A unifying model involving a categorical and/or dimensional reduction for multimode data

A unifying model is presented that implies a categorical and/or dimensional reduction of one or several modes of a multiway data set. The model encompasses a broad range of (existing as well as to be developed) discrete, continuous, as well as hybrid discrete-continuous reduction models as special cases, which all imply a decomposition of the reconstructed data on the basis of quantifications of the different data modes and a linking array. An analysis of the objective or loss function associated with the model leads to two generic algorithmic strategies, the possibilities and limitations of which are the object of a subsequent discussion.