Computational Statistics & Data Analysis
A dual latent class unfolding model for two-way two-mode preference rating data
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
Parallel branch and bound for multidimensional scaling with city-block distances
Journal of Global Optimization
Cluster Differences Unfolding for Two-Way Two-Mode Preference Rating Data
Journal of Classification
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It is well known that considering a non-Euclidean Minkowski metric in Multidimensional Scaling, either for the distance model or for the loss function, increases the computational problem of local minima considerably. In this paper, we propose an algorithm in which both the loss function and the composition rule can be considered in any Minkowski metric, using a multivariate randomly alternating Simulated Annealing procedure with permutation and translation phases. The algorithm has been implemented in Fortran and tested over classical and simulated data matrices with sizes up to 200 objects. A study has been carried out with some of the common loss functions to determine the most suitable values for the main parameters. The experimental results confirm the theoretical expectation that Simulated Annealing is a suitable strategy to deal by itself with the optimization problems in Multidimensional Scaling, in particular for City-Block, Euclidean and Infinity metrics.