再谈谱聚类：隐藏在Fiedler向量中的信息
Spectral Clustering Revisited: Information Hidden in the Fiedler Vector
摘要：
我们感兴趣的是图上的聚类问题：众所周知，如果有两个潜在的集群，那么对应于邻接矩阵的第二大特征值的特征向量的符号可以可靠地重建这两个集群。我们认为，顶点的特征向量具有最大和最小的条目，分别是异常强烈地连接到自己的集群和更可靠的分类比其余的。这可以被看作是热点猜想的离散版本，并且应该在应用中是有用的。给出了随机块模型的严格证明和几个例子。
英文摘要：
We are interested in the clustering problem on graphs: it is known that if there are two underlying clusters, then the signs of the eigenvector corresponding to the second largest eigenvalue of the adjacency matrix can reliably reconstruct the two clusters. We argue that the vertices for which the eigenvector has the largest and the smallest entries, respectively, are unusually strongly connected to their own cluster and more reliably classified than the rest. This can be regarded as a discrete version of the Hot Spots conjecture and should be useful in applications. We give a rigorous proof for the stochastic block model and several examples.
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