Robust, fuzzy, and parsimonious clustering, based on mixtures of Factor Analyzers

• Published in: International journal of approximate reasoning Vol. 94; pp. 60 - 75
• Main Authors: García-Escudero, Luis Angel, Greselin, Francesca, Iscar, Agustin Mayo
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.03.2018
• Subjects: Dimension reduction; Factor analysis; Fuzzy clustering; Hard contrast; Outliers identification; Robust clustering; Unsupervised learning; Robust clustering; Dimension reduction; Fuzzy clustering; Factor analysis; Hard contrast; Outliers identification; Unsupervised learning
• ISSN: 0888-613X; 1873-4731
• DOI: 10.1016/j.ijar.2018.01.001

A clustering algorithm that combines the advantages of fuzzy clustering and robust statistical estimators is presented. It is based on mixtures of Factor Analyzers, endowed by the joint usage of impartial trimming and constrained estimation of scatter matrices, in a modified maximum likelihood approach. The algorithm generates a set of membership values, that are used to fuzzy partition the data set and to contribute to the robust estimates of the mixture parameters. The adoption of clusters modeled by Gaussian Factor Analysis allows for dimension reduction and for discovering local linear structures in the data. The new methodology has been shown to be resistant to different types of contamination, by applying it on artificial data. A brief discussion on the tuning parameters, such as the trimming level, the fuzzifier parameter, the number of clusters and the value of the scatter matrices constraint, has been developed, also with the help of some heuristic tools for their choice. Finally, a real data set has been analyzed, to show how intermediate membership values are estimated for observations lying at cluster overlap, while cluster cores are composed by observations that are assigned to a cluster in a crisp way. •This model allows to discover underlying linear structures in the data groups.•This methodology performs dimension reduction.•The joint usage of trimming and constrained estimation assures robust estimation.•Our proposal encompasses soft and hard robust clustering, and enjoys the “hard contrast” property.•Tools for helping the user in setting tuning parameters are presented.