Scholarlink

<p>In this paper, we propose a novel real structure-preserving simultaneous diagonalization algorithm for quaternion Hermitian matrix pencils. The core of the new algorithm lies in our design of an efficient quaternion Cholesky decomposition, which not only preserves the structure but also offers advantages in execution speed and storage efficiency. Two-dimensional quaternion linear discriminant analysis (2D-QLDA) can be applied to color image recognition and reconstruction, which is mathematically equivalent to a generalized quaternion eigenvalue problem. The proposed real structure-preserving simultaneous diagonalization algorithm can effectively solve this generalized quaternion eigenvalue problem. Numerical experiments based on both synthetic data and real facial image data demonstrate the effectiveness and efficiency of the proposed method.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A novel algorithm for simultaneous diagonalization of quaternion hermitian matrix pencils with applications in face recognition

  • 期刊论文

  • 发表日期：

    2025年5月12日

查看全文
  • Shan-Qi Duan,
  • Qing-Wen Wang

摘要

In this paper, we propose a novel real structure-preserving simultaneous diagonalization algorithm for quaternion Hermitian matrix pencils. The core of the new algorithm lies in our design of an efficient quaternion Cholesky decomposition, which not only preserves the structure but also offers advantages in execution speed and storage efficiency. Two-dimensional quaternion linear discriminant analysis (2D-QLDA) can be applied to color image recognition and reconstruction, which is mathematically equivalent to a generalized quaternion eigenvalue problem. The proposed real structure-preserving simultaneous diagonalization algorithm can effectively solve this generalized quaternion eigenvalue problem. Numerical experiments based on both synthetic data and real facial image data demonstrate the effectiveness and efficiency of the proposed method.