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. 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, splines and nonmetric 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>), curvilinear distance analysis (Lee, Lendasse & Verleysen, 2004, <doi:10.1016/j.neucom.2004.01.007>), nonlinear MDS with optimal dissimilarity powers functions (De Leeuw, 2024, <https://github.com/deleeuw/smacofManual/blob/main/smacofPO(power)/smacofPO.pdf>), sparsified (power) MDS and sparsified multidimensional (power) distance analysis aka extended curvilinear (power) component analysis and extended curvilinear (power) distance analysis (Rusch, 2024, <doi:10.57938/355bf835-ddb7-42f4-8b85-129799fc240e>). 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, splines or nonmetric optimal scaling of the input proximities. Most functions use a Majorization-Minimization algorithm. Currently the methods are only available for one-mode two-way 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