Finite Mixtures of Multivariate Wrapped Normal Distributions for Model Based Clustering of p-Torus Data

We consider a finite mixture model of multivariate Wrapped Normal distributions to handle non homogeneous circular data on a p-dimensional torus ((Formula presented.)). The Wrapped Normal distribution is a valid alternative to model multivariate circular or directional data on a p-torus. Parameter estimation is carried out through a nested (classification) EM algorithm, by exploiting the ideas of unwrapping circular data. The source of incompleteness in the outer E-step is represented by unobserved group memberships, whereas the source of incompleteness in the inner E-step is given by the unobserved vectors of wrapping coefficients. The finite sample behavior of the proposed method has been investigated by Monte Carlo numerical studies and real data examples. Supplemental materials for the article, including data and R codes for implementing methods, running simulations and replicate data analyses, are available online.