融合块对角约束的鲁棒低秩多核聚类
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作者单位:

1.西南科技大学信息工程学院;2.西南科技大学计算机科学与技术学院

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中图分类号:

TP301.6

基金项目:

四川省科技计划资助,2020YJ0432;西南科技大学研究生创新基金资助,20ycx0032.


Low-rank robust multiple kernel clustering with block diagonal constraints
Author:
Affiliation:

1.School of Information Engineering, Southwest University of Science and Technology;2.School of Computer Science and Technology,Southwest University of Science and Technology

Fund Project:

Supported by Sichuan Science and Technology Program,2020YJ0432;Supported by Postgraduate Innovation Fund Project by Southwest University of Science and Technology,,20ycx0032.

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    摘要:

    针对现有的多核学习(Multiple Kernel Learning, MKL)子空间聚类方法忽略噪声和特征空间中数据的低秩结构的问题,提出一种新的鲁棒多核子空间聚类方法(Low-rank Robust Multiple Kernel Clustering, LRMKC),该方法结合块对角表示({Block Diagonal Representation, BDR)和低秩共识核(Low-Rank Consensus Kernel, LRCK)学习,可以更好地挖掘数据的潜在结构. 主要体现在, (1)为了学习最优共识核,设计了一种基于混合相关熵度量(Mixture Correntropy Induced Metric, MCIM)的自动加权策略,它不仅为每个核设置最优权重,而且通过抑制噪声提高模型的鲁棒性; (2)为了探索特征空间数据的低秩结构,提出一种非凸低秩共识核学习方法; (3)考虑到亲和度矩阵的块对角性质,对系数矩阵应用块对角约束. LRMKC 将 MKL、LRCK 和 BDR 巧妙融合起来,以迭代提高各种方法的效率,最终形成一个处理非线性结构数据的全局优化方法. 与最先进的 MKL 子空间聚类方法相比,在图像和文本数据集上的大量实验证明了 LRMKC 的优越性.

    Abstract:

    Existing MKL subspace clustering algorithms ignore the noise and the low-rank structure of the data in the feature space. We propose a new low-rank robust multiple kernel clustering algorithm (LRMKC) with block diagonal representation (BDR) and low-rank consensus kernel (LRCK), which is better for mining the underlying structure of the data. In particular, (1) to learn the optimal consensus kernel, we design an automatic weighting strategy using Mixture Correntropy Induced Metric (MCIM), which not only sets the optimal weight for each kernel but also improves the robustness of LRMKC by suppressing noise; (2) to explore the low-rank structure of input data in feature space, we learn low-rank consensus kernel by Schatten p-norm constraint on the optimal consensus kernel; (3) considering the block diagonal property of the affinity matrix, we apply block diagonal constraint to the coefficient matrix. LRMKC combines MKL, LRCK, and BDR to solve these problems at the same time. Through the interaction of three technologies, the results of other technologies are used in the overall optimal solution to iteratively improve the efficiency of each technology, and finally form an overall optimal algorithm for processing nonlinear structural data. Compared with the most advanced MKL subspace clustering algorithms, extensive experiments on image and text datasets verify the competitiveness of LRMKC.

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  • 收稿日期:2021-04-05
  • 最后修改日期:2021-08-16
  • 录用日期:2021-08-18
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