Three-way asymmetric hierarchical clustering based on regularized similarity models

摘要

Three-way two-mode asymmetric data are observed in various situations such as brand switching, psychological research, and web mining. When clustering algorithms are applied to such data, several problems occur. One problem involves dealing with asymmetries. For two-way asymmetric data, there are two approaches to deal with asymmetries when using clustering algorithms. The first approach is to convert asymmetric similarities to symmetric similarities. The other approach is to introduce objective functions that consider internal variations of each cluster. However, for these clustering algorithms, it is difficult to understand the asymmetric features of the clustering results. The second problem involves determining the effects of occasions. Sato and Jain (2006) proposed fuzzy clustering for three-way two-mode asymmetric data and considered the effects of occasions[9]. In this paper, we propose two types of regularized similarity models and three-way asymmetric hierarchical clustering using entropy regularization. One regularized similarity model can provide us with factors of the direction of asymmetries, while the other model can provide us with factors comprising symmetric and asymmetric parts of asymmetric data. In addition, we introduce the factors of occasions using entropy regularization. Therefore, an advantage of the proposed algorithm is that researchers can easily interpret the clustering results.