apStressMin {smacofx}

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: Configuration dissimilarities

• 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")