  The widely applied density peak clustering (DPC) algorithm makes an intuitive
cluster formation assumption that cluster centers are often surrounded by data
points with lower local density and far away from other data points with higher
local density. However, this assumption suffers from one limitation that it is
often problematic when identifying clusters with lower density because they
might be easily merged into other clusters with higher density. As a result,
DPC may not be able to identify clusters with variational density. To address
this issue, we propose a variational density peak clustering (VDPC) algorithm,
which is designed to systematically and autonomously perform the clustering
task on datasets with various types of density distributions. Specifically, we
first propose a novel method to identify the representatives among all data
points and construct initial clusters based on the identified representatives
for further analysis of the clusters' property. Furthermore, we divide all data
points into different levels according to their local density and propose a
unified clustering framework by combining the advantages of both DPC and
DBSCAN. Thus, all the identified initial clusters spreading across different
density levels are systematically processed to form the final clusters. To
evaluate the effectiveness of the proposed VDPC algorithm, we conduct extensive
experiments using 20 datasets including eight synthetic, six real-world and six
image datasets. The experimental results show that VDPC outperforms two
classical algorithms (i.e., DPC and DBSCAN) and four state-of-the-art extended
DPC algorithms.
