Current contrastive graph clustering approaches suffer from insufficient integration of structural and semantic information, coupled with the absence of reliable sample selection strategies. To address these dual limitations, we introduce Structure-Semantic Synergized Deep Contrastive Graph Clustering (S³-DCGC), a novel framework that jointly models topological structure and semantic features through two synergistic mechanisms. First, a structure-aware curriculum negative sampling strategy progressively identifies hard negative samples using dynamic-range masking, enhancing discriminative structural learning. Second, a semantic confidence-guided contrastive mechanism quantifies node reliability via composite confidence scores—integrating cluster affinity and cross-view consistency—to select high-confidence positive/negative pairs. Dynamically coordinated by a soft-alignment strategy that shifts optimization focus from structural to semantic dominance during training, these components achieve balanced synergy. Comprehensive experiments conducted on five benchmark datasets demonstrate S³-DCGC's superiority, achieving significant performance gains. Ablation studies and visual analyses further corroborate the critical importance of structure-semantic synergy in achieving robust clustering performance.

Density peaks clustering (DPC) is an excellent clustering algorithm that does not need any prior knowledge. However, DPC still has the following shortcomings: (1) The Euclidean distance used by it is not applicable to manifold data with multiple peaks. (2) The local density calculation for DPC is too simple, and the final results may fluctuate due to the cutoff-distancedc. (3) Manually selected centers by decision-graph may lead to a wrong number of clusters and poor performance. To address these shortcomings and improve the performance, a robust density peaks clustering algorithm for manifold data with multiple peaks (RDPCM) is proposed to reduce the sensitivity of clustering results to parameters. Motivated by DPC-GD, RDPCM replaces the Euclidean distance with geodesic distance, which is optimized by the improved mutual K-nearest neighbors. It better considers the local manifold structure of the datasets and obtains excellent results. In addition, the Davies-Bouldin Index based on Minimum Spanning Tree (MDBI) is proposed to select the ideal number of classes adaptively. Numerous experiments have established that RDPCM is more effective and superior than other advanced clustering algorithms.

Density peaks clustering (DPC) is one of the density-based clustering algorithms and has been widely studied and applied in recent years because of its unique parameter, non-iteration and good robustness. However, it cannot effectively identify the cluster centers, and time and space complexities are too high. To this end, this paper proposes a fast density peaks clustering algorithm based on approximatek-nearest neighbors (FDPAN). Firstly, it uses Balanced K-means based Hierarchical K-means (BKHK) method to partition the data and quickly find the approximatek-nearest neighbors (AKNN), improving the algorithm’s efficiency on large-scale high-dimensional data. Meanwhile, three-way clustering is used to improve the neighbor search of the boundary points of the partition. Then, the local density and relative distance of DPC are recalculated by AKNN. Finally, according to the similar density chain, the connected high-density points are labeled while searching for the cluster center, and the remaining points are assigned to the clusters where their nearest higher-density points are located. Theoretical analysis and experiments on synthetic and real datasets show that FDPAN can obtain higher clustering results and shorten the operation time on large-scale high-dimensional data compared with DPC and its variants.

As the representative density-based clustering algorithm, density peaks clustering (DPC) has wide recognition, and many improved algorithms and applications have been extended from it. However, the DPC involving privacy protection has not been deeply studied. In addition, there is still room for improvement in the selection of centers and allocation methods of DPC. To address these issues, vertical federated density peaks clustering under nonlinear mapping (VFDPC) is proposed to address privacy protection issues in vertically partitioned data. Firstly, a hybrid encryption privacy protection mechanism is proposed to protect the merging process of distance matrices generated by client data. Secondly, according to the merged distance matrix, a more effective cluster merging under nonlinear mapping is proposed to ameliorate the process of DPC. Results on man-made, real, and multi-view data fully prove the improvement of VFDPC on clustering accuracy.

Density peaks clustering (DPC) is a popular clustering algorithm, which has been studied and favored by many scholars because of its simplicity, fewer parameters, and no iteration. However, in previous improvements of DPC, the issue of privacy data leakage was not considered, and the "Domino" effect caused by the misallocation of noncenters has not been effectively addressed. In view of the above shortcomings, a horizontal federated DPC (HFDPC) is proposed. First, HFDPC introduces the idea of horizontal federated learning and proposes a protection mechanism for client parameter transmission. Second, DPC is improved by using similar density chain (SDC) to alleviate the "Domino" effect caused by multiple local peaks in the flow pattern dataset. Finally, a novel data dimension reduction and image encryption are used to improve the effectiveness of data partitioning. The experimental results show that compared with DPC and some of its improvements, HFDPC has a certain degree of improvement in accuracy and speed.