  Data clustering with uneven distribution in high level noise is challenging.
Currently, HDBSCAN is considered as the SOTA algorithm for this problem. In
this paper, we propose a novel clustering algorithm based on what we call graph
of density topology (GDT). GDT jointly considers the local and global
structures of data samples: firstly forming local clusters based on a density
growing process with a strategy for properly noise handling as well as cluster
boundary detection; and then estimating a GDT from relationship between local
clusters in terms of a connectivity measure, givingglobal topological graph.
The connectivity, measuring similarity between neighboring local clusters, is
based on local clusters rather than individual points, ensuring its robustness
to even very large noise. Evaluation results on both toy and real-world
datasets show that GDT achieves the SOTA performance by far on almost all the
popular datasets, and has a low time complexity of O(nlogn). The code is
available at https://github.com/gaozhangyang/DGC.git.
