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.

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 approximate k-nearest neighbors (FDPAN). Firstly, it uses Balanced K-means based Hierarchical K-means (BKHK) method to partition the data and quickly find the approximate k-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.

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 .

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-distance d_c. (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.