In clustering algorithms, the selection of neighbors significantly affects the quality of the final clustering results. While various neighbor relationships exist, such as K-nearest neighbors, natural neighbors, and shared neighbors, most neighbor relationships can only handle single structural relationships, and the identification accuracy is low for datasets with multiple structures. In life, people’s first instinct for complex things is to divide them into multiple parts to complete. Partitioning the dataset into more sub-graphs is a good idea approach to identifying complex structures. Taking inspiration from this, we propose a novel neighbor method: Shared Natural Neighbors (SNaN). To demonstrate the superiority of this neighbor method, we propose a shared natural neighbors-based hierarchical clustering algorithm for discovering arbitrary-shaped clusters (HC-SNaN). Our algorithm excels in identifying both spherical clusters and manifold clusters. Tested on synthetic datasets and real-world datasets, HC-SNaN demonstrates significant advantages over existing clustering algorithms, particularly when dealing with datasets containing arbitrary shapes.

Various kinds of $k$-Nearest Neighbor (KNN) based classification methods are the bases of many well-established and high-performance pattern recognition techniques. However, such methods are vulnerable to parameter choice. Essentially, the challenge is to detect the neighborhood of various datasets while ignoring the data characteristics. This article introduces a new supervised classification algorithm, Natural Neighborhood Based Classification Algorithm (NNBCA). Findings indicate that this new algorithm provides a good classification result without artificially selecting the neighborhood parameter. Unlike the original KNN-based method, which needs a prior $k$, NNBCA predicts different $k$ for different samples. Therefore, NNBCA is able to learn more from flexible neighbor information both in the training and testing stages. Thus, NNBCA provides a better classification result than other methods.