Least-squares bilinear clustering of three-way data

Abstract A least-squares bilinear clustering framework for modelling three-way data, where each observation consists of an ordinary two-way matrix, is introduced. The method combines decompositions the matrices with over observations. Different clusterings are defined part decomposition, which decomposes matrix-valued observations into overall means, row margins, column margins and row–column interactions. Therefore up to four different classifications jointly, one type effect. computational burden greatly reduced by orthogonality model, such that joint problem reduces separate problems can be handled independently. Three these sub-problems specific cases k -means clustering; a special algorithm formulated interactions, displayed in clusterwise biplots. illustrated via empirical example interpreting interaction biplots discussed. Supplemental materials this paper available online, includes dedicated R package, .