An Adaptive Density Peaks Clustering Method With Fisher Linear Discriminant

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.

Density Peaks Clustering (DPC) algorithm identifies cluster centers based on local density and relative distance, disregarding the effect of the sample's environment on its density. This makes it challenging to identify cluster centers in low-density regions. Moreover, the single-step allocation strategy of DPC algorithm lacks fault tolerance. If a sample point is incorrectly allocated, it can trigger a cascade of subsequent allocation error. To solve the aforementioned issue, a density peak clustering algorithm based on natural neighbors and diffusion allocation (NNDA-DPC) is proposed. Firstly, the concept of natural neighbors is introduced, and the local density of sample points is redefined by considering the density of sample points and the environment in which the sample points are located. This is done to reduce the influence of the sparsity of class clusters on the selection of class cluster centers. The clustering centers are automatically determined by computing the decision value. Secondly, the natural neighbor points of the selected clustering centers are assigned to the corresponding clustering centers to form the initial microclusters. Finally, the initial microclusters are formed based on the remaining sample points and the initial clusters. The final clustering result is obtained by assigning the sample points based on the correlation between the remaining sample points and the initial clusters, which helps prevent the cascading effect of assignment errors. We compared the NNDA-DPC algorithm with DPC and its enhanced versions on artificial and UCI datasets. The experimental results demonstrate that the NNDA-DPC algorithm can efficiently cluster the datasets.

A robust clustering algorithm based on the identification of core points and KNN kernel density estimation

Density peak clustering (DPC) is a density-based clustering method that has attracted much attention in the academic community. DPC works by first searching density peaks in the dataset, and then assigning each data point to the same cluster as its nearest higher-density point. One problem with DPC is the determination of the density peaks, where poor selection of the density peaks could yield poor clustering results. Another problem with DPC is its cluster assignment strategy, which often makes incorrect cluster assignments for data points that are far from their nearest higher-density points. This study modifies DPC and proposes a new clustering algorithm to resolve the above problems. The proposed algorithm uses the radius of the neighborhood to automatically select a set of the likely density peaks, which are far from their nearest higher-density points. Using the potential density peaks as the density peaks, it then applies DPC to yield the preliminary clustering results. Finally, it uses single-linkage clustering on the preliminary clustering results to reduce the number of clusters, if necessary. The proposed algorithm avoids the cluster assignment problem in DPC because the cluster assignments for the potential density peaks are based on single-linkage clustering, not based on DPC. Our performance study shows that the proposed algorithm outperforms DPC for datasets with irregularly shaped clusters.

Density peak clustering with attribute-level similarity and two-stage allocation

Aiming at the problem of fuzzy C-means (FCM) in the estimation of underdetermined mixing matrix, that the estimation accuracy is not high and the robustness is poor, a density peak clustering (DPC) based on density peak clustering (DPC) is proposed. Improved Kernel-based Fuzzy C-means (KFCM). The kernel function is introduced into the FCM algorithm to construct the KFCM algorithm based on the Gaussian kernel function, which can effectively overcome the influence of noise points and isolated points on the clustering results and improve the estimation accuracy of the mixed matrix; the traditional DPC algorithm is improved and merged with the KFCM algorithm, and thresholds are set for the local density and high-density distance to achieve the initial clustering center of the KFCM algorithm and the automatic determination of the number of cluster centers improves the robustness of the algorithm. Experimental results show that the algorithm has greatly improved the estimation accuracy and robustness of the underdetermined mixed matrix.

