论文标题
部分可观测时空混沌系统的无模型预测
Perfect Spectral Clustering with Discrete Covariates
论文作者
论文摘要
在社区检测方法中，光谱聚类具有两个理想的特性：计算效率和一致性的理论保证。光谱聚类的大多数研究仅将网络的边缘视为算法的输入。在这里，我们考虑在存在离散节点协变量的情况下执行社区检测的问题，其中网络结构是由潜在块模型结构的组合和观察到的协变量均匀的组合确定的。我们提出了一种光谱算法，我们证明，在具有离散协变量的一类大型稀疏网络上具有很高的可能性，可以有效地将潜在网络结构与观察到的协变量分开。据我们所知，我们的方法是第一个提供保证在边缘形成取决于潜在因素和观察因素的环境中使用光谱聚类恢复一致的潜在结构恢复的保证。
Among community detection methods, spectral clustering enjoys two desirable properties: computational efficiency and theoretical guarantees of consistency. Most studies of spectral clustering consider only the edges of a network as input to the algorithm. Here we consider the problem of performing community detection in the presence of discrete node covariates, where network structure is determined by a combination of a latent block model structure and homophily on the observed covariates. We propose a spectral algorithm that we prove achieves perfect clustering with high probability on a class of large, sparse networks with discrete covariates, effectively separating latent network structure from homophily on observed covariates. To our knowledge, our method is the first to offer a guarantee of consistent latent structure recovery using spectral clustering in the setting where edge formation is dependent on both latent and observed factors.
