B1114
Title: Regularized maximum likelihood for data on the sphere
Authors: Andriette Bekker - University of Pretoria (South Africa)
Mohammad Arashi - Ferdowsi University of Mashhad (Iran)
Priyanka Nagar - Stellenbosch University (South Africa) [presenting]
Abstract: The von Mises-Fisher distribution is a well-established probability distribution that characterises directional data. Finite mixtures of von Mises-Fisher distributions have been used for various purposes, including clustering data on the unit hypersphere. The focus is on constructing a regularized maximum likelihood estimation approach incorporating a penalty function to efficiently perform maximum likelihood estimation for a mixture of von Mises-Fisher distributions. The approach considers an approximation for the $L_1$ norm, which results in closed-form expressions. An expectation-maximization algorithm is developed for the regularized likelihood function, and its performance is evaluated via data applications.
