lmds {stops}

An function for local MDS (Chen & Buja 2006)

Description

An function for local MDS (Chen & Buja 2006)

Usage

lmds(delta, init = NULL, ndim = 3, k = 2, tau = 1, itmax = 5000, verbose = 0)

Arguments

delta

dissimilarity or distance matrix

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 progress if > 4.

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 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

• tau: tau parameter

• k: k parameter

Author(s)

Lisha Chen & Thomas Rusch

Examples

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