Active Learning on Graphs with Geodesically Convex Classes

Abstract

We study the problem of actively learning the vertex labels of a graph, assuming the classes form geodesically convex subgraphs, which is related to linear separability in the Euclidean setting. The main result of this paper is a novel query-efficient active learning algorithm with label-independent upper bounds on the number of queries needed to learn all labels. For that, we use shortest path covers and provide a logarithmic approximation for the sub-problem of computing a shortest path cover of minimum size. We extend the approach to arbitrarily labeled graphs using a convexity-based selection criterion. Finally, we discuss whether the convexity assumption holds on real-world data and give some first preliminary results on citation and image benchmark datasets.