Summary: In spite of the current availability of numerous methods of cluster analysis, evaluating a clustering configuration is questionable without the definition of a true population structure, representing the ideal partition that clustering methods should try to approximate. A precise statistical notion of cluster, unshared by most of the mainstream methods, is provided by the density-based approach, which assumes that clusters are associated to some specific features of the probability distribution underlying the data. The non-parametric formulation of this approach, known as modal clustering, draws a correspondence between the groups and the modes of the density function. An appealing implication is that the ill-specified task of cluster detection can be regarded to as a more circumscribed problem of estimation, and the number of clusters is also conceptually well defined. In this work, modal clustering is critically reviewed from both conceptual and operational standpoints. The main directions of current research are outlined as well as some challenges and directions of further research.
{© 2015 The Authors. International Statistical Review © 2015 International Statistical Institute}