# SDC-HSDD-NDSA: Structure Detecting Cluster by Hierarchical Secondary Directed Differential with Normalized Density and Self-Adaption

arXiv: https://arxiv.org/abs/2307.00677 · HTML: https://mlsanity.com/paper/2307.00677/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 77 references that are in the map.
- First posted on arXiv 2 Jul 2023.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Accelerated Hierarchical Density Clustering](https://mlsanity.com/paper/1705.07321/) (2017)
- [DBSCAN++: Towards fast and scalable density clustering](https://mlsanity.com/paper/1810.13105/) (2018)
- [Nearest-Neighbour-Induced Isolation Similarity and its Impact on Density-Based Clustering](https://mlsanity.com/paper/1907.00378/) (2019)
- [ADBSCAN: Adaptive Density-Based Spatial Clustering of Applications with Noise for Identifying Clusters with Varying Densities](https://mlsanity.com/paper/1809.06189/) (2018)
- [Hierarchical clustering that takes advantage of both density-peak and density-connectivity](https://mlsanity.com/paper/1810.03393/) (2018)
- [CRAD: Clustering with Robust Autocuts and Depth](https://mlsanity.com/paper/1904.04020/) (2019)
- [AMD-DBSCAN: An Adaptive Multi-density DBSCAN for datasets of extremely variable density](https://mlsanity.com/paper/2210.08162/) (2022)
- [Unimodal clustering using isotonic regression: ISO-SPLIT](https://mlsanity.com/paper/1508.04841/) (2015)
- [Efficient Large Scale Clustering based on Data Partitioning](https://mlsanity.com/paper/1704.03421/) (2017)
- [An efficient density-based clustering algorithm using reverse nearest neighbour](https://mlsanity.com/paper/1811.07615/) (2018)
- [An Improved Probability Propagation Algorithm for Density Peak Clustering Based on Natural Nearest Neighborhood](https://mlsanity.com/paper/2207.01178/) (2022)

## Built on by (most cited first, 1 of 1)

- [Symmetrization Weighted Binary Cross-Entropy: Modeling Perceptual Asymmetry for Human-Consistent Neural Edge Detection](https://mlsanity.com/paper/2501.13365/) (2025)

## Abstract (arXiv)

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 rst 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.