IMDS: Multidimensional Scaling of Interval-Valued Dissimilarities

In mdsOpt: Searching for Optimal MDS Procedure for Metric, Nonmetric and Interval-Valued Data

Multidimensional Scaling of Interval-Valued Dissimilarities

Description

Internal function for multidimensional scaling of interval-valued dissimilarities using either the hypersphere or hyperbox model. Optimization can be performed using the majorization-minimization algorithm or the BFGS quasi-Newton method.

Usage

.IMDS(
  IDM,
  p = 2,
  eps = 1e-5,
  maxit = 1000,
  model = c("sphere", "box"),
  opt.method = c("MM", "BFGS"),
  ini = "auto",
  report = 100,
  grad.num = FALSE,
  rel = 0,
  dil = 1
)

Arguments

IDM	Interval-valued dissimilarity matrix represented as a three-dimensional array. IDM[1,,] contains the lower dissimilarity matrix and IDM[2,,] contains the upper dissimilarity matrix.
p	Number of dimensions of the multidimensional scaling configuration.
eps	Convergence criterion used by the majorization-minimization algorithm.
maxit	Maximum number of optimization iterations.
model	Character string specifying the symbolic representation. "sphere" uses the hypersphere model and "box" uses the hyperbox model.
opt.method	Optimization method. "MM" uses the majorization-minimization algorithm and "BFGS" uses the BFGS quasi-Newton method.
ini	Initial configuration. If "auto", the coordinates obtained from classical multidimensional scaling of the midpoint dissimilarity matrix are used as the initial centers and initial radii are generated automatically. Alternatively, a list containing an initial coordinate matrix and an initial radius vector or matrix can be supplied.
report	Frequency with which optimization progress is reported.
grad.num	Logical value indicating whether a numerical gradient should be used for BFGS optimization. If FALSE, the analytical gradient is used.
rel	Control parameter for the relaxed update used by the majorization-minimization procedure. A nonzero value enables the relaxed update. This argument is not used for BFGS optimization.
dil	Control parameter for optimal dilation of the configuration in the majorization-minimization procedure. A nonzero value enables dilation. This argument is not used for BFGS optimization.

Details

The function performs multidimensional scaling for interval-valued dissimilarities.

Two representations are available. In the hypersphere model each object is represented by a center and a radius. In the hyperbox model each object is represented by a center and dimension-specific half-ranges.

The stress criterion can be minimized either by the majorization-minimization method or by the BFGS optimization method.

This is an internal function used by higher-level procedures in the mdsOpt package and is not normally intended to be called directly by users.

Value

An object containing the fitted interval multidimensional scaling configuration. Depending on the selected model, components can include:

X

Matrix of coordinates of the object centers with p columns.

r

Radius vector for the hypersphere model.

R

Radius or half-range matrix for the hyperbox model.

str

Value of the stress criterion for the fitted configuration.

IDM

Original interval-valued dissimilarity matrix.

EIDM

Interval-valued dissimilarities implied by the fitted configuration.

References

Nash, J. C. (1990). Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation. Adam Hilger.

Borg, I., Groenen, P. J. F., and Mair, P. (2013). Applied Multidimensional Scaling. Springer.

See Also

optSmacofSymInterval

mdsOpt documentation built on Oct. 2, 2026, 5:09 p.m.