HC3: A Three-Way Clustering Method Based on Hierarchical Clustering

Three-way decision is a field of research pertaining to human-inspired computation. Guided by the principle of three-way decision, three-way clustering addresses the information uncertainty problem by using the core region and the fringe region to characterize a cluster. The universe is split into three parts by these two regions, which capture three kinds of relationships between objects and a cluster, namely, belonging to, partially belonging to, and not belonging to. In recent years, there have been considerable three-way clustering algorithms. However, the generalization and scalability of current three-way cluster algorithms remain relatively weak, with most algorithms adhering to a fixed allocation strategy or fixed threshold parameters. In order to overcome this problem, this paper proposes a multilevel three-way clustering algorithm based on a hierarchical strategy (HC3 for short). The proposed algorithm uses kernel density estimation information of data to adaptively construct a multilevel structure of data, where the higher levels (or the internal layers) with the high-density objects are closer to core regions of clusters, and the lower levels (or the external layers) with the low-density objects are closer to fringe regions of clusters. Under the multilevel structure, we establish a three-way allocation strategy based on the stability of subclass clusters, obtaining the correct attribution of data after fully considering neighboring information. The experiments are conducted on 13 data sets with different dimensions. By comparing to other 8 clustering algorithms, the effectiveness of the proposed HC3 is verified through accuracy (ACC), adjusted Rand index (ARI), and adjusted mutual information (AMI).