Flexible Multidimensional Scaling and 'smacof' Extensions
ALSCAL - MDS via S-Stress Minimization
Approximate Power Stress MDS
Box-Cox MDS
Calculates the blended Chi-square distance matrix between n vectors
S3 method for bcmds objects
S3 method for lmds objects
S3 method for smacofP objects
MDS Bootstrap for smacofP objects
Curvilinear Component Analysis (CLCA)
Curvilinear Distance Analysis (CLDA)
Classical Scaling
Wrapper to cmdscale for S3 class
conf_adjust: a function to procrustes adjust two matrices
Double centering of a matrix
Elastic Scaling SMACOF
Explicit Normalization Normalizes distances
Exploring initial configurations in an agnostic way
MDS Jackknife for smacofP objects
Local MDS
Auxfunction1
Take matrix to a power
Multiscale SMACOF
Multistart MDS function
Squared p-distances
Permutation test for smacofP objects
S3 plot method for smacofP objects
Power stress minimization by NEWUOA (nloptr)
Power Stress SMACOF
procruster: a procrustes function
Restricted Power Stress SMACOF
R stress SMACOF
Wrapper to sammon for S3 class
Sammon Mapping SMACOF
Adjusts a configuration
Secular Equation
smacofx: Flexible multidimensional scaling methods and SMACOF extensio...
Helper function to conduct jackknife MDS
Sparse (POST-)Multidimensional Distance Analysis (SPMDDA or SMDDA) eit...
Sparsified (POST-) Multidimensional Scaling (SPMDS or SMDS) either as ...
Calculating stress per point
Squared distances
Flexible multidimensional scaling (MDS) methods and extensions to the package 'smacof'. This package 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and classes for fitting, plotting and displaying a large number of different flexible MDS models (some as of yet unpublished). These are: 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, <https://rpubs.com/deleeuw/142619>) 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, <https://jmlr.org/papers/v14/chen13a.html>), 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. Currently the methods are only available for one-mode data (symmetric dissimilarity matrices).
Useful links