Finite Mixtures of Multivariate Wrapped Normal Distributions for Model Based Clustering of p -Torus Data
提出了一种多元缠绕正态分布的有限混合模型，用于处理p维环面上的非均匀圆形数据，通过嵌套EM算法估计参数，并利用蒙特卡洛模拟和真实数据验证了方法的有效性。
We consider a finite mixture model of multivariate Wrapped Normal distributions to handle non homogeneous circular data on a p-dimensional torus ( p≥2). 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.