The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the introduction of immense scale presents challenges to traditional methods. Spectral clustering in distributed memory, for example, requires hundreds of expensive bulk-synchronous communication rounds to compute an embedding of vertices to a few eigenvectors of a graph associated matrix. Furthermore, the whole computation may need to be repeated if the underlying graph changes some low percentage of edge updates. We present a method inspired by spectral clustering where we instead use matrix sketches derived from random dimension-reducing projections. We show that our method produces embeddings that yield performant clustering results given a fully-dynamic stochastic block model stream using both the fast Johnson-Lindenstrauss and CountSketch transforms. We also discuss the effects of stochastic block model parameters upon the required dimensionality of the subsequent embeddings, and show how random projections could significantly improve the performance of graph clustering in distributed memory.

该研究使用基于矩阵草图的方法来解决在大规模图分析中传统方法遇到的挑战，尤其是无监督学习的社区结构划分问题，实验表明该方法在分配内存中可以获得出色的聚类效果，同时提高了聚类速度。

分布式草图缩放图聚类