opmds: Nonlinear ratio MDS with optimal power of dissimilarities

In smacofx: Flexible Multidimensional Scaling and 'smacof' Extensions

Nonlinear ratio MDS with optimal power of dissimilarities

Description

An implementation to minimize explicitly normalized stress over dissimilarities to a power by majorization with ratio optimal scaling in an alternating minimization algorithm. The optimal power transformation lambda of the dissimilarities is found by an inner optimization step via the Brent-Dekker method.

Usage

opmds(
  delta,
  type = "ratio",
  weightmat = 1 - diag(nrow(delta)),
  init = NULL,
  ndim = 2,
  itmax = 1000,
  acc = 1e-10,
  verbose = FALSE,
  principal = FALSE,
  interval = c(0, 4)
)

Arguments

delta	dist object or a symmetric, numeric data.frame or matrix of distances
type	what type of MDS to fit. Currently only "ratio".
weightmat	a matrix of finite weights.
init	starting configuration
ndim	dimension of the configuration; defaults to 2
itmax	maximum number of iterations. Default is 10000.
acc	numeric accuracy of the iteration. Default is 1e-6.
verbose	should iteration output be printed; defaults to 'FALSE'.
principal	If 'TRUE', principal axis transformation is applied to the final configuration.
interval	the line constraints c(upper, lower), within which to look for the optimal power transformation lambda. Defaults to c(0,4).

Value

a 'smacofP' object (inheriting from 'smacofB', see smacofSym). It is a list with the components

• delta: Observed, untransformed dissimilarities

• tdelta: Observed explicitly transformed dissimilarities, normalized

• dhat: Explicitly transformed dissimilarities (dhats), optimally scaled and normalized

• confdist: Transformed fitted configuration distances

• iord: optimal scaling ordering

• conf: Matrix of fitted configuration

• stress: Default stress (stress 1; sqrt of explicitly normalized stress)

• spp: Stress per point

• ndim: Number of dimensions

• model: Name of smacof model

• niter: Number of iterations

• nobj: Number of objects

• type: Type of MDS model

• weightmat: weighting matrix as supplied

• stress.m: Default stress (stress-1^2)

• tweightmat: transformed weighting matrix (here NULL)

• pars, theta: The optimal transformation parameter lambda

See Also

See stops for a similar, more flexible idea.

Examples

dis<-smacof::kinshipdelta
res<-opmds(dis,itmax=1000)
res
summary(res)
plot(res)

smacofx documentation built on Aug. 8, 2025, 6:28 p.m.