| lmds {smacofx} | R Documentation |
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,
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. |
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)