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<p>We propose two random low-rank approximation algorithms based on sparse projection, SEMHMT and SEMTropp. Compared with HMT and Tropp algorithms, we mainly introduce Sparse Embedding Matrix (SEM) as sparse projection to speed up the computation. We analyze the convergence of the algorithms and compare the complexity of the proposed algorithms with the prototype algorithms. In addition, we expand these two algorithms to Tucker and TT formats of nonnegative tensors. By employing NSTHOSVD and NTTSVD with alternating projection, we preserve the nonnegativity of the original data, allowing for more efficient handling of large nonnegative tensor data. In numerical experiments, We first test the algorithms on matrix and verify its effectiveness. Then we apply them to Hilbert tensor, Multidimensional Gaussian mixture, and Hyperspectral image, and achieve good performance in terms of running speed and nonnegative preservation.</p>

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Low-rank approximation algorithm using sparse projection and its applications

  • 期刊论文

  • 发表日期：

    2025年3月22日

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  • Han Xiao,
  • Feng Yue-Hua,
  • Dong Yong-xin

摘要

We propose two random low-rank approximation algorithms based on sparse projection, SEMHMT and SEMTropp. Compared with HMT and Tropp algorithms, we mainly introduce Sparse Embedding Matrix (SEM) as sparse projection to speed up the computation. We analyze the convergence of the algorithms and compare the complexity of the proposed algorithms with the prototype algorithms. In addition, we expand these two algorithms to Tucker and TT formats of nonnegative tensors. By employing NSTHOSVD and NTTSVD with alternating projection, we preserve the nonnegativity of the original data, allowing for more efficient handling of large nonnegative tensor data. In numerical experiments, We first test the algorithms on matrix and verify its effectiveness. Then we apply them to Hilbert tensor, Multidimensional Gaussian mixture, and Hyperspectral image, and achieve good performance in terms of running speed and nonnegative preservation.