Learning-based EM algorithm for normal-inverse Gaussian mixture model with application to extrasolar planets

Karlis and Santourian [14] proposed a model-based clustering algorithm, the expectation–maximization (EM) algorithm, to fit the mixture of multivariate normal-inverse Gaussian (NIG) distribution. However, the EM algorithm for the mixture of multivariate NIG requires a set of initial values to begin the iterative process, and the number of components has to be given a priori. In this paper, we present a learning-based EM algorithm: its aim is to overcome the aforementioned weaknesses of Karlis and Santourian's EM algorithm [14]. The proposed learning-based EM algorithm was first inspired by Yang et al. [24]: the process of how they perform self-clustering was then simulated. Numerical experiments showed promising results compared to Karlis and Santourian's EM algorithm. Moreover, the methodology is applicable to the analysis of extrasolar planets. Our analysis provides an understanding of the clustering results in the ln P−ln M and ln P−e spaces, where M is the planetary mass, P is the orbital period and e is orbital eccentricity. Our identified groups interpret two phenomena: (1) the characteristics of two clusters in ln P−ln M space might be related to the tidal and disc interactions (see [9]); and (2) there are two clusters in ln P−e space.