Rule sets are highly interpretable logical models in which the predicates for decision are expressed in disjunctive normal form (DNF, OR-of-ANDs), or, equivalently, the overall model comprises an unordered collection of if-then decision rules. In this paper, we consider a submodular optimization based approach for learning rule sets. The learning problem is framed as a subset selection task in which a subset of all possible rules needs to be selected to form an accurate and interpretable rule set. We employ an objective function that exhibits submodularity and thus is amenable to submodular optimization techniques. To overcome the difficulty arose from dealing with the exponential-sized ground set of rules, the subproblem of searching a rule is casted as another subset selection task that asks for a subset of features. We show it is possible to write the induced objective function for the subproblem as a difference of two submodular (DS) functions to make it approximately solvable by DS optimization algorithms. Overall, the proposed approach is simple, scalable, and likely to be benefited from further research on submodular optimization. Experiments on real datasets demonstrate the effectiveness of our method.

Abstract In social network analysis, community detection on plain graphs has been widely studied. With the proliferation of available data, each user in the network is usually associated with additional attributes for elaborate description. However, many existing methods only concentrate on the topological structure and fail to deal with node‐attributed networks. These approaches are incapable of extracting clear semantic meanings for communities detected. In this paper, we combine the topological structure and attribute information into a unified process and propose a novel algorithm to detect overlapping semantic communities. Moreover, a new metric is designed to measure the density of semantic communities. The proposed algorithm is divided into 3 phases. First, we detect local semantic subcommunities from each node's perspective using a greedy strategy on the metric. Then, a supergraph, which consists of all these subcommunities is created. Finally, we find global semantic communities on the supergraph. The experimental results on real‐world data sets show the efficiency and effectiveness of our approach against other state‐of‐the‐art methods.