Three-way component analysis with smoothness constraints

Abstract

Tucker3 Analysis and CANDECOMP/PARAFAC (CP) are closely related methods for three-way component analysis. Imposing constraints on the Tucker3 or CP solutions can be useful to improve estimation of the model parameters. In the present paper, a method is proposed for applying smoothness constraints on Tucker3 or CP solutions, which is particularly useful in analysing functional three-way data. The usefulness of smoothness constraints on Tucker3 and CP solutions is examined by means of a simulation experiment. Generally, the results of the experiments indicate better estimations of the model parameters. An empirical example illustrates the use of smoothness constraints. The constrained model is more stable and easier to interpret than the unconstrained model.