Abstract
The R package MixSim is a new tool that allows simulating mixtures of Gaussian distributions with different levels of overlap between mixture components. Pairwise overlap, defined as a sum of two misclassification probabilities, measures the degree of interaction between components and can be readily employed to control the clustering complexity of datasets simulated from mixtures. These datasets can then be used for systematic performance investigation of clustering and finite mixture modeling algorithms. Among other capabilities of MixSim, there are computing the exact overlap for Gaussian mixtures, simulating Gaussian and non-Gaussian data, simulating outliers and noise variables, calculating various measures of agreement between two partitionings, and constructing parallel distribution plots for the graphical display of finite mixture models. All features of the package are illustrated in great detail. The utility of the package is highlighted through a small comparison study of several popular clustering algorithms.
Highlights
The main goal of clustering is to form groups of similar observations while separating dissimilar ones
Many clustering algorithms have been developed, such as the iterative k-means (Forgy 1965; MacQueen 1967) and k-medoids (Kaufman and Rousseuw 1990) algorithms, hierarchical algorithms with different merging/splitting criteria called linkages – e.g., Ward’s (Ward 1963), single (Sneath 1957), complete (Sorensen 1948) and other – and the probabilistic model-based clustering algorithms, where the observations are assumed to be sampled from an underlying finite mixture model (Melnykov and Maitra 2010)
Maitra and Melnykov (2010) have provided the only known exact measure capable of measuring interaction between two clusters in terms of the pairwise overlap ω, which is defined for Gaussian mixtures as the sum of two misclassification probabilities and can be calculated in a univariate as well as multivariate framework
Summary
The main goal of clustering is to form groups of similar observations while separating dissimilar ones. Very recently, Maitra and Melnykov (2010) have provided the only known exact measure capable of measuring interaction between two clusters in terms of the pairwise overlap ω, which is defined for Gaussian mixtures as the sum of two misclassification probabilities and can be calculated in a univariate as well as multivariate framework.
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