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.

Most clustering algorithms require setting one or more parameters, which rely on prior knowledge or are constantly adjusted based on external indicators. To address the issues of requiring external index guidance, blindness, and time-consuming parameter setting for clustering algorithms on complex data, we propose a novel Parameter-Adaptive Border Peeling clustering algorithm (PABP). The PABP algorithm initially employs the maximum number of neighbors identified through natural neighbor search to automatically ascertain the number of local neighborhoods. At the same time, the Gaussian kernel bandwidth can be adaptively obtained in density measurement, which can highlight high-density areas. Secondly, the number of peels is adaptively determined by the coefficient of variation of density during the iterative border peeling process. Lastly, labels are assigned to core points based on graph connections, while the clustering of border points is accomplished via label propagation. PABP does not require users to adjust parameters based on prior knowledge or external indicators throughout the entire process. In the experiment, PABP was compared with seven other advanced clustering algorithms on 13 synthetic datasets, 10 UCI datasets, and Olivetti Face and MNIST datasets. The results indicate that the clustering performance of PABP is superior to the compared algorithms.

Deep graph clustering (DGC) has been a promising method for clustering graph data in recent years. However, existing research primarily focuses on optimizing clustering outcomes by improving the quality of embedded representations, resulting in slow-speed complex models. Additionally, these methods do not consider changes in node similarity and corresponding adjustments in the original structure during the iterative optimization process after updating node embeddings, which easily falls into the representation collapse issue. We introduce an Efficient Graph Auto-Encoder (EGAE) and a dynamic graph weight updating strategy to address these issues, forming the basis for our proposed Fast DGC (FastDGC) network. Specifically, we significantly reduce feature dimensions using a linear transformation that preserves the original node similarity. We then employ a single-layer graph convolutional filtering approximation to replace multiple layers of graph convolutional neural network, reducing computational complexity and parameter count. During iteration, we calculate the similarity between nodes using the linearly transformed features and periodically update the original graph structure to reduce edges with low similarity, thereby enhancing the learning of discriminative and cohesive representations. Theoretical analysis confirms that EGAE has lower computational complexity. Extensive experiments on standard datasets demonstrate that our proposed method improves clustering performance and achieves a speedup of 2–3 orders of magnitude compared to state-of-the-art methods, showcasing outstanding performance. The code for our model is available at https://github.com/Marigoldwu/FastDGC . Furthermore, we have organized a portion of the DGC code into a unified framework, available at https://github.com/Marigoldwu/A-Unified-Framework-for-Deep-Attribute-Graph-Clustering .