HOSVD-Based Algorithm for Weighted Tensor Completion

TL;DR

This paper introduces a weighted HOSVD algorithm for tensor completion that handles deterministic, non-uniform sampling patterns, providing theoretical error bounds and demonstrating effectiveness on synthetic and real data.

Contribution

The paper proposes a novel weighted HOSVD method for tensor completion with deterministic sampling, including error analysis and empirical validation.

Findings

The algorithm achieves accurate tensor recovery under noisy observations.

Error bounds are established for the proposed weighted HOSVD approach.

Numerical experiments confirm the method's efficiency and accuracy.

Abstract

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute missing tensor entries from similar low-rank type assumptions. In this paper, we study the tensor completion problem when the sampling pattern is deterministic and possibly non-uniform. We first propose an efficient weighted HOSVD algorithm for recovery of the underlying low-rank tensor from noisy observations and then derive the error bounds under a properly weighted metric. Additionally, the efficiency and accuracy of our algorithm are both tested using synthetic and real datasets in numerical simulations.