On Social Network De-Anonymization With Communities: A Maximum A Posteriori Perspective

Abstract

A crucial privacy-driven issue nowadays is re-identifying anonymized social networks by mapping them to correlated cross-domain auxiliary networks. Prior works are typically based on modeling social networks as random graphs representing users and their relations, and subsequently quantify the quality of mappings through varied cost functions. However, many cost functions are empirically proposed without sufficient theoretical support. For some other works probing the theoretical bound, it remains unknown how to algorithmically meet the demand of such quantifications, i.e., to minimize the cost functions. Besides, only few prior works have discussed the de-anonymization of social networks with communities. We address those concerns in a social network modeling parameterized by community structures that can be leveraged as side information for de-anonymization. Based on the Maximum A Posteriori (MAP) estimation, our first contribution is a series of MAP-based cost functions, which, when minimized, enjoy superiority to previous ones in finding the correct mapping with the highest probability. The feasibility of the cost functions is then for the first time algorithmically characterized. We prove the general multiplicative inapproximability and thus propose two heuristics, which, respectively, enjoy an <inline-formula><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -additive approximation and a conditional optimality in carrying out successful user re-identification. Our theoretical findings are also empirically validated under classical synthetic and real-wrold social networks. Both theoretical and empirical observations manifest the importance of community in enhancing privacy inferencing.