Multilevel–Multigroup Analysis Using a Hierarchical Tensor SOM Network

Abstract

This paper describes a method of multilevel–multigroup analysis based on a nonlinear multiway dimensionality reduction. To analyze a set of groups in terms of the probabilistic distribution of their constituent member data, the proposed method uses a hierarchical pair of tensor self-organizing maps (TSOMs), one for the member analysis and the other for the group analysis. This architecture enables more flexible analysis than ordinary parametric multilevel analysis, as it retains a high level of translatability supported by strong visualization. Furthermore, this architecture provides a consistent and seamless computation method for multilevel–multigroup analysis by integrating two different levels into a hierarchical tensor SOM network. The proposed method is applied to a dataset of football teams in a university league, and successfully visualizes the types of players that constitute each team as well as the differences or similarities between the teams.