HM-LDM: A Hybrid-Membership Latent Distance Model

A central aim of modeling complex networks is to accurately embed in order detect structures and predict link node properties. The Latent Space Model (LSM) has become a prominent framework for embedding includes the Distance (LDM) Eigenmodel (LEM) as most widely used LSM specifications. For latent community detection, space LDMs been endowed with clustering model whereas LEMs have constrained part-based non-negative matrix factorization (NMF) inspired representations promoting discovery. We presently reconcile LSMs detection by constraining LDM representation D-simplex forming Hybrid-Membership (HM-LDM). show that sufficiently large simplex volumes this can be achieved without loss expressive power extending squared Euclidean distances, we recover LEM formulation constraints akin NMF. Importantly, systematically reducing volume simplex, becomes unique ultimately leads hard assignments nodes corners. demonstrate experimentally how proposed HM-LDM admits accurate regimes ensuring identifiability valid extraction. naturally reconciles soft network embeddings exploring simple continuous optimization procedure on systematic investigation trade-offs between mixed membership detection.