Nowadays, it is common for one natural person to join multiple social networks to enjoy different services. Linking identical users across different social networks, also known as the User Identity Linkage (UIL), is an important problem of great research challenges and practical value. Most existing UIL models are supervised or semi-supervised and a considerable number of manually matched user identity pairs are required, which is costly in terms of labor and time. In addition, existing methods generally rely heavily on some discriminative common user attributes, and thus are hard to be generalized. Motivated by the isomorphism across social networks, in this paper we consider all the users in a social network as a whole and perform UIL from the user space distribution level. The insight is that we convert the unsupervised UIL problem to the learning of a projection function to minimize the distance between the distributions of user identities in two social networks. We propose to use the earth mover's distance (EMD) as the measure of distribution closeness, and propose two models UUIL$_gan $ and UUIL$_omt $ to efficiently learn the distribution projection function. Empirically, we evaluate the proposed models over multiple social network datasets, and the results demonstrate that our proposal significantly outperforms state-of-the-art methods.
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