Title: Kernel-estimated Nonparametric Overlap-Based Syncytial Clustering,
Abstract: Standard clustering algorithms usually find regular-structured clusters such
as ellipsoidally- or spherically-dispersed groups, but are more challenged with
groups lacking formal structure or definition. Syncytial clustering is the name
that we introduce for methods that merge groups obtained from standard
clustering algorithms in order to reveal complex group structure in the data.
Here, we develop a distribution-free fully-automated syncytial clustering
algorithm that can be used with $k$-means and other algorithms. Our approach
computes the cumulative distribution function of the normed residuals from an
appropriately fit $k$-groups model and calculates the nonparametric overlap
between each pair of groups. Groups with high pairwise overlaps are merged as
long as the generalized overlap decreases. Our methodology is always a top
performer in identifying groups with regular and irregular structures in
several datasets. The approach is also used to identify the distinct kinds of
gamma ray bursts in the Burst and Transient Source Experiment 4Br catalog and
also the distinct kinds of activation in a functional Magnetic Resonance
Imaging study.