bcStressMin {stops}

An MDS version for minimizing BoxCox Stress (Chen & Buja 2013)

Description

An MDS version for minimizing BoxCox Stress (Chen & Buja 2013)

Usage

bcStressMin(
  delta,
  init = NULL,
  verbose = 0,
  ndim = 2,
  mu = 1,
  lambda = 1,
  rho = 0,
  itmax = 2000,
  addD0 = 1e-04
)

Arguments

delta

dissimilarity or distance matrix

init

initial configuration. If NULL a classical scaling solution is used.

verbose

prints progress if > 3.

ndim

the dimension of the configuration

mu

mu parameter. Should be 0 or larger for everything working ok. If mu<0 it works but the model is strange and normalized stress tends towards 0 regardless of fit. Use normalized stress at your own risk in that case.

lambda

lambda parameter. Must be larger than 0.

rho

the rho parameter.

itmax

number of optimizing iterations, defaults to 2000.

addD0

a small number that's added for D(X)=0 for numerical evaluation of worst fit (numerical reasons, see details). If addD0=0 the normalized stress for mu!=0 and mu+lambda!=0 is correct, but will give useless normalized stress for mu=0 or mu+lambda!=0.

Details

For numerical reasons with certain parameter combinations, the normalized stress uses a configuration as worst result where every d(X) is 0+addD0. The same number is not added to the delta so there is a small inaccuracy of the normalized stress (but negligible if min(delta)>>addD0). Also, for mu<0 or mu+lambda<0 the normalization cannot generally be trusted (in the worst case of D(X)=0 one would have an 0^(-a)).

Value

an object of class 'bcmds' (also inherits from 'smacofP'). It is a list with the components

• delta: Observed dissimilarities, not normalized

• obsdiss: Observed transformed dissimilarities, not normalized

• confdist: Configuration dissimilarities, NOT normalized

• conf: Matrix of fitted configuration, NOT normalized

• stress: Default stress (stress 1; sqrt of explicitly normalized stress)

• ndim: Number of dimensions

• model: Name of MDS model

• niter: Number of iterations

• nobj: Number of objects

• pars: hyperparameter vector theta

and some additional components

• stress.m: default stress is the explicitly normalized stress on the normalized, transformed dissimilarities

• deltaorig: observed, untransformed dissimilarities

• mu: mu parameter (for attraction)

• lambda: lambda parameter (for repulsion)

• rho: rho parameter (for weights)

Author(s)

Lisha Chen & Thomas Rusch

Examples

dis<-smacof::kinshipdelta
res<-bcStressMin(as.matrix(dis),mu=2,lambda=1.5,rho=0)
res
summary(res)
plot(res)