Finding groups in the presence of scattered or outlying observations can
be challenging. In this work, we propose a distribution-free approach for
developing a diagnostic tool to identify potential outliers in a given
clustering solution. The proposed methodology is based on a smooth
estimate of the distribution function of the normed residuals obtained
from a k-means solution. We also incorporate an adaptive threshold for
the detection of potential outliers. We study the performance of the
proposed diagnostic tool through several simulation experiments using
existing clustering algorithms that are designed to identify outliers in
homogeneous spherical groups. Finally, we apply the proposed
diagnostic tool to a functional Magnetic Resonance Imaging (fMRI) data
from a single-task finger-tapping experiment to identify potential
outlying observation as activated brain regions.
