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<p>The transformed low tubal rankness of third-order tensors has many applications in data science, scientific computation and practical engineering. The transformed rank fully depends on the specific selection of transformation. For a given third-order tensor, how to find an orthogonal transformation such that the transformed tubal rank of the tensor is minimized or approximately minimized has become an important research issue. In this paper, an optimization model for the orthogonal transformed lowest tubal rank of third-order tensor is established, and an inexact augmented Lagrange algorithm for solving the established optimization model is proposed. This algorithm has global convergence under mild conditions. Numerical examples on synthetic and real-world data tensors demonstrate the effectiveness of the proposed approach.</p>

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An optimization approach for transformed low tubal rank of third-order tensors

  • 期刊论文

  • 发表日期：

    2026年1月30日

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  • Jinjie Liu,
  • Chen Ling,
  • Erbo Zhao,
  • Xinmin Yang

摘要

The transformed low tubal rankness of third-order tensors has many applications in data science, scientific computation and practical engineering. The transformed rank fully depends on the specific selection of transformation. For a given third-order tensor, how to find an orthogonal transformation such that the transformed tubal rank of the tensor is minimized or approximately minimized has become an important research issue. In this paper, an optimization model for the orthogonal transformed lowest tubal rank of third-order tensor is established, and an inexact augmented Lagrange algorithm for solving the established optimization model is proposed. This algorithm has global convergence under mild conditions. Numerical examples on synthetic and real-world data tensors demonstrate the effectiveness of the proposed approach.