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HOSVD-Based Algorithm for Weighted Tensor Completion.

Zehan Chao1, Longxiu Huang1, Deanna Needell1

  • 1Department of Mathematics, University of California, Los Angeles, CA 90095, USA.

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|July 31, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient weighted Higher Order Singular Value Decomposition (HOSVD) algorithm for tensor completion, effectively recovering low-rank tensors from incomplete data. The method demonstrates accuracy and efficiency in simulations, advancing data imputation techniques.

Keywords:
HOSVD decompositiontensor completionweighted tensor

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Area of Science:

  • Data Science
  • Applied Mathematics
  • Numerical Analysis

Background:

  • Matrix completion addresses missing data in matrices with low-dimensional structures.
  • Tensor completion extends these principles to higher-order tensors, aiming to impute missing entries based on low-rank assumptions.

Purpose of the Study:

  • To develop an efficient algorithm for tensor completion with deterministic and potentially non-uniform sampling patterns.
  • To derive error bounds for the proposed tensor completion method.

Main Methods:

  • Proposed an efficient weighted Higher Order Singular Value Decomposition (HOSVD) algorithm.
  • Derived error bounds using a weighted metric for noisy tensor observations.

Main Results:

  • The weighted HOSVD algorithm demonstrates efficient and accurate recovery of underlying low-rank tensors.
  • Error bounds were established for the proposed method under specific conditions.

Conclusions:

  • The developed weighted HOSVD algorithm is effective for tensor completion, even with complex sampling patterns.
  • Numerical simulations confirm the algorithm's efficiency and accuracy on synthetic and real datasets.