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图学学报

图学学报 ›› 2020, Vol. 41 ›› Issue (6): 954-961.DOI: 10.11996/JG.j.2095-302X.2020060954

• 图像处理与计算机视觉 • 上一篇    下一篇

基于快速凸无穷范数极小化的 大量子空间的子空间分割

  

  1. (辽宁师范大学数学学院，辽宁 大连 116029)
  • 出版日期:2020-12-31 发布日期:2021-01-11
  • 基金资助:
    基金项目：国家自然科学基金项目(61702243，62076115，61702245，61771229)；辽宁省“兴辽英才计划”项目(XLYC1907169)；辽宁省教育厅项 目(L201783642)；大连市青年科技之星项目(2019RQ033) 

Large subspace number subspace segmentation via fast convex infinity norm minimization 

  1. (School of Mathematics, Liaoning Normal University, Dalian Liaoning 116029, China) 
  • Online:2020-12-31 Published:2021-01-11
  • Supported by:
    Keywords: subspace segmentation; spectral clustering-based methods; large subspace number; infinity norm; fast algorithm 

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摘要： 摘 要：子空间分割是计算机视觉和机器学习中的一个基本问题。由于实际问题中的数据 往往类数较多，使得大量子空间的子空间分割问题显得尤为重要。近年来基于谱聚类的方法在 子空间分割领域得到了越来越多的关注，但是在相关工作的实验中，子空间的个数却往往不超 过 10 个。无穷范数极小化是近年来提出的一个专门针对大量子空间的子空间分割问题的方法， 其通过降低表示系数矩阵的差异性能有效地处理该问题，但是仍有一定的局限，例如计算速度 仍不够快，缺乏针对独立子空间问题的理论保证。为此，提出快速凸无穷范数极小化，该个方 法不仅能够降低表示系数矩阵的差异性，而且能够对独立子空间情况提供理论保障且计算速度 更快，大量的实验证明了该方法的有效性。

关键词: 关 键 词：子空间分割, 基于谱聚类的方法, 大量子空间, 无穷范数, 快速算法

Abstract: Abstract: Subspace segmentation is one of the fundamentals in computer vision and machine learning. Given the large number of categories in practical problems concerning the data set, it is of great significance to address the issue of large subspace number subspace segmentation. Although spectral clustering-based methods received more attention in the field of subspace segmentation, the subspace number in the past experiments was usually less than 10. The infinity norm minimization was a recently proposed method specially for large subspace number subspace segmentation. It could effectively address this problem by reducing the difference of the representation matrix, but there remained some limitations. For example, the computation speed was not fast enough, and there was no theoretical guarantee for the independent subspaces. Therefore, a method named fast convex infinity norm minimization was proposed. This method can not only reduce the difference of the representation matrix, but also provide the theoretical guarantee for the independent subspace and enhance the computation speed, which has been testified by a large number of experiments.

Key words: Keywords: subspace segmentation, spectral clustering-based methods, large subspace number; infinity norm, fast algorithm 

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