论文标题
正则光谱聚类的一致性在经度校正的混合会员模型中
Consistency of regularized spectral clustering in degree-corrected mixed membership model
论文作者
论文摘要
网络分析中的社区发现最近是一个有吸引力的研究领域。在这里，根据度过度校正的混合成员资格（DCMM）模型，我们提出了一种基于正则化laplacian矩阵的有效方法称为混合正则光谱聚类（简称混合RSC）。混合-RSC的设计基于变体的理想锥结构，用于种群正规化拉普拉斯基质的特征分类。我们表明，在温和条件下，通过为每个节点的推断成员矢量提供误差范围，该算法在温和条件下渐近一致。作为我们界限的副产品，我们为正则化参数τ提供了理论的最佳选择。为了证明我们的方法的性能，我们将其应用于模拟和现实世界网络上的先前基准方法。据我们所知，这是基于正规化Laplacian矩阵的应用，在DCMM模型下设计光谱聚类算法的第一项工作。
Community detection in network analysis is an attractive research area recently. Here, under the degree-corrected mixed membership (DCMM) model, we propose an efficient approach called mixed regularized spectral clustering (Mixed-RSC for short) based on the regularized Laplacian matrix. Mixed-RSC is designed based on an ideal cone structure of the variant for the eigen-decomposition of the population regularized Laplacian matrix. We show that the algorithm is asymptotically consistent under mild conditions by providing error bounds for the inferred membership vector of each node. As a byproduct of our bound, we provide the theoretical optimal choice for the regularization parameter τ. To demonstrate the performance of our method, we apply it with previous benchmark methods on both simulated and real-world networks. To our knowledge, this is the first work to design spectral clustering algorithm for mixed membership community detection problem under DCMM model based on the application of regularized Laplacian matrix.
