Learning safe graph construction from multiple graphs

Graph-based method is one important paradigm of semi-supervised learning (SSL). Its learning performance typically relies on excellent graph construction which, however, remains challenging for general cases. What is more serious, constructing graph improperly may even deteriorate performance, which means its performance is worse than that of its supervised counterpart with only labeled data. For this reason, we consider learning a safe graph construction for graph-based SSL in this work such that its performance will not significantly perform worse than its supervised counterpart. Our basic idea is that, given a data distribution, there often exist some dense areas which are robust to graph construction. We then propose to combine trustable subgraphs in these areas from a set of candidate graphs to derive a safe graph, which remains to be a convex problem. Experimental results on a number of datasets show that our proposal is able to effectively avoid performance degeneration compared with many graph-based SSL methods.