A1119
Title: Principal graph encoder embedding and principal community detection
Authors: Yuexiao Dong - Temple University (United States) [presenting]
Cencheng Shen - University of Delaware (United States)
Carey Priebe - Johns Hopkins University (United States)
Youngser Park - Johns Hopkins University (United States)
Abstract: The purpose is to introduce the concept of principal communities and propose a principal graph encoder embedding method that concurrently detects these communities and achieves vertex embedding. Given a graph adjacency matrix with vertex labels, the method computes a sample community score for each community, ranking them to measure community importance and estimate a set of principal communities. The method then produces a vertex embedding by retaining only the dimensions corresponding to these principal communities. Theoretically, we define the population version of the encoder embedding and the community score based on a random Bernoulli graph distribution. It is proven that the population principal graph encoder embedding preserves the conditional density of the vertex labels and that the population community score successfully distinguishes the principal communities. A variety of simulations is conducted to demonstrate the finite-sample accuracy in detecting ground-truth principal communities, as well as the advantages in embedding visualization and subsequent vertex classification. The method is further applied to a set of real-world graphs, showcasing its numerical advantages, including robustness to label noise and computational scalability.
