Dealing with label switching in mixture models under genuine multimodality

Authors:
Bettina Grün;Friedrich Leisch
Affiliations:
Department für Statistik und Mathematik, Wirtschaftsuniversität Wien, Augasse 2-6, A-1090 Wien, Austria;Institut für Statistik, Ludwig-Maximilians-Universität München, Ludwigstraíe 33, D-80539 München, Germany
Venue:
Journal of Multivariate Analysis
Year:
2009

Citing 4
Cited 3

Combinatorial optimization: algorithms and complexity

Combinatorial optimization: algorithms and complexity
On the number of clusters

Computational Statistics & Data Analysis - Special issue on classification
Constrained K-means Clustering with Background Knowledge

ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
A toolbox for K-centroids cluster analysis

Computational Statistics & Data Analysis

A Survey of Statistical Network Models

Foundations and Trends® in Machine Learning
Model based labeling for mixture models

Statistics and Computing
Latent class CUB models

Advances in Data Analysis and Classification

Quantified Score

Hi-index	0.00

Visualization

Abstract

The fitting of finite mixture models is an ill-defined estimation problem, as completely different parameterizations can induce similar mixture distributions. This leads to multiple modes in the likelihood, which is a problem for frequentist maximum likelihood estimation, and complicates statistical inference of Markov chain Monte Carlo draws in Bayesian estimation. For the analysis of the posterior density of these draws, a suitable separation into different modes is desirable. In addition, a unique labelling of the component specific estimates is necessary to solve the label switching problem. This paper presents and compares two approaches to achieve these goals: relabelling under multimodality and constrained clustering. The algorithmic details are discussed, and their application is demonstrated on artificial and real-world data.