Three-way Spectral Clustering

In this paper, we present a spectral clustering approach for clustering three-way data. Three-way data concern data characterized by three modes: n units, p variables, and t different occasions. In other words, three-way data contain a t × p observedmatrix for each statistical observation. The units generated by simultaneous observation of variables in different contexts are usually structured as three-way data, so each unit is basically represented as a matrix. In order to cluster the n units in K groups, the spectral clustering application to three-way data can be a powerful tool for unsupervised classification. Here, one example on real three-way data have been presented showing that spectral clustering method is a competitivemethod to cluster this type of data.