lmds {smacofx}

Local MDS

Description

This function minimizes the Local MDS Stress of Chen & Buja (2006) via gradient descent. This is a ratio metric scaling method.

Usage

lmds(
  delta,
  init = NULL,
  ndim = 2,
  k = 2,
  tau = 1,
  itmax = 5000,
  verbose = 0,
  principal = FALSE
)

Arguments

delta

dissimilarity or distance matrix, dissimilarity or distance data frame or 'dist' object

init

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

ndim

the dimension of the configuration

k

the k neighbourhood parameter

tau

the penalty parameter (suggested to be in [0,1])

itmax

number of optimizing iterations, defaults to 5000.

verbose

prints info if > 0 and progress if > 1.

principal

If 'TRUE', principal axis transformation is applied to the final configuration

Details

Note that k and tau are not independent. It is possible for normalized stress to become negative if the tau and k combination is so that the absolute repulsion for the found configuration dominates the local stress substantially less than the repulsion term does for the solution of D(X)=Delta, so that the local stress difference between the found solution and perfect solution is nullified. This can typically be avoided if tau is between 0 and 1. If not, set k and or tau to a smaller value.

Value

an object of class 'lmds' (also inherits from 'smacofP'). See powerStressMin. It is a list with the components as in power stress

• delta: Observed, untransformed dissimilarities

• tdelta: Observed explicitly transformed dissimilarities, normalized

• dhat: Explicitly transformed dissimilarities (dhats)

• confdist: Configuration dissimilarities

• conf: Matrix of fitted configuration

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

• ndim: Number of dimensions

• model: Name of MDS model

• type: Is "ratio" here.

• niter: Number of iterations

• nobj: Number of objects

• pars: explicit transformations hyperparameter vector theta

• weightmat: 1-diagonal matrix (for compatibility with smacof classes)

• parameters, pars, theta: The parameters supplied

• call the call

and some additional components

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

• tau: tau parameter

• k: k parameter

Author(s)

Lisha Chen & Thomas Rusch

Examples

dis<-smacof::kinshipdelta
res<- lmds(dis,k=2,tau=0.1)
res
summary(res)
plot(res)