Three-way space structure and clustering of categorical data

Measures of similarity and dissimilarity play a pivotal role in discovering the structural characteristics of categorical data, which is crucial in various fields and applications because many real-world problems involve qualitative information. However, co-occurrence probability, a popular similarity measure widely used to construct a linear representation space for analyzing categorical data, has been verified to be inefficient in describing the global similarity of objects. In this paper, drawing inspiration from three-way concept theory, a novel three-way representation scheme is developed through the tripartite definition of Common Feature Values (CV), Non-common Feature Values (NV), and Respective Feature Values (RV), which enables comprehensive characterization of intrinsic feature relationships while maintaining interpretative granularity. These three concepts correspond to the positive, negative, and boundary domains of the feature universe, respectively, which map a set of categorical objects into three Euclidean spaces. Utilizing the three-way categorical data representation scheme, we develop a unified framework for three-way space structure based categorical clustering algorithms (TWSBC). Finally, to verify the performance of the TWSBC algorithm, which combines the representation scheme with the k-means algorithm, we employ the SBC- type algorithm as a reference. Extensive experiments show that our proposed TWSBC-type algorithms distinctly outperform SBC-type methods in terms of space correlation and clustering performance.