secularEq

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and classes for fitting, plotting and displaying a large number of different flexible MDS models (some as of yet unpublished).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).

Thomas Rusch

smacofx

Flexible Multidimensional Scaling and 'smacof' Extensions

Jan de Leeuw

Lisha Chen

Patrick Mair

secularEq function

<dl><dt>a</dt>
<dd>matrix</dd>
<dt>b</dt>
<dd>matrix</dd></dl>

Arguments

Secular Equation — secularEq

<dl>

<dt>a</dt>
<dd>matrix</dd>


<dt>b</dt>
<dd>matrix</dd>

</dl>

secularEq: Secular Equation

Description

Usage

Arguments