We address general-shaped clustering problems under very weak parametric assumptions with a two-step hybrid robust clustering algorithm based on trimmed k-means and hierarchical agglomeration. The algorithm has low computational complexity and effectively identifies the clusters also in presence of data contamination. We also present natural generalizations of the approach as well as an adaptive procedure to estimate the amount of contamination in a data-driven fashion. Our proposal outperforms state-of-the-art robust, model-based methods in our numerical simulations and real-world applications related to color quantization for image analysis, human mobility patterns based on GPS data, biomedical images of diabetic retinopathy, and functional data across weather stations.

Mixtures of Gaussian distributions are a popular choice in model-based clustering. Outliers can affect parameters estimation and, as such, must be accounted for. Algorithms such as TCLUST discern the most likely outliers, but only when the proportion of outlying points is known \textit{a priori}. It is proved that, for a finite Gaussian mixture model, the log-likelihoods of the subset models are beta-distributed. An algorithm is then proposed that predicts the proportion of outliers by measuring the adherence of a set of subset log-likelihoods to a beta reference distribution. This algorithm removes the least likely points, which are deemed outliers, until model assumptions are met.