HS2: Active learning over hypergraphs with pointwise and pairwise queries

We propose a hypergraph-based active learning scheme which we term HS2; HS2 generalizes the previously reported algorithm S-2 originally proposed for graph-based active learning with pointwise queries [1]. Our HS2 method can accommodate hypergraph structures and allows one to ask both pointwise queries and pairwise queries. Based on a novel parametric system particularly designed for hypergraphs, we derive theoretical results on the query complexity of HS2 for the above described generalized settings. Both the theoretical and empirical results show that HS2 requires a significantly fewer number of queries than S-2 when one uses S-2 over a graph obtained from the corresponding hypergraph via clique expansion.