Cluster analysis of curved-shaped data with species-sampling mixture models

We are interested in clustering data whose support is “curved”. Recently we have addressed this problem, introducing a model which combines two ingredients: species sampling mixtures of parametric densities on one hand, and a deterministic clustering procedure (DBSCAN) on the other. In short, under this model two observations share the same cluster if the distance between the densities corresponding to their latent parameters is smaller than a threshold. However, in this case, the prior cluster assignment is based on the geometry of the space of kernel densities rather than a direct random partition prior elicitation. Following the latter alternative, a new hierarchical model for clustering is proposed here, where the data in each cluster are parametrically distributed around a curve (principal curve), and the prior cluster assignment is given on the latent variables at the second level of hierarchy according to a species sampling model. These two mixture models are compared here with respect to cluster estimates obtained for a simulated bivariate dataset from two clusters, one being banana-shaped.