Identifying multiple influence sources in social networks based on latent space mapping

We are currently in a network era which enables us to communicate more widely and more easily via the social networks. Meanwhile, negative information, such as fake news, rumors and computer viruses, often spread in social network. In order to restrain the propagation of such negative influence, we must find its sources in the network. But in real-world applications, we usually only know the scope of the negative influence spreading, and do not know who first propagates the negative influence. However, we can identify the sources of the negative influence based on the information of some observed nodes which are negatively influenced. This is the problem of influence sources locating. To tackle this problem, we present a latent space mapping-based method for identifying the multiple influence sources in the independent cascade model. The method first detects the candidate sources of the observed nodes based on message passing in a reversed network. An algorithm is presented to calculate the activation probability between nodes according to the influence spreading pattern in the independent cascade model. To evaluate each node's rationality as the propagation source, we use the difference between the length of the path influencing an observed node and its activation time. We define two latent spaces, namely the influence senders and receivers’ latent spaces, and map the nodes into these two latent spaces to form a model describing the influence propagation. An estimation-maximization-based algorithm is proposed to optimize the propagation model. Based on this model, we propose a latent space mapping-based algorithm to identify the influence sources. The probability for each node to be a source is calculated by its positions in the latent spaces. Finally, k nodes with the largest probabilities are selected as the sources. Empirical results demonstrate that the influence sources identified by the proposed method can influence more observed nodes at more accurate time than other methods.