Ergodic Limits, Relaxations, and Geometric Properties of Random Walk Node Embeddings

Random walk based node embedding algorithms learn vector representations of nodes by optimizing an objective function of node embedding vectors and skip-bigram statistics computed from random walks on the network. They have been applied to many supervised learning problems such as link prediction and node classification and have demonstrated state-of-the-art performance. Yet, their properties remain poorly understood. This paper studies properties of random walk based node embeddings in the unsupervised setting of discovering hidden block structure in the network, i.e., learning node representations whose cluster structure in Euclidean space reflects their adjacency structure within the network. We characterize the ergodic limits of the embedding objective, its generalization, and related convex relaxations to derive corresponding non-randomiz

Node Embedding via Word Embedding for Network Community Discovery

Neural node embeddings have recently emerged as a powerful representation for supervised learning tasks involving graph-structured data. We leverage this recent advance to develop a novel algorithm for unsupervised community discovery in graphs. Through extensive experimental studies on simulated and real-world data, we demonstrate that the proposed approach consistently improves over the current state-of-the-art. Specifically, our approach empirically attains the information-theoretic limits for community recovery under the benchmark Stochastic Block Models for graph generation and exhibits better stability and accuracy over both Spectral Clustering and Acyclic Belief Propagation in the community recovery limits.