Attribute independence has been taken as a major assumption in the limited research that has been conducted on similarity analysis for categorical data, especially unsupervised learning. However, in real-world data sources, attributes are more or less associated with each other in terms of certain coupling relationships. Accordingly, recent works on attribute dependency aggregation have introduced the co-occurrence of attribute values to explore attribute coupling, but they only present a local picture in analyzing categorical data similarity. This is inadequate for deep analysis, and the computational complexity grows exponentially when the data scale increases. This paper proposes an efficient data-driven similarity learning approach that generates a coupled attribute similarity measure for nominal objects with attribute couplings to capture a global picture of attribute similarity. It involves the frequency-based intra-coupled similarity within an attribute and the inter-coupled similarity upon value co-occurrences between attributes, as well as their integration on the object level.
In particular, four measures are designed for the inter-coupled similarity to calculate the similarity between two categorical values by considering their relationships with other attributes in terms of power set, universal set, joint set, and intersection set. The theoretical analysis reveals the equivalent accuracy and superior efficiency of the measure based on the intersection set, particularly for large-scale data sets. Intensive experiments of data structure and clustering algorithms incorporating the coupled dissimilarity metric achieve a significant performance improvement on state-of-the-art measures and algorithms on 13 UCI data sets, which is confirmed by the statistical analysis. The experiment results show that the proposed coupled attribute similarity is generic, and can effectively and efficiently capture the intrinsic and global interactions within and between attrib- tes for especially large-scale categorical data sets. In addition, two new coupled categorical clustering algorithms, i.e., CROCK and CLIMBO are proposed, and they both outperform the original ones in terms of clustering quality on UCI data sets and bibliographic data.