论文标题
有关社区检测的双正规化拉普拉斯光谱聚类方法
Dual regularized Laplacian spectral clustering methods on community detection
论文作者
论文摘要
光谱聚类方法被广泛用于检测网络中的集群以进行社区检测，而图形拉普拉斯矩阵的小变化可能会带来巨大的改进。在本文中，我们提出了一个双正规化图拉普拉斯矩阵，然后在该学位校正的随机块模型下采用三种经典光谱聚类方法。如果社区的数量被称为$ K $，我们将考虑$ k $领先的特征向量，并通过光谱聚类程序中相应的特征值来加重它们，以提高性能。三种改进的光谱聚类方法是双正规化光谱聚类（DRSC）方法，对元素比率（DRSCORE）方法的双重正则光谱聚类和双正则化对称的Laplacian逆矩阵（DRSLIM）方法。对DRSC和DRSLIM的理论分析表明，在轻度条件下DRSC和DRSLIM在理想情况下会产生稳定的稳定社区检测，DRSCORE返回完美的聚类。我们通过大量的模拟网络和八个现实世界网络将DRSC，DRSCORE和DRSLIM的性能与多种光谱方法进行了比较。
Spectral clustering methods are widely used for detecting clusters in networks for community detection, while a small change on the graph Laplacian matrix could bring a dramatic improvement. In this paper, we propose a dual regularized graph Laplacian matrix and then employ it to three classical spectral clustering approaches under the degree-corrected stochastic block model. If the number of communities is known as $K$, we consider more than $K$ leading eigenvectors and weight them by their corresponding eigenvalues in the spectral clustering procedure to improve the performance. Three improved spectral clustering methods are dual regularized spectral clustering (DRSC) method, dual regularized spectral clustering on Ratios-of-eigenvectors (DRSCORE) method, and dual regularized symmetrized Laplacian inverse matrix (DRSLIM) method. Theoretical analysis of DRSC and DRSLIM show that under mild conditions DRSC and DRSLIM yield stable consistent community detection, moreover, DRSCORE returns perfect clustering under the ideal case. We compare the performances of DRSC, DRSCORE and DRSLIM with several spectral methods by substantial simulated networks and eight real-world networks.
