smacofx

Flexible multidimensional scaling (MDS) methods centered around scaling with majorization and extensions to the package 'smacof'. This package enhances 'smacof' and contains various functions, wrappers, methods and classes for fitting, plotting and displaying a large number of different flexible MDS models (some as of yet unpublished) such as Torgerson scaling (Torgerson, 1958, ISBN:978-0471879459) with powers, Sammon mapping (Sammon, 1969, doi:10.1109/T-C.1969.222678) with ratio and interval optimal scaling, Multiscale MDS (Ramsay, 1977, doi:10.1007/BF02294052) with ratio and interval optimal scaling, S-stress MDS (ALSCAL; Takane, Young & De Leeuw, 1977, doi:10.1007/BF02293745) with ratio and interval optimal scaling, elastic scaling (McGee, 1966, doi:10.1111/j.2044-8317.1966.tb00367.x) with ratio and interval optimal scaling, r-stress MDS (De Leeuw, Groenen & Mair, 2016, ) with ratio, interval and non-metric optimal scaling, power-stress MDS (POST-MDS; Buja & Swayne, 2002 doi:10.1007/s00357-001-0031-0) with ratio and interval optimal scaling, restricted power-stress (Rusch, Mair & Hornik, 2021, doi:10.1080/10618600.2020.1869027) with ratio and interval optimal scaling, approximate power-stress with ratio optimal scaling (Rusch, Mair & Hornik, 2021, doi:10.1080/10618600.2020.1869027), Box-Cox MDS (Chen & Buja, 2013, ), local MDS (Chen & Buja, 2009, doi:10.1198/jasa.2009.0111), curvilinear component analysis (Demartines & Herault, 1997, doi:10.1109/72.554199) and curvilinear distance analysis (Lee, Lendasse & Verleysen, 2004, doi:10.1016/j.neucom.2004.01.007). There also are experimental models (e.g., sparsified MDS and sparsified POST-MDS). Some functions are suitably flexible to allow any other sensible combination of explicit power transformations for weights, distances and input proximities with implicit ratio, interval or non-metric optimal scaling of the input proximities. Most functions use a Majorization-Minimization algorithm.