Subspace Hierarchical Clustering for Three-way Three-mode Data using Quadratic Regularization

Recent advances in information technology have enabled the analysis of large and complex data. Three-way three- mode data X̄ ∈ R|I|×|J|×|K| and I, J and K are represented by a set of objects, variables and occasions, respectively, and where |·| is defined as the cardinality of a set, are observed in various fields such as panel research or psychological research. For obtaining clustering structures from three-way three-mode data, it is important that clustering algorithms are applied to the data as an initial analysis. Vichi, et al., [6], proposed two types of subspace clustering algorithms that consider the structure of three-way three-mode data. However, Lance, et al., [3] reported that such types of subspaces are affected by noise and include complicated assumptions.In this paper, we propose subspace hierarchical clustering for three-way three-mode data using quadratic regular- izations. In the proposed method, a clustering algorithm, variable selection and occasion selection are simultaneously applied to the data. More precisely, the subspace comprises a subset of varables and occasions. Further, the clustering results are easy to interplet because the subspace does not include complex assumptions and can exclude noise effects.