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 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.