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The idea behind density-based clustering is to associate groups to the connected components of the level sets of the density of the data to be estimated by a nonparametric method. This approach claims some advantages over both distance- and model-based clustering. Some researchers developed this technique by proposing a graph theory–based method for identifying local modes of the underlying density being estimated by the well-known kernel density estimation (KDE) with normal and t kernels. The present work proposes a semi-parametric KDE with a more flexible family of kernels including skew-normal (SN) and skew-t (ST). We show that the proposed estimator not only reduces boundary bias but it is also closer to the actual density compared to that of the usual estimator employing the Gaussian kernel. Finding optimal bandwidth for one-dimensional and multidimensional cases under the mentioned asymmetric kernels is another main result of this paper where we shrink the bandwidth more than the one obtained under the normal assumption. Finally, through a comprehensive numerical study, we will illustrate the application of the proposed semi-parametric KDE on the density-based clustering using some simulated and real data sets. [ABSTRACT FROM AUTHOR]

Compositional data have peculiar characteristics that pose significant challenges to traditional statistical methods and models. Within this framework, we use a convenient mode parametrized Dirichlet distribution across multiple fields of statistics. In particular, we propose finite mixtures of unimodal Dirichlet (UD) distributions for model-based clustering and classification. Then, we introduce the contaminated UD (CUD) distribution, a heavy-tailed generalization of the UD distribution that allows for a more flexible tail behavior in the presence of atypical observations. Thirdly, we propose finite mixtures of CUD distributions to jointly account for the presence of clusters and atypical points in the data. Parameter estimation is carried out by directly maximizing the maximum likelihood or by using an expectation-maximization (EM) algorithm. Two analyses are conducted on simulated data to illustrate the effects of atypical observations on parameter estimation and data classification, and how our proposals address both aspects. Furthermore, two real datasets are investigated and the results obtained via our models are discussed. [ABSTRACT FROM AUTHOR]