  Density-based clustering could be the most popular clustering algorithm since
it can identify clusters of arbitrary shape as long as different (high-density)
clusters are separated by low-density regions. However, the requirement of the
separateness of clusters by low-density regions is not trivial since a
high-density region might have different structures which should be clustered
into different groups. Such a situation demonstrates the main flaw of all
previous density-based clustering algorithms we have known--structures in a
high-density cluster could not be detected. Therefore, this paper aims to
provide a density-based clustering scheme that not only has the ability
previous ones have but could also detect structures in a high-density region
not separated by low-density ones. The algorithm employs secondary directed
differential, hierarchy, normalized density, as well as the self-adaption
coefficient, and thus is called Structure Detecting Cluster by Hierarchical
Secondary Directed Differential with Normalized Density and Self-Adaption,
dubbed by SDC-HSDD-NDSA for short. To illustrate its effectiveness, we run the
algorithm in several data sets. The results verify its validity in structure
detection, robustness over noises, as well as independence of granularities,
and demonstrate that it could outperform previous ones. The Python code of the
paper could be found on https://github.com/Hao-B-Shu/SDC-HSDD-NDSA.
