  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. A common ground to these
diffusions is their {\em linearity}, which does not distinguish between
contributions of few "strong" relations and many "weak" relations.
  Recently, non-linear methods such as node embeddings and graph convolutional
networks (GCN) demonstrated a large gain in quality for SSL tasks. These
methods introduce multiple components and greatly vary on how the graph
structure, seed label information, and other features are used.
  We aim here to study the contribution of non-linearity, as an isolated
ingredient, to the performance gain. To do so, we place classic linear graph
diffusions in a self-training framework. Surprisingly, we observe that SSL
using the resulting {\em bootstrapped diffusions} not only significantly
improves over the respective non-bootstrapped baselines but also outperform
state-of-the-art non-linear SSL methods. Moreover, since the self-training
wrapper retains the scalability of the base method, we obtain both higher
quality and better scalability.
