Improvements on SCORE, Especially for Weak Signals

A network may have weak signals and severe degree heterogeneity, be very sparse in one occurrence but dense another. SCORE (Ann. Statist. 43, 57–89, 2015) is a recent approach to community detection. It accommodates heterogeneity adaptive different levels of sparsity, its performance for networks with unclear. In this paper, we show that broad class settings where allow signals, wide range achieves prefect clustering has the so-called “exponential rate” Hamming errors. The proof uses most advancement on entry-wise bounds leading eigenvectors adjacency matrix. theoretical analysis assures us continues work well signal settings, it does not rule out possibility further improved better real applications, especially signals. As second contribution propose SCORE+ as an version SCORE. We investigate 8 data sets found outperforms several representative approaches. particular, 6 relatively strong similar SCORE, 2 (Simmons, Caltech) possibly much lower error rates. proposes changes carefully explain rationale underlying each these changes, using mixture numerical study.