Finite Mixture Models

Abstract

The important role of finite mixture models in the statistical analysis of data is underscored by the ever-increasing rate at which articles on mixture applications appear in the statistical and general scientific literature. The aim of this article is to provide an up-to-date account of the theory and methodological developments underlying the applications of finite mixture models. Because of their flexibility, mixture models are being increasingly exploited as a convenient, semiparametric way in which to model unknown distributional shapes. This is in addition to their obvious applications where there is group-structure in the data or where the aim is to explore the data for such structure, as in a cluster analysis. It has now been three decades since the publication of the monograph by McLachlan & Basford (1988) with an emphasis on the potential usefulness of mixture models for inference and clustering. Since then, mixture models have attracted the interest of many researchers and have found many new and interesting fields of application. Thus, the literature on mixture models has expanded enormously, and as a consequence, the bibliography here can only provide selected coverage.

Informative tools for characterizing individual differences in learning: Latent class, latent profile, and latent transition analysis

“…Readers interested in related techniques are further referred to available books and edited volumes (Bartolucci, Farcomeni, & Pennoni, 2012;Collins & Lanza, 2010;Hagenaars & McCutcheon, 2002;McLachlan & Peel, 2000).…”

A New Semiparametric Approach to Finite Mixture of Regressions using Penalized Regression via Fusion

“…Using the language of McLachlan and Peel (2000) and notation of Khalili and Chen (2007), suppose Y i represents the value of a continuous random variable, or response, for subject i = 1, ..., n. Let X ji equal subject i's value for covariate j = 1, ..., p; therefore, X i = (x 1i , x 2i , ..., x pi ) is the vector of covariates for subject i. Next, let f (y; θ k (x), φ k ) for k = 1, .…”

Single-Class Data Descriptors for Mapping Panax notoginseng through P-Learning

“…In this study, due to only the target class (i.e., Panax notoginseng fields) is the class of interest, and the task of mapping Panax notoginseng fields can be regarded as a specific single-class data description problem. Hence, 10 SCDDs [47], i.e., the simple Gaussian target distribution data description (SGTD coded as c1) [60]; the robust Gaussian target distribution data description (RGTD coded as c2) [60]; the minimum covariance determinant Gaussian data description (MCDG coded as c3) [60]; the mixture of Gaussian data description (MoG coded as c4) [60]; the auto-encoder neural network data description (AENN coded as c6) [61]; the k-means clustering data description (k-means coded as c7) [62]; the self-organizing map data description (SOM coded as c10) [63]; the minimum spanning tree data description (MST coded as c11) [64]; the k-nearest neighbor data description (K-NN coded as c13) [65]; the incremental support vector data description (IncSVDD coded as c17) [66]; the Parzen density estimator data description (PDE coded as c5, which is a known underestimated descriptor) [67]; and the principal component analysis data description (PCA coded as c9, which is known as an overestimated descriptor) [68].…”