SDENK: Unbiased subspace density- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mi>k</mml:mi> </mml:math> -clustering

Clustering is one of the most important data analysis techniques, as it extracts knowledge without requiring data labels, making it crucial in many unsupervised application scenarios. However, conventional k -clustering struggles to detect irregularly distributed clusters owing to its inherent preference for convex clusters, while density-based clustering often lacks the ability to customise an appropriate metric space for different clustering tasks owing to the lack of a task-oriented optimisation process. To simultaneously address these biases in cluster shape and metric space, this paper proposes an unbiased hybrid framework to perform density-based clustering in subspaces. These subspaces are constructed through a newly developed attribute-weighted k -clustering paradigm. To exploit the irregularly distributed clusters obtained via density-based clustering for subspace learning, a novel strategy is designed to subdivide the clusters into compact sub-clusters, which are more suitable for evaluating attribute importance through k -clustering. As a result, the proposed subspace density K -clustering algorithm inherits the shape flexibility of density-based clustering and the metric adaptiveness of k -clustering. Moreover, the learnable design enables mutual optimisation between density clusters and subspaces, yielding robust and superior clustering performance across various datasets. Comprehensive evaluations, including comparative clustering performance evaluation, ablation studies, significance tests, noise-robustness evaluation, and hyper-parameter sensitivity studies, are conducted. Among 10 compared methods, the proposed Subspace DENsity-K-clustering (SDENK) achieves an average rank of 1.75 on 12 datasets in terms of the clustering accuracy metric ARI. • The merits of density and k -clustering are integrated, serving as a hybrid general framework for unbiased clustering. • A novel re-clustering mechanism is proposed to subdivide the density clusters for more appropriately determining the subspace. • The proposed unbiased clustering algorithm is suitable for datasets with various cluster distributions.