Towards Robust and Scalable Density-based Clustering via Graph Propagation

Clustering is a cornerstone of modern data analysis. Detecting clusters in exploratory data analyses (EDA) requires algorithms that make few assumptions about the data. Density-based clustering algorithms are particularly well-suited for EDA because they describe high-density regions, assuming only that a density exists. Applying density-based clustering algorithms in practice, however, requires selecting appropriate hyperparameters, which is difficult without prior knowledge of the data distribution. For example, DBSCAN requires selecting a density threshold, and HDBSCAN* relies on a minimum cluster size parameter. In this work, we propose Persistent Leaves Spatial Clustering for Applications with Noise (PLSCAN), a multiscale density-based clustering algorithm that replaces HDBSCAN*'s fixed minimum cluster size pruning of a mutual-reachability linkage hierarchy with a persistence-based cluster selection procedure. Effectively, PLSCAN identifies all minimum cluster sizes for which HDBSCAN* produces stable (leaf) clusters. In concept, PLSCAN applies scale-space clustering principles and is equivalent to persistent homology on a novel metric space. We compare its performance to HDBSCAN* on several real-world datasets, demonstrating that it achieves a higher median ARI, is less sensitive to changes in the number of mutual reachability neighbours, and has higher stability under resampling. Additionally, we compare PLSCAN's computational costs to $k$-Means++, demonstrating competitive run-times on low-dimensional datasets. At higher dimensions, run times scale more similarly to HDBSCAN*.

Clustering is a fundamental data mining technique for pattern recognition through unsupervised learning. Among various clustering methods, hierarchical clustering, density-based clustering, and graph clustering stand out as representative approaches. For hierarchical clustering, it can be categorized into agglomerative and divisive modes to construct clusters in a recursive manner. The key aspect of both modes is the calculation of inter-cluster similarity, which determines whether to merge the sub-clusters into one cluster or divide a current cluster into sub-clusters. Traditionally, the similarity is derived from pairwise distances, often overlooking density variations and structural connectivity in graphs. To address this, we propose a density-aware hierarchical clustering method based on element-categorized connection subgraphs (DHC-ECS), which effectively integrates the hierarchical clustering, density-based clustering, and graph clustering. Particularly, a novel inter-cluster similarity metric is introduced that considers not only distances but also the element categorization in the KNN connection subgraphs, kernel density estimation, and local connectivity within sub-clusters. Extensive evaluations on heterogeneous benchmark datasets demonstrate that DHC-ECS exhibits superior overall performance in terms of clustering accuracy and parameter robustness compared with the baseline methods (including AChameleon, RNN-DBSCAN, McDPC, and G-RMS). The work indicates the great potential of the proposed clustering algorithm for low-dimensional datasets by leveraging local density and graph-structured connectivity (i.e., the duality of vertices and edges), as well as the possibility to determine an intrinsic threshold, reducing the reliance on manual parameter tuning.

In the Big Data era, the scalability of clustering algorithms constitutes a key challenge. Traditional density-based methods (e.g., DBSCAN) offer robustness to noise and the ability to detect non-linear clusters, yet their quadratic time complexity $O(N^2)$ drastically limits their applicability. Conversely, partitional algorithms (e.g., K-Means), with their linear complexity $O(N)$, impose sphericity on the resulting groups and fail in the presence of outliers. This paper presents K-SCAN -- a novel hybrid algorithm that optimizes this trade-off. The method integrates preliminary vector quantization (stochastic Mini-Batch K-Means) to extract a reduced set of weighted micro-clusters, followed by a subsequent density-based structural analysis. Empirical evaluation on datasets of up to $10^6$ samples confirms the linear computational complexity of the proposed solution. K-SCAN achieves more than a 3-fold speed-up over the hierarchical BIRCH algorithm, avoiding the costly management of tree-based structures. The method precisely identifies non-linear manifolds while maintaining structural stability (Adjusted Rand Index > 0.99), even with noise levels reaching 55% of the data volume. The main limitation of the proposed algorithm, which could not be fully eliminated in the present study, remains its susceptibility to over-smoothing and its difficulty in separating clusters with highly heterogeneous local density. In complex visual spaces, this can lead to the loss of the finest topological details.