Monotone Submodular Diversity functions for Categorical Vectors with Application to Diversification of Seeds for Targeted Influence Maximization
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Embedding diversity into knowledge discovery tasks is of crucial importance to enhance the meaningfulness of the mined patterns with high-impact aspects related to novelty, serendipity, and ethics. Surprisingly, in the classic problem of influence maximization in social networks, relatively little study has been devoted to diversity and its integration into the objective function of an influence maximization method. In this work, we propose the integration of a side-information-based notion of seed diversity into the objective function of a targeted influence maximization problem. Starting from the assumption that side-information is available at node level in the general form of categorical attribute values, we design a class of monotone submodular functions specifically conceived for determining the diversity within a set of categorical profiles associated with the seeds to be discovered. This allows us to develop an efficient scalable approximate method, with a constant-factor guarantee of optimality. More precisely, we formulate the attribute-based diversity-sensitive targeted influence maximization problem under the state-of-the-art reverse influence sampling framework, and we develop a method, dubbed ADITUM, that ensures a (1-1/e-ϵ)-approximate solution under the general triggering diffusion model. We experimentally evaluated ADITUM on five real-world networks, including comparison with methods that exploit numerical-attribute-based diversity and topology-driven diversity in influence maximization.
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