multiscale: Multiscale SMACOF

Description

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.

Usage

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

Value

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)

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

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

Run this code

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