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Tensor wheel completion for visual data with sparsity and smoothness on latent space.

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Tensor wheel decomposition for tensor completion faces overfitting challenges due to rank selection. This study introduces a novel model analyzing sparsity and smoothness to prevent overfitting, improving tensor completion performance.

Keywords:
Rank robustnessSmoothnessSparsityTensor completionTensor wheel decomposition

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Area of Science:

  • Multivariate calculus
  • Machine learning
  • Data science

Background:

  • Tensor wheel decomposition offers advantages for exploring intrinsic relationships in tensor completion.
  • Rank selection in tensor wheel models can lead to overfitting, especially in rank-sensitive scenarios.

Purpose of the Study:

  • To theoretically analyze the relationship between sparsity, smoothness, and overfitting in tensor wheel decomposition.
  • To propose a novel tensor completion model that mitigates overfitting by incorporating sparsity and smoothness on the latent space.

Main Methods:

  • Theoretical analysis of sparsity and smoothness effects on overfitting within the tensor wheel structure.
  • Development of a new tensor completion model leveraging latent space sparsity and smoothness.
  • Optimization of the proposed model using an efficient alternating direction method of multipliers (ADMM)-based algorithm.

Main Results:

  • The proposed tensor completion method demonstrates superior performance compared to existing techniques.
  • The model maintains robust results across a wide range of rank selections.
  • The method exhibits reduced susceptibility to overfitting as rank increases.

Conclusions:

  • The novel tensor wheel completion model effectively addresses overfitting issues related to rank selection.
  • The incorporation of sparsity and smoothness principles enhances model stability and performance.
  • The ADMM-based optimization ensures an efficient and practical solution for tensor completion.