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Abstract Mixtures of multivariate contaminated shifted asymmetric Laplace distributions are developed for handling asymmetric clusters in the presence of outliers (also referred to as bad points herein). In addition to the parameters of the related non-contaminated mixture, for each (asymmetric) cluster, our model has one parameter controlling the proportion of outliers and another specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori , adding a flexibility to our approach that is absent from other approaches such as trimming. Moreover, each observation is given an a posteriori probability of belonging to a particular cluster, and of being an outlier or not; advantageously, this allows for the automatic detection of outliers. An expectation–conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. The behavior of the proposed model is investigated, and compared with well-established finite mixture approaches, on artificial and real data. Highlights • A model-based clustering method for handling asymmetric clusters in the presence of outliers. • Possibility to detect outliers. • Each parameter of the model has a clear interpretation of practical usefulness. [ABSTRACT FROM AUTHOR]

Abstract: A novel family of twelve mixture models with random covariates, nested in the linear cluster-weighted model (CWM), is introduced for model-based clustering. The linear CWM was recently presented as a robust alternative to the better known linear Gaussian CWM. The proposed family of models provides a unified framework that also includes the linear Gaussian CWM as a special case. Maximum likelihood parameter estimation is carried out within the EM framework, and both the BIC and the ICL are used for model selection. A simple and effective hierarchical–random initialization is also proposed for the EM algorithm. The novel model-based clustering technique is illustrated in some applications to real data. Finally, a simulation study for evaluating the performance of the BIC and the ICL is presented. [Copyright &y& Elsevier]