Model-based clustering for network data via a latent shrinkage position cluster model

Low-dimensional representation and clustering of network data are tasks of great interest across various fields. Latent position models are routinely used for this purpose by assuming that each node has a location in a low-dimensional latent space and by enabling node clustering. However, these models fall short through their inability to simultaneously determine the latent space dimension and number of clusters. Here we introduce the latent shrinkage position cluster model (LSPCM), which addresses this limitation. The LSPCM posits an infinite-dimensional latent space and assumes a Bayesian nonparametric shrinkage prior on the latent positions’ variance parameters resulting in higher dimensions having increasingly smaller variances, aiding the identification of dimensions with non-negligible variance. Further, the LSPCM assumes the latent positions follow a sparse finite Gaussian mixture model, allowing for automatic inference on the number of clusters related to non-empty mixture components. As a result, the LSPCM simultaneously infers the effective dimension of the latent space and the number of clusters, eliminating the need to fit and compare multiple models. The performance of the LSPCM is assessed via simulation studies and demonstrated through application to two real Twitter network datasets from sporting and political contexts. Open-source software is available to facilitate widespread use of the LSPCM.