Rough maximal cliques enumeration in incomplete graphs based on partially-known concept learning

Abstract

The emerging massive noisy and incomplete data is transforming the conventional graph to the uncertain graph. In this paper, we study rough maximal cliques enumeration (RMCE) in incomplete graphs, which we define as the novel problem of enumerating all maximal cliques where some of edges are unknown to users. The hardness of RMCE is proved to NP-complete. To tackle this problem, an efficient framework for obtaining the rough maximal cliques based on Partially-Known Concept Learning (PKCL). With this framework, a given incomplete graph is initially represented as an incomplete formal context. Then, the partially-known SE-ISI concept lattice is generated through the constructed incomplete formal context. Based on the constructed SE-ISI concept lattice, an equivalence theorem between SE-ISI equiconcepts and rough maximal cliques is presented. The detailed topological structural analysis from the point of views of roughness and SE-ISI concept stability of rough maximal cliques are separately discussed. The evaluation results demonstrate that our proposed PKCL algorithm can better identify the rough maximal cliques under different probability distribution models of links compared to the existing baseline algorithms.