apStressMin function

Approximate Power Stress MDS

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.

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

Returns

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+2lambda(1-(1/kappa)) and tau=lambda/kappa. They are not output.

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")

References

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