系统仿真学报 ›› 2021, Vol. 33 ›› Issue (11): 2533-2544.doi: 10.16182/j.issn1004731x.joss.21-0950

• 专栏:智能制造 •    下一篇

核块对角表达子空间聚类及收敛性分析

刘茂山, 纪志成, 王艳, 王建锋   

  1. 江南大学 教育部物联网技术应用工程中心,江苏 无锡 214122
  • 收稿日期:2021-09-14 修回日期:2021-10-26 出版日期:2021-11-18 发布日期:2021-11-17
  • 作者简介:刘茂山(1992-),男,博士生,研究方向为数据挖掘与模式识别。E-mail:maoshanliu@aliyun.com
  • 基金资助:
    国家重点研发计划(2018YFB1701903); 国家自然科学基金(61973138)

Kernel Block Diagonal Representation Subspace Clustering and Its Convergence Analysis

Liu Maoshan, Ji Zhicheng, Wang Yan, Wang Jianfeng   

  1. Engineering Research Center of Internet of Things Technology Applications Ministry of Education, Jiangnan University, Wuxi 214122, China
  • Received:2021-09-14 Revised:2021-10-26 Online:2021-11-18 Published:2021-11-17

摘要: 针对线性块对角表达子空间聚类算法不能有效处理非线性视觉数据,以及常规的正则化器不能直接追求k块对角矩阵等缺点,提出了核块对角表达子空间聚类算法。将原始输入空间映射到线性可分的核希尔伯特空间,在该特征空间中进行谱聚类,同时给出了算法的收敛性分析,利用变量的强凸性和函数的有界性来验证目标函数单调递减和亲和力矩阵有界且收敛。与核稀疏子空间聚类、块对角表达子空间聚类等算法相比,结果表明:该算法在Extended Yale B,ORL(Olivetti Research Laboratory)和MVTec ITODD数据集上取得了较低的聚类误差和较高的归一化互信息。

关键词: 视觉数据, 核子空间聚类, 块对角表达, 收敛性分析

Abstract: Focus on the problems that the linear block diagonal representation subspace clustering cannot effectively handle non-linear visual data, and the regular regularizers cannot directly pursue the k-block diagonal matrix, a kernel block diagonal representation subspace clustering is proposed. In the proposed algorithm, the original input space is mapped into the kernel Hilbert space which is linearly separable, and the spectral clustering is performed in the feature space. The convergence analysis is given, and the strong convex of variables and the boundedness of function is utilized to verify the monotonically decreasing of objective function and the boundedness and convergence of the affinity matrix, which breaks through the difficulty of convergence proof. Compared with other algorithms such as the kernel sparse subspace clustering and the block diagonal representation algorithm tested, the algorithm has achieved the lower clustering error and higher normalized mutual information on Extended Yale B, ORL and MVtec ITODD.

Key words: visual data, kernel subspace clustering, block diagonal representation, convergence analysis

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