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<p>Tensor wheel (TW) decomposition is an innovative combination of the popular tensor ring and fully connected tensor network decompositions, and has achieved excellent performance in some tensor problems. The famous alternating least squares (ALS) is a standard method for computing the decomposition. However, it typically faces issues of high computational cost. In this paper, we propose two strategies to address the aforementioned issues. The first one is to speed up the calculation of the coefficient matrices in normal equations for ALS subproblems by fully using the structures in the coefficient matrices of the subproblems. In the second strategy, we introduce the randomized techniques and combine them with the first strategy. The resulting error bounds are also investigated. Further, the above two acceleration methods are applied to the tensor regression based on TW decomposition. For the proposed algorithms, we provide theoretical complexity analysis and conduct numerical experiments. Results on synthetic and real data show that our methods perform remarkably well.</p>

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Accelerated Alternating Least Squares for Tensor Wheel Decomposition with Applications

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Fukang Li,
  • Mengyu Wang,
  • Hanyu Li

摘要

Tensor wheel (TW) decomposition is an innovative combination of the popular tensor ring and fully connected tensor network decompositions, and has achieved excellent performance in some tensor problems. The famous alternating least squares (ALS) is a standard method for computing the decomposition. However, it typically faces issues of high computational cost. In this paper, we propose two strategies to address the aforementioned issues. The first one is to speed up the calculation of the coefficient matrices in normal equations for ALS subproblems by fully using the structures in the coefficient matrices of the subproblems. In the second strategy, we introduce the randomized techniques and combine them with the first strategy. The resulting error bounds are also investigated. Further, the above two acceleration methods are applied to the tensor regression based on TW decomposition. For the proposed algorithms, we provide theoretical complexity analysis and conduct numerical experiments. Results on synthetic and real data show that our methods perform remarkably well.