Cluster Optimized Proximity Scaling

Cluster optimized proximity scaling (COPS) refers to multidimensional scaling (MDS) methods that aim at pronouncing the clustered appearance of the configuration. They achieve this by transforming proximities/distances with power functions and augment the fitting criterion with a clusteredness index, the OPTICS Cordillera (Rusch, Hornik & Mair, 2018, ). There are two variants: One for finding the configuration directly for given parameters (COPS-C) for ratio, interval and non-metric MDS (Borg & Groenen, 2005, ISBN:978-0-387-28981-6), and one for using the augmented fitting criterion to find optimal parameters (P-COPS). The package contains various functions, wrappers, methods and classes for fitting, plotting and displaying different MDS models in a COPS framework like ratio, interval and non-metric MDS for COPS-C and P-COPS with Torgerson scaling (Torgerson, 1958, ISBN:978-0471879459), scaling by majorizing a complex function (SMACOF; de Leeuw, 1977, <>), Sammon mapping (Sammon, 1969, ), elastic scaling (McGee, 1966, ), s-stress (Takane, Young & de Leeuw, 1977, , r-stress (de Leeuw, Groenen & Mair, 2016, <>), power-stress (Buja & Swayne, 2002 ) and power elastic scaling, power Sammon mapping and approximated power stress (Rusch, Mair & Hornik, 2015, <>). All of these models can also solely be fit as MDS with power transformations. The package further contains a function for pattern search optimization, the "Adaptive Luus-Jakola Algorithm" (Rusch, Mair & Hornik, 2015, <>).


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1.0-2 by Thomas Rusch, a year ago

Browse source code at

Authors: Thomas Rusch [aut, cre] , Jan de Leeuw [aut] , Patrick Mair [aut]

Documentation:   PDF Manual  

Task views: Psychometric Models and Methods

GPL-2 | GPL-3 license

Imports MASS, minqa, pso, scatterplot3d, NlcOptim, Rsolnp, dfoptim, subplex, cmaes, crs, nloptr, rgl, rgenoud, GenSA

Depends on cordillera, smacof

Suggests testthat

Enhances stats

See at CRAN