cops: Cluster Optimized Proximity Scaling

Multidimensional scaling (MDS) methods that aim at pronouncing the clustered appearance of the configuration (Rusch, Mair & Hornik, 2021, <doi:10.1080/10618600.2020.1869027>). 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 (COPS-C) for ratio, power, 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>), restricted power stress, approximate power stress, power elastic scaling, power Sammon mapping (for all Rusch, Mair & Hornik, 2021, <doi:10.1080/10618600.2020.1869027>). 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-Jaakola Algorithm” (Rusch, Mair & Hornik, 2021,<doi:10.1080/10618600.2020.1869027>).

Version: 1.3-1
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, rgenoud, GenSA
Suggests: R.rsp, rmarkdown
Published: 2023-01-19
DOI: 10.32614/CRAN.package.cops
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
Vignettes: A Tutorial on Cluster Optimized Proximity Scaling (COPS)


Package source: cops_1.3-1.tar.gz
Windows binaries: r-devel:, r-release:, r-oldrel:
macOS binaries: r-release (arm64): cops_1.3-1.tgz, r-oldrel (arm64): cops_1.3-1.tgz, r-release (x86_64): cops_1.3-1.tgz, r-oldrel (x86_64): cops_1.3-1.tgz
Old sources: cops archive


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