Tensor Completion using Subspace Information

2026-09-21

AI Summary

本文提出了一种利用子空间信息的张量补全算法TCSI，通过将张量补全转化为矩阵回归问题，降低了采样复杂度，提高了在高缺失情况下的补全效果。

Abstract

Tensor completion has attracted significant attention in both applications and theoretical research. Under standard uniform sampling, existing polynomial-time guarantees generally require more observations than the number of degree of freedom, motivating the study of a possible statistical-to-computational gap in highly missing regimes. Fortunately, in many practical scenarios, side information is available, which can provide valuable insights to mitigate these challenges. In this paper, we introduce an algorithm called Tensor Completion using Subspace Information (TCSI) that incorporates side information through an estimated subspace. Our approach first extracts the subspace from the available side information and then reformulates tensor completion as a matrix regression problem. We provide a theoretical analysis showing that, when accurate subspace information is available, the required sample complexity is reduced to nearly linear order in the uncoupled ambient dimensions, removing the coupled-mode dimension from the leading term. Leveraging the estimated subspace information, we obtain a less stringent sufficient signal-to-noise ratio requirement than those in several existing passive-uniform-sampling guarantees. Under additional mild conditions, we obtain a sharper statistical error bound. Our theoretical findings are supported by numerical simulations. We apply TCSI to the reconstruction of global Total Electron Content (TEC) maps and observe lower reconstruction errors than the compared methods in our experiments.

Problem

• Tensor Completion
• Subspace Information
• Sample Complexity
• Signal-to-Noise Ratio
• Total Electron Content

Innovation

• Tensor Completion
• Subspace Information
• Matrix Regression
• Sample Complexity
• Signal-to-Noise Ratio