On the Procrustean analogue of individual differences scaling (INDSCAL)

In this paper, individual differences scaling (INDSCAL) is revisited, considering INDSCAL as being embedded within a hierarchy of individual difference scaling models. We explore the members of this family, distinguishing (i) models, (ii) the role of identification and substantive constraints, (iii) criteria for fitting models and (iv) algorithms to optimise the criteria. Model formulations may be based either on data that are in the form of proximities or on configurational matrices. In its configurational version, individual difference scaling may be formulated as a form of generalized Procrustes analysis. Algorithms are introduced for fitting the new models. An application from sensory evaluation illustrates the performance of the methods and their solutions

First and second-order derivatives for CP and INDSCAL

In this paper we provide the means to analyse the second-order differential structure of optimization functions concerning CANDECOMP/PARAFAC and INDSCAL. Closed-form formulas are given under two types of constraint: unit-length columns or orthonormality of two of the three component matrices. Some numerical problems that might occur during the computation of the Jacobian and Hessian matrices are addressed. The use of these matrices is illustrated in three applications. (C) 2010 Elsevier B.V. All rights reserved

Orthonormality-constrained INDSCAL with nonnegative saliences

INDSCAL is a specific model for simultaneous metric multidimensional scaling (MDS) of several data matrices. In the present work the INDSCAL problem is reformulated and studied as a dynamical system on the product manifold of orthonormal and diagonal matrices. The problem for fitting of the INDSCAL model to the data is solved. The resulting algorithms are globally convergent. Numerical examples illustrate their application