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Rank-Adaptive Tensor Completion Based on Tucker Decomposition.

Siqi Liu1, Xiaoyu Shi1, Qifeng Liao1

  • 1School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China.

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Summary
This summary is machine-generated.

This study introduces a novel tensor completion algorithm using Tucker decomposition to accurately estimate missing data. The method adaptively adjusts tensor ranks, improving accuracy in applications like image recovery and traffic data completion.

Keywords:
HOOI algorithmSVT algorithmTucker decompositionrank-adaptive methodstensor completion

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Area of Science:

  • Multivariate statistics
  • Data science
  • Signal processing

Background:

  • Tensor completion is crucial for reconstructing incomplete datasets in various fields.
  • Existing decomposition-based methods struggle with accurate tensor rank estimation, leading to inaccuracies.
  • Tucker decomposition offers a framework for tensor factorization but requires careful rank selection.

Purpose of the Study:

  • To develop a robust tensor completion algorithm that overcomes the limitations of fixed tensor rank selection.
  • To improve the accuracy of estimating missing entries in tensors by adaptively determining the multilinear rank.
  • To provide a more reliable method for data recovery in applications with incomplete tensor data.

Main Methods:

  • Proposes a novel tensor completion algorithm based on Tucker decomposition.
  • Employs an alternative iterating method that decomposes the tensor completion problem into multiple matrix completion subproblems.
  • Introduces adaptive adjustment of the multilinear rank during the optimization process.

Main Results:

  • The proposed method effectively estimates tensor ranks, addressing underestimation and overestimation issues.
  • Numerical experiments on synthetic and real-world image data demonstrate superior performance in predicting missing entries.
  • The adaptive rank adjustment leads to more accurate tensor completion compared to traditional methods.

Conclusions:

  • The developed algorithm offers a significant advancement in tensor completion by adaptively determining multilinear ranks.
  • This approach enhances data recovery accuracy in diverse applications, including image processing and traffic data analysis.
  • The method provides a more reliable and accurate solution for handling incomplete tensor data.