Estimation and clustering in popularity adjusted block model
Estimation and clustering in popularity adjusted block model
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DOI：
10.1111/rssb.12410
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
M. Noroozi;R. Rimal;M. Pensky
中科院分区：
文献类型：
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作者：
M. Noroozi;R. Rimal;M. Pensky
本文考虑了Sengupta和Chen（皇家统计学会期刊系列B，2018，80，365 - 386）引入的流行度调整区组模型（PABM）。我们认为，PABM的主要吸引力是灵活的频谱特性的图形，这使得PABM的一个有吸引力的选择，在生物科学中出现的网络建模。我们扩展的PABM理论的情况下，任意数量的社区可能增长的网络中的节点数量，并不假定是已知的。我们给出了概率矩阵和社区结构的估计，此外，还提供了估计和聚类误差的非渐近上界。我们使用稀疏子空间聚类（SSC）的方法将网络划分为社区，该方法，据我们所知，尚未用于聚类网络数据。该理论是由模拟研究补充。此外，我们展示了PABM建模蝴蝶相似性网络和人脑功能网络的优势。
The paper considers the Popularity Adjusted Block model (PABM) introduced by Sengupta and Chen (Journal of the Royal Statistical Society Series B, 2018, 80, 365–386). We argue that the main appeal of the PABM is the flexibility of the spectral properties of the graph which makes the PABM an attractive choice for modelling networks that appear in biological sciences. We expand the theory of PABM to the case of an arbitrary number of communities which possibly grows with a number of nodes in the network and is not assumed to be known. We produce estimators of the probability matrix and of the community structure and, in addition, provide non‐asymptotic upper bounds for the estimation and the clustering errors. We use the Sparse Subspace Clustering (SSC) approach for partitioning the network into communities, the approach that, to the best of our knowledge, has not been used for the clustering network data. The theory is supplemented by a simulation study. In addition, we show advantages of the PABM for modelling a butterfly similarity network and a human brain functional network.