in practice, tucker decomposition is used as a modelling tool. for instance, it is used to model three-way (or higher way) data by means of relatively small numbers of components for each of the three or more modes, and the components are linked to each other by a three- (or higher-) way core array. the model parameters are estimated in such a way that, given fixed numbers of components, the modelled data optimally resemble the actual data in the least squares sense. the model gives a summary of the information in the data, in the same way as principal components analysis does for two-way data.