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.

翻译：基于密度的聚类算法因其能够识别任意形状的聚类（只要不同高密度聚类被低密度区域分隔）而成为最流行的聚类算法之一。然而，要求聚类被低密度区域分隔并非易事，因为一个高密度区域内部可能存在应被划分为不同聚类的不同结构。这一现象揭示了现有所有密度聚类算法的核心缺陷——无法探测高密度聚类内部的子结构。为此，本文提出一种密度聚类方案，该方案不仅保留传统密度聚类算法的能力，还能探测未被低密度区域分隔的高密度区域内部结构。该算法融合了二次有向差分、层级结构、归一化密度及自适应系数，故命名为基于归一化密度与自适应的层级二次有向差分结构探测聚类算法（简称SDC-HSDD-NDSA）。为验证其有效性，我们在多个数据集上运行该算法。结果证实了其在结构探测、噪声鲁棒性及粒度独立性方面的有效性，并表明其性能优于现有算法。本文Python代码见https://github.com/Hao-B-Shu/SDC-HSDD-NDSA。