基于上界单纯形投影图张量学习的多核聚类算法

近年来，多核图聚类（MKGC）受到了广泛的关注，这得益于多核学习能有效地避免核函数与核参数的选择，而图聚类能充分挖掘样本间的复杂结构信息。然而现有的MKGC方法存在着如下问题：图学习技术使得模型复杂化，图拉普拉斯矩阵的高秩特性使其难以保证学到的关系图包含精确的c个连通分量（块对角性质），以及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。针对以上问题，提出了一种新的MKGC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，在上界单纯形投影空间中引入低秩张量学习来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MKGC方法相比，所提出方法计算量小、稳定性高，在聚类精度（ACC）和标准互信息（NMI）指标上具有较大的优势。

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

Because multiple kernel learning can avoid selection of kernel functions and parameters effectively， and graph clustering can fully mine complex structural information between samples， Multiple Kernel Graph Clustering （MKGC） has received widespread attention in recent years. However， the existing MKGC methods suffer from the following problems： graph learning technique complicates the model， the high rank of graph Laplacian matrix cannot ensure the learned affinity graph to contain accurate c connected components （block diagonal property）， and most of the methods ignore the high-order structural information among the candidate affinity graphs， making it difficult to fully utilize the multiple kernel information. To tackle these problems， a novel MKGC method was proposed. First， a new graph learning method based on capped simplex projection was proposed to directly project the kernel matrices onto graph simplex， which reduced the computational complexity. Meanwhile， a new block diagonal constraint was introduced to keep the accurate block diagonal property of the learned affinity graphs. Moreover， the low-rank tensor learning was introduced in capped simplex projection space to fully mine the high-order structural information of multiple candidate affinity graphs. Compared with the existing MKGC methods on multiple datasets， the proposed method has less computational cost and high stability， and has great advantages in Accuracy （ACC） and Normalized Mutual Information （NMI）.