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Title: Distribution-free clustering diagnostic for outlier detection Authors:  Israel Almodovar Rivera - University of Puerto Rico (United States) [presenting]
Abstract: Finding groups in the presence of scatter can be challenging. Scatter (or outliers) observations in clustering are referred to as those observations that do not necessarily belong or fit into any cluster. We proposed a distribution-free approach to perform a diagnostic to a clustering solution to find potential outliers in it. Our approach uses a $k$-means solution to find the potential outliers in a homogeneous spherical group. The method uses a smooth estimation of the distribution function of the normed residuals from a given clustering solution. Further, we propose a rule-of-thumb method to compute an estimate of the smoothing parameter for the estimation of the distribution function. Then, we study the proposed diagnostic tool in several experiments with the presence of outliers in a homogeneous spherical group. Our diagnostic tool is, in general, a top performer in finding the potential outliers in these groups. Finally, we apply the distribution-free diagnostics in a functional Magnetic Resonance Imaging study to determine activated regions in a single-subject single-task experiment.