SDC-HSDD-NDSA: Structure detecting cluster by hierarchical secondary directed differential with normalized density and self-adaption

Density-based clustering is the most popular clustering algorithm since it can identify clusters of arbitrary shape as long as they are separated by low-density regions. However, a high-density region that is not separated by low-density ones might also have different structures belonging to multiple clusters. As far as we know, all previous density-based clustering algorithms fail to detect such structures. In this paper, we provide a novel density-based clustering scheme to address this problem. It is the first clustering algorithm that can detect meticulous structures in a high-density region that is not separated by low-density ones and thus extends the range of applications of clustering. The algorithm employs secondary directed differential, hierarchy, normalized density, as well as the self-adaption coefficient, called Structure Detecting Cluster by Hierarchical Secondary Directed Differential with Normalized Density and Self-Adaption, dubbed SDC-HSDD-NDSA. Experiments on synthetic and real datasets are implemented to verify the effectiveness, robustness, and granularity independence of the algorithm, and the scheme is compared to unsupervised schemes in the Python package Scikit-learn. Results demonstrate that our algorithm outperforms previous ones in many situations, especially significantly when clusters have regular internal structures. For example, averaging over the eight noiseless synthetic datasets with structures employing ARI and NMI criteria, previous algorithms obtain scores below 0.6 and 0.7, while the presented algorithm obtains scores higher than 0.9 and 0.95, respectively.¹