We study the statistical and computational properties of a network Lasso method for local graph clustering. The clusters delivered by nLasso can be characterized elegantly via network flows between cluster boundaries and seed nodes. While spectral clustering methods are guided by a minimization of the graph Laplacian quadratic form, nLasso minimizes the total variation of cluster indicator signals. As demonstrated theoretically and numerically, nLasso methods can handle very sparse clusters (chain-like) which are difficult for spectral clustering. We also verify that a primal-dual method for non-smooth optimization allows to approximate nLasso solutions with optimal worst-case convergence rate.

中文翻译：

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使用网络套索进行局部图聚类

我们研究了用于局部图聚类的网络套索方法的统计和计算特性。nLasso 提供的集群可以通过集群边界和种子节点之间的网络流来优雅地表征。虽然谱聚类方法由图拉普拉斯二次形式的最小化指导，但 nLasso 最小化了聚类指示信号的总变化。从理论上和数值上证明，nLasso 方法可以处理非常稀疏的集群（链状），这对于光谱聚类来说很困难。我们还验证了用于非平滑优化的原始对偶方法允许以最佳最坏情况收敛速度逼近 nLasso 解。