A common question arising in the study of graphs is how to partition nodes into well-connected clusters. One standard methodology, known as spectral clustering, utilizes an eigenvector embedding as a starting point for clustering the nodes. Utilizing the same eigenvector embedding, we present a new algorithm for spectral clustering based on a column-pivoted QR factorization. Our method is simple to implement, direct, and scalable. Furthermore, in contrast to many existing techniques, our algorithm does not require an initial guess of the clusters. We provide theoretical motivation for our algorithm and experimentally demonstrate that its performance tracks recent information theoretic bounds for exact recovery in the stochastic block model.
Assistant Professor, Computer Science