Density Peaks Clustering (DPC) is a density-based clustering algorithm that has the advantage of not requiring clustering parameters and detecting non-spherical clusters. The density peaks algorithm obtains the actual cluster center by inputting the cutoff distance and manually selecting the cluster center. Thus, the clustering center point is not selected on the basis of considering the whole data set. This paper proposes a method called G-KNN-DPC to calculate the cutoff distance based on the Gini coefficient and K-nearest neighbor. G-KNN-DPC first finds the optimal cutoff distance with Gini coefficient, and then the center point with the K-nearest neighbor. The automatic clustering center method can not only avoid the error that a cluster detects two center points but also effectively solve the traditional DPC algorithm defect that cannot handle complex data sets. Compared with DPC, Fuzzy C-Means, K-means, KDPC and DBSCAN, the proposed algorithm creates better clusters on different data sets.

Density peaks clustering (DPC) is a well-known density-based clustering algorithm that can deal with nonspherical clusters well. However, DPC has high computational complexity and space complexity in calculating local density ρ and distance δ , which makes it suitable only for small-scale data sets. In addition, for clustering high-dimensional data, the performance of DPC still needs to be improved. High-dimensional data not only make the data distribution more complex but also lead to more computational overheads. To address the above issues, we propose an improved density peaks clustering algorithm, which combines feature reduction and data sampling strategy. Specifically, features of the high-dimensional data are automatically extracted by principal component analysis (PCA), auto-encoder (AE), and t-distributed stochastic neighbor embedding (t-SNE). Next, in order to reduce the computational overhead, we propose a novel data sampling method for the low-dimensional feature data. Firstly, the data distribution in the low-dimensional feature space is estimated by the Quasi-Monte Carlo (QMC) sequence with low-discrepancy characteristics. Then, the representative QMC points are selected according to their cell densities. Next, the selected QMC points are used to calculate ρ and δ instead of the original data points. In general, the number of the selected QMC points is much smaller than that of the initial data set. Finally, a two-stage classification strategy based on the QMC points clustering results is proposed to classify the original data set. Compared with current works, our proposed algorithm can reduce the computational complexity from O n 2 to O N n , where N denotes the number of selected QMC points and n is the size of original data set, typically N ≪ n . Experimental results demonstrate that the proposed algorithm can effectively reduce the computational overhead and improve the model performance.

Density-peak clustering has garnered significant attention due to its ability to identify non-convex cluster shapes without requiring a predefined number of clusters. However, traditional DPC still exhibits shortcomings in cluster center selection and density estimation, often resulting in unstable clustering performance under complex data distributions. This paper proposes an enhanced algorithm—Region-based Density Peak Clustering (RDPC). The method first constructs a more robust candidate center set through region-based sub-cluster formation and regional peak selection. Subsequently, it introduces a multi-factor decision metric combining density, relative distance, and affinity to screen the final clustering centers. Extensive experiments on synthetic and real-world datasets validate RDPC's effectiveness. Results demonstrate superior performance over traditional methods in terms of ARI and AMI metrics, exhibiting notably higher robustness and stability in complex distributions and noisy data.

Density peak clustering based on relative density relationship

A novel density peaks clustering algorithm based on Hopkins statistic

As a relatively novel density-based clustering algorithm, Density peak clustering (DPC) has been widely studied in recent years. DPC sorts all points in descending order of local density and finds neighbors for each point in turn to assign all points to the appropriate clusters. The algorithm is simple and effective but has some limitations in applicable scenarios. If the density difference between clusters is large or the data distribution is in a nested structure, the clustering effect of this algorithm is poor. This study incorporates the idea of connectivity into the original algorithm and proposes an improved density peak clustering algorithm ConDPC. ConDPC modifies the strategy of obtaining clustering center points and assigning neighbors and improves the clustering accuracy of the original density peak clustering algorithm. In this study, clustering comparison experiments were conducted on synthetic data sets and real-world data sets. The compared algorithms include original DPC, DBSCAN, K-means and two improved algorithms over DPC. The comparison results prove the effectiveness of ConDPC.

DPC-FSC: An approach of fuzzy semantic cells to density peaks clustering

Density peaks clustering based on superior nodes and fuzzy correlation

An improved density peaks clustering algorithm based on natural neighbor with a merging strategy