Bootstrapped Graph Diffusions: Exposing the Power of Nonlinearity

Graph-based semi-supervised learning (SSL) algorithms predict labels for all nodes based on provided labels of a small set of seed nodes. Classic methods capture the graph structure through some underlying diffusion process that propagates through the graph edges. Spectral diffusion, which includes personalized page rank and label propagation, propagates through random walks. Social diffusion propagates through shortest paths. These diffusions are linear in the sense of not distinguishing between contributions of few "strong" relations or many "weak'' relations. Recent methods such as node embeddings and graph convolutional networks (GCN) attained significant gains in quality for SSL tasks. These methods vary on how the graph structure, seed label information, and other features are used, but do share a common thread of nonlinearity that suppresses weak relations and re-enforces stronger ones. Aiming for quality gain with more scalable methods, we revisit classic linear diffusion methods and place them in a self-training framework. The resulting bootstrapped diffusions are nonlinear in that they re-enforce stronger relations, as with the more complex methods. Surprisingly, we observe that SSL with bootstrapped diffusions not only significantly improves over the respective non-bootstrapped baselines but also outperform state-of-the-art SSL methods. Moreover, since the self-training wrapper retains the scalability of the base method, we obtain both higher quality and better scalability.