multiscale function

Multiscale SMACOF

An implementation for maximum likelihood MDS aka multiscale that minimizes the multiscale stress by majorization with ratio and interval optimal scaling. Uses a repeat loop. Note that since this done via the route of r-sytress, the multiscale stress is approximate and only accuarte for kappa->0.

multiscale(
  delta,
  type = c("ratio", "interval"),
  weightmat,
  init = NULL,
  ndim = 2,
  acc = 1e-06,
  itmax = 10000,
  verbose = FALSE,
  kappa = 0.01,
  principal = FALSE
)

Arguments

• delta: dist object or a symmetric, numeric data.frame or matrix of distances. Warning: these will get transformed to the log scale, so make sure that log(delta)>=0.
• type: what optimal scaling type of MDS to fit. Currently one of "ratio" or "interval". Default is "ratio".
• weightmat: a matrix of finite 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
• kappa: As this is not exactly multiscale but an r-stress approximation, we have multiscale only for kappa->0. This argument can therefore be used to make the approximation more accurate by making it smaller. Default is 0.1.
• 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 dissimilarities
• tdelta: Observed explicitly transformed (log) dissimilarities, normalized
• dhat: Explicitly transformed dissimilarities (dhats), optimally scaled and normalized
• confdist: Transformed 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
• stress.m: Default stress (stress-1^2)

Warning

The input delta will internally get transformed to the log scale, so make sure that log(delta)>=0 otherwise it throws an error. It is often a good idea to use 1+delta in this case.

Examples

dis<-smacof::kinshipdelta
res<-multiscale(as.matrix(dis),type="interval",itmax=1000)
res
summary(res)
plot(res)

See Also

rStressMin