Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions
Adelaide Figueiredo*Faculty of Economics of University of Porto and LIAAD-INESC TEC, Porto, Portugal
Abstract
Background:
In the statistical analysis of directional data, the von Mises-Fisher distribution plays an important role to model unit vectors. The estimation of the parameters of a mixture of von Mises-Fisher distributions can be done through the Estimation-Maximization algorithm.
Objective:
In this paper we propose a dynamic clusters type algorithm based on the estimation of the parameters of a mixture of von Mises-Fisher distributions for clustering directions, and we compare this algorithm with the Estimation-Maximization algorithm. We also define the between-groups and within-groups variability measures to compare the solutions obtained with the algorithms through these measures.
Results:
The comparison of the clusters obtained with both algorithms is provided for a simulation study based on samples generated from a mixture of two Fisher distributions and for an illustrative example with spherical data.
Keywords: Directional data, Dynamic Clusters algorithm, EM algorithm, Hypersphere, Monte Carlo method, Simulation, Von Mises-Fisher distribution.
Article Information
Article History:
Received Date: 11/09/2017
Revision Received Date: 28/11/2017
Acceptance Date: 29/11/2017
Electronic publication date: 29/12/2017
Collection year: 2017
© 2017 Adelaide Figueiredo.
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at:
https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
* Address correspondence to this author at the University of Porto, Faculty of Economics, Porto and LIAAD-INESC TEC, Portugal,
Tel: (+351)220426449; E-mail: Adelaide@fep.up.pt
Open Peer Review Details |
Manuscript submitted on 11-09-2017 |
Original Manuscript |
Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions |