  This paper presents a parallel adaptive clustering (PAC) algorithm to
automatically classify data while simultaneously choosing a suitable number of
classes. Clustering is an important tool for data analysis and understanding in
a broad set of areas including data reduction, pattern analysis, and
classification. However, the requirement to specify the number of clusters in
advance and the computational burden associated with clustering large sets of
data persist as challenges in clustering. We propose a new parallel adaptive
clustering (PAC) algorithm that addresses these challenges by adaptively
computing the number of clusters and leveraging the power of parallel
computing. The algorithm clusters disjoint subsets of the data on parallel
computation threads. We develop regularized set \mi{k}-means to efficiently
cluster the results from the parallel threads. A refinement step further
improves the clusters. The PAC algorithm offers the capability to adaptively
cluster data sets which change over time by reusing the information from
previous time steps to decrease computation. We provide theoretical analysis
and numerical experiments to characterize the performance of the method,
validate its properties, and demonstrate the computational efficiency of the
method.
