Fourier transform, capturing both smooth and localized variations more efficiently than existing methods.

Findings

FLoST outperforms traditional models in accuracy.

FLoST requires fewer parameters, enhancing computational efficiency.

FLoST effectively models both low-frequency and high-frequency data components.

Abstract

Tensor completion is crucial in many scientific domains with missing data problems. Traditional low-rank tensor models, including CP, Tucker, and Tensor-Train, exploit low-dimensional structures to recover missing data. However, these methods often treat all tensor modes symmetrically, failing to capture the unique spatiotemporal patterns inherent in scientific data, where the temporal component exhibits both low-frequency stability and high-frequency variations. To address this, we propose a novel model, \underline{F}ourier \underline{Lo}w-rank and \underline{S}parse \underline{T}ensor (FLoST), which decomposes the tensor along the temporal dimension using a Fourier transform. This approach captures low-frequency components with low-rank matrices and high-frequency fluctuations with sparsity, resulting in a hybrid structure that efficiently models both smooth and localized variations. Compared to the well-known tubal-rank model, which assumes low-rankness across all frequency components, FLoST requires significantly fewer parameters, making it computationally more efficient, particularly when the time dimension is large. Through theoretical analysis and empirical experiments, we demonstrate that FLoST outperforms existing tensor completion models in terms of both accuracy and computational efficiency, offering a more interpretable solution for spatiotemporal data reconstruction.