lmds function

Local MDS

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

lmds(
  delta,
  k = 2,
  tau = 1,
  type = "ratio",
  ndim = 2,
  weightmat = 1 - diag(nrow(delta)),
  itmax = 5000,
  init = NULL,
  verbose = 0,
  principal = FALSE,
  normconf = FALSE
)

Arguments

• delta: dissimilarity or distance matrix, dissimilarity or distance data frame or 'dist' object
• k: the k neighbourhood parameter
• tau: the penalty parameter (suggested to be in [0,1])
• type: what type of MDS to fit. Only "ratio" currently.
• ndim: the dimension of the configuration
• weightmat: a matrix of finite weights. Not implemented.
• itmax: number of optimizing iterations, defaults to 5000.
• init: initial configuration. If NULL a classical scaling solution is used.
• verbose: prints info if > 0 and progress if > 1.
• principal: If 'TRUE', principal axis transformation is applied to the final configuration
• normconf: normalize the configuration to sum(delta^2)=1 (as in the power stresses). Note that then the distances in confdist do not match the manually calculated ones.

Returns

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

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.

Examples

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

Author(s)

Lisha Chen & Thomas Rusch