Multiple kernel graph tensor clustering algorithm based on capped simplex projection learning

  

  • Received:2021-08-04 Revised:2021-08-30 Published:2021-10-14

CCML2021+234: 基于上界单纯形投影图张量学习的多核聚类算法

雷皓云1,任珍文1,汪彦龙2,薛爽1,李浩然1   

  1. 1. 西南科技大学国防科技学院
    2. 浙江传媒学院
  • 通讯作者: 雷皓云

Abstract: Abstract: Because multiple kernel learning can avoid selection of kernel function and parameter effectively, graph-based clustering can fully exploit complex structure information of datasets, so Multiple Kernel Graph Clustering (MKGC) had received widespread attention in recent years. However, both of them had demerits: graph-based learning would complicate the model, and the high rank of Laplacian matrix cannot ensure affinity graph contains c connected components accurately. Moreover, most of methods ignored the high order structure information among the candidate graphs, which made it difficult to fully utilize the multi-kernel information. Therefore, to tackle these problems, a novel MKGC method was proposed. To begin with, a new graph learning method based capped simplex projection was introduced to project kernel matrices onto graphs simplicity, which reduced the computational complexity. Meanwhile, used a new block diagonal constraint to keep the precise block diagonal property of learned affinity graphs; Moreover, low-rank tensor learning was introduced in capped simplex projection space to fully exploit the high-order structure information of multiple base kernels. Extensive experiments validate that proposed method has good clustering effect.

Key words: Multiple kernel graph clustering, capped simplex, tensor learning, block diagonal property, high-order affinity

摘要: 摘 要: 近年来,多核图聚类(MKGC)受到了广泛的关注,得益于多核学习能有效地避免核函数与核参数的选择、图聚类能充分挖掘样本间的复杂结构信息。然而现有的方法存在着:图学习技术使得模型复杂化、图拉普拉斯矩阵难以保证学到的关系图包含精确的c个连通分量(块对角)、大部分方法忽略了候选关系图间的高阶结构信息,使得多核信息难以被充分利用等问题。针对以上问题,提出了一种新的多核聚类方法:首先提出一种新的上界单纯形投影图学习方法,直接将核矩阵投影到图单纯形上,降低了计算复杂度;同时,引入了一种新的块对角约束,使学到的关系图能保持精确的块对角属性;此外,在该投影空间中引入低秩张量学习,充分挖掘多个候选关系图的高阶结构信息。在多个数据集上与现有的多核图聚类方法相比,所提出方法计算量小、稳定性高,在ACC和NMI指标方面聚类性能具有较大的优势。

关键词: 关键词: 多核图聚类, 上界单纯形, 张量学习, 块对角性质, 高阶结构信息