A fuzzy membership-based enhancement to density peak clustering with comparative performance evaluation

Clustering is a basic data mining operation that groups data points with similar inherent structure. Among clustering techniques, Density Peak Clustering (DPC) is notable for detecting clusters of arbitrary shapes without requiring the number of clusters in advance. However, DPC suffers from parameter-sensitive local density estimation, inadequate handling of noise and boundary points, and rigid binary cluster assignments. To overcome these limitations, fuzzy logic is often embedded in DPC, but the selection of the most appropriate membership function is still an open research question. In this paper, we propose an enhanced DPC variant with three methodological improvements: (i) substituting cutoff distance-based density estimation with a K-Nearest Neighbors (KNN) functioned kernel to achieve stable and robust density estimation, (ii) adding a noise parameter Lambda ( λ ) to better identify and distinguish noise and boundary points, and (iii) using fuzzy membership functions to allow for probabilistic and soft cluster assignments of data points. Comparative analyses of four fuzzy membership functions (i.e., Gaussian, Combination Gaussian, Trapezoidal, and Triangular) were performed on real, synthetic, and high-dimensional datasets. The experimental results indicate that the proposed algorithm with the Gaussian fuzzy membership function outperforms other membership functions and traditional clustering algorithms including the original DPC, FKNN, and DPC-DBFN in terms of clustering accuracy, stability, adaptability, and noise resistance, and is therefore part of our final suggested method. The proposed method overall relieves original DPC shortcomings by strengthening adaptability, accuracy, and applicability to complex real-world clustering tasks. • Substituting standard cutoff-distance-based kernel with KNN for enhanced clustering. • Introducing λ parameter to manage noise and boundary points for separating clusters. • Introducing fuzzy neighborhood kernel for soft cluster membership assignment. • Investigating the impact of several fuzzy membership functions on clustering. • Proposed strategy outperforms original DPC, FKNN, and DPC-DBFN on datasets.