cops: 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, <doi:10.1080/10618600.2017.1349664>). 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, <doi:10.1109/T-C.1969.222678>), elastic scaling (McGee, 1966, <doi:10.1111/j.2044-8317.1966.tb00367.x>), s-stress (Takane, Young & de Leeuw, 1977, <doi:10.1007/BF02293745>, r-stress (de Leeuw, Groenen & Mair, 2016, <>), power-stress (Buja & Swayne, 2002 <doi:10.1007/s00357-001-0031-0>) 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, <>).

Version: 1.0-2
Depends: R (≥ 3.1.2), cordillera (≥ 0.7-2), smacof (≥ 1.10-4)
Imports: MASS, minqa, pso, scatterplot3d, NlcOptim, Rsolnp, dfoptim, subplex, cmaes, crs, nloptr, rgl, rgenoud, GenSA
Suggests: testthat
Enhances: stats
Published: 2019-11-01
Author: Thomas Rusch ORCID iD [aut, cre], Jan de Leeuw [aut], Patrick Mair [aut]
Maintainer: Thomas Rusch <thomas.rusch at>
License: GPL-2 | GPL-3
NeedsCompilation: no
Citation: cops citation info
Materials: NEWS
In views: Psychometrics
CRAN checks: cops results


Reference manual: cops.pdf
Package source: cops_1.0-2.tar.gz
Windows binaries: r-devel:, r-release:, r-oldrel:
macOS binaries: r-release: cops_1.0-2.tgz, r-oldrel: cops_1.0-2.tgz


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