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Graph representation learning (GRL) has become a prominent tool forfurthering the understanding of complex networks providing tools for networkembedding, link prediction, and node classification. In this paper, we proposethe Hybrid Membership-Latent Distance Model (HM-LDM) by exploring how a LatentDistance Model (LDM) can be constrained to a latent simplex. By controlling theedge lengths of the corners of the simplex, the volume of the latent space canbe systematically controlled. Thereby communities are revealed as the spacebecomes more constrained, with hard memberships being recovered as the simplexvolume goes to zero. We further explore a recent likelihood formulation forsigned networks utilizing the Skellam distribution to account for signedweighted networks and extend the HM-LDM to the signed Hybrid Membership-LatentDistance Model (sHM-LDM). Importantly, the induced likelihood functionexplicitly attracts nodes with positive links and deters nodes from havingnegative interactions. We demonstrate the utility of HM-LDM and sHM-LDM onseveral real networks. We find that the procedures successfully identifyprominent distinct structures, as well as how nodes relate to the extractedaspects providing favorable performances in terms of link prediction whencompared to prominent baselines. Furthermore, the learned soft membershipsenable easily interpretable network visualizations highlighting distinctpatterns.

A Hybrid Membership Latent Distance Model for Unsigned and Signed Integer Weighted Networks