caa a22 4500 605478295 CHVBK 20210128100405.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10994-015-5493-0 doi (NATIONALLICENCE)springer-10.1007/s10994-015-5493-0 Minimum message length estimation of mixtures of multivariate Gaussian and von Mises-Fisher distributions [Elektronische Daten] [Parthan Kasarapu, Lloyd Allison] Mixture modelling involves explaining some observed evidence using a combination of probability distributions. The crux of the problem is the inference of an optimal number of mixture components and their corresponding parameters. This paper discusses unsupervised learning of mixture models using the Bayesian Minimum Message Length (MML) criterion. To demonstrate the effectiveness of search and inference of mixture parameters using the proposed approach, we select two key probability distributions, each handling fundamentally different types of data: the multivariate Gaussian distribution to address mixture modelling of data distributed in Euclidean space, and the multivariate von Mises-Fisher (vMF) distribution to address mixture modelling of directional data distributed on a unit hypersphere. The key contributions of this paper, in addition to the general search and inference methodology, include the derivation of MML expressions for encoding the data using multivariate Gaussian and von Mises-Fisher distributions, and the analytical derivation of the MML estimates of the parameters of the two distributions. Our approach is tested on simulated and real world data sets. For instance, we infer vMF mixtures that concisely explain experimentally determined three-dimensional protein conformations, providing an effective null model description of protein structures that is central to many inference problems in structural bioinformatics. The experimental results demonstrate that the performance of our proposed search and inference method along with the encoding schemes improve on the state of the art mixture modelling techniques. The Author(s), 2015 Mixture modelling nationallicence Minimum message length nationallicence Multivariate Gaussian nationallicence von Mises-Fisher nationallicence Protein structure nationallicence Kasarapu Parthan Faculty of Information Technology, Monash University, 3800, Melbourne, VIC, Australia aut Allison Lloyd Faculty of Information Technology, Monash University, 3800, Melbourne, VIC, Australia aut Machine Learning Springer US; http://www.springer-ny.com 100/2-3(2015-09-01), 333-378 0885-6125 100:2-3<333 2015 100 10994 https://doi.org/10.1007/s10994-015-5493-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10994-015-5493-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kasarapu Parthan Faculty of Information Technology, Monash University, 3800, Melbourne, VIC, Australia aut NATIONALLICENCE 700 1- Allison Lloyd Faculty of Information Technology, Monash University, 3800, Melbourne, VIC, Australia aut NATIONALLICENCE 773 0- Machine Learning Springer US; http://www.springer-ny.com 100/2-3(2015-09-01), 333-378 0885-6125 100:2-3<333 2015 100 10994