Density-based clustering with non-continuous data

Density-based clustering relies on the idea of associating groups with regions of the sample space characterized by high density of the probability distribution underlying the observations. While this approach to cluster analysis exhibits some desirable properties, its use is necessarily limited to continuous data only. The present contribution proposes a simple but working way to circumvent this problem, based on the identification of continuous components underlying the non-continuous variables. The basic idea is explored in a number of variants applied to simulated data, confirming the practical effectiveness of the technique and leading to recommendations for its practical usage. Some illustrations using real data are also presented.