apStressMin: Approximate Power Stress MDS

In smacofx: Flexible Multidimensional Scaling and 'smacof' Extensions

Approximate Power Stress MDS

Description

An implementation to minimize approximate power stress by majorization with ratio or interval optimal scaling. This approximates the power stress objective in such a way that it can be fitted with SMACOF without distance transformations. See Rusch et al. (2021) for details.

Usage

apStressMin(
  delta,
  kappa = 1,
  lambda = 1,
  nu = 1,
  type = "ratio",
  weightmat = 1 - diag(nrow(delta)),
  init = NULL,
  ndim = 2,
  acc = 1e-06,
  itmax = 10000,
  verbose = FALSE,
  principal = FALSE
)

apowerstressMin(
  delta,
  kappa = 1,
  lambda = 1,
  nu = 1,
  type = "ratio",
  weightmat = 1 - diag(nrow(delta)),
  init = NULL,
  ndim = 2,
  acc = 1e-06,
  itmax = 10000,
  verbose = FALSE,
  principal = FALSE
)

apostmds(
  delta,
  kappa = 1,
  lambda = 1,
  nu = 1,
  type = "ratio",
  weightmat = 1 - diag(nrow(delta)),
  init = NULL,
  ndim = 2,
  acc = 1e-06,
  itmax = 10000,
  verbose = FALSE,
  principal = FALSE
)

apstressMin(
  delta,
  kappa = 1,
  lambda = 1,
  nu = 1,
  type = "ratio",
  weightmat = 1 - diag(nrow(delta)),
  init = NULL,
  ndim = 2,
  acc = 1e-06,
  itmax = 10000,
  verbose = FALSE,
  principal = FALSE
)

apstressmds(
  delta,
  kappa = 1,
  lambda = 1,
  nu = 1,
  type = "ratio",
  weightmat = 1 - diag(nrow(delta)),
  init = NULL,
  ndim = 2,
  acc = 1e-06,
  itmax = 10000,
  verbose = FALSE,
  principal = FALSE
)

Arguments

delta	dist object or a symmetric, numeric data.frame or matrix of distances
kappa	power of the transformation of the fitted distances; defaults to 1
lambda	the power of the transformation of the proximities; defaults to 1
nu	the power of the transformation for weightmat; defaults to 1
type	what type of MDS to fit. Only "ratio" currently.
weightmat	a binary matrix of finite nonegative weights.
init	starting configuration
ndim	dimension of the configuration; defaults to 2
acc	numeric accuracy of the iteration. Default is 1e-6.
itmax	maximum number of iterations. Default is 10000.
verbose	should iteration output be printed; if > 1 then yes
principal	If 'TRUE', principal axis transformation is applied to the final configuration

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: Tranformed configuration distances

• 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 weightmat^nu)

Note

Internally we calculate the approximation parameters upsilon=nu+2*lambda*(1-(1/kappa)) and tau=lambda/kappa. They are not output.

References

Rusch, Mair, Hornik (2021). Cluster Optimized Proximity Scaling. JCGS <doi:10.1080/10618600.2020.1869027>

Examples

dis<-smacof::kinshipdelta
res<-apStressMin(as.matrix(dis),kappa=2,lambda=1.5,itmax=1000)
res
summary(res)
plot(res)
plot(res,"Shepard")
plot(res,"transplot")

smacofx documentation built on Sept. 22, 2024, 5:07 p.m.