Context and Motivation Clustering is an unsupervised learning approach for the task of partitioning data into meaningful subsets. The huge literature on cluster analysis is difficult to survey in a few sentences, but a concise description of well-known approaches is offered by Hastie et al. (2009), Everitt et al. (2011), and King (2014). Examples of mainstream methods for clustering data include model-based (Bouveyron et al., 2019), similarity-based (MacQueen, 1967; Kaufman and Rousseeuw, 1987), and hierarchical clustering (Hastie et al., 2009, Section 14.3). In this paper we propose a novel model-based approach for cluster analysis that lies at the interface of model-based clustering (i.e., via mixture models) and similarity-based clustering (i.e., via K-means and K-medoids). The proposed approach aims to benefit from the flexibility and soundness of model-based clustering, while attempting to mitigate Pitfalls 1 and 2 below. Model-based clustering is a fast-evolving and intradisciplinary research topic as can be seen from the recent Handbook on Mixture Analysis (Fruhwirth-Schnatter et al., 2019) as well as the survey papers of Melnykov and Maitra (2010), McNicholas (2016), Gormley et al. (2023), and the references therein.