Fitting the CANDCLUS/MUMCLUS Models with Partitioning and Other Constraints
The CANDCLUS (for CANonical Decompositon CLUStering) model and method is described for analysis of multiway data arrays in terms of multilinear models in which some ways (or modes) are modeled by continuous parameters defining spatial dimensions, other ways/modes by discrete parameters defining cluster or other categorical structures, and still others by mixtures of continuous and discrete parameters defining “hybrid” models in which spatial dimensional structure is combined with cluster-like categorical structure. A generalization of CANDCLUS, called MUMCLUS (for MUltiMode CLUStering), whose two-way special case corresponds to DeSarbo’s GENNCLUS model, is also defined and discussed. Methods previously published for unconstrained fitting of the CANDCLUS/MUMCLUS family of models, based on a separability property observed by Chaturvedi, are extended to allow certain constraints on the discrete parameters—in particular a constraint that the cluster structure be a partition, and another that each entity in a particular mode may be a member of no more than C clusters. These constraints are implemented via an extended separability property (for vectors of discrete parameters, rather than for single parameters) which is defined. The possibility of fitting other constrained versions of these models within this general framework is discussed.
KeywordsLoss Function Weighted Little Square Separability Property Discrete Parameter Less Absolute Deviation
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