smacofSphere: Spherical SMACOF

In smacof: Multidimensional Scaling

Spherical SMACOF

Description

Dual and primal approach for spherical SMACOF.

Usage

smacofSphere(delta, ndim = 2, type = c("ratio", "interval", "ordinal","mspline"), 
             algorithm = c("dual", "primal"), weightmat = NULL, 
             init = "torgerson", ties = "primary", verbose = FALSE, penalty = 100, 
             relax = FALSE, modulus = 1, itmax = 1000, eps = 1e-6,
             spline.degree = 2, spline.intKnots = 2)

Arguments

delta	Either a symmetric dissimilarity matrix or an object of class dist
ndim	Number of dimensions
type	MDS type: "interval", "ratio", or "ordinal" (nonmetric MDS)
algorithm	Algorithm type (see details)
weightmat	Optional matrix with dissimilarity weights
init	Either "torgerson" (classical scaling starting solution), "random" (random configuration), or a user-defined matrix
ties	Tie specification for non-metric MDS only
verbose	If TRUE, intermediate stress is printed out
penalty	Penalty parameter for dual algorithm (larger 0), see details
relax	If TRUE, block relaxation is used for majorization (dual algorithm)
modulus	Number of smacof iterations per monotone regression call
itmax	Maximum number of iterations
eps	Convergence criterion
spline.degree	Degree of the spline for "mspline" MDS type
spline.intKnots	Number of interior knots of the spline for "mspline" MDS type

Details

For large scale problems it is suggested to use the dual algorithm. Using the penalty parameter (dual algorithm), the user allow for slight point deviations from the circle (the higher the penalty, the stricter the algorithm is in terms of placing points in the sphere, see examples section below).

Value

delta	Observed dissimilarities
obsdiss	Observed dissimilarities, normalized
obsdiss1	Dual SMACOF: Observed dissimilarities
obsdiss2	Dual SMACOF: Restriction matrix
confdist	Configuration dissimilarities
conf	Matrix with fitted configurations
spp	Stress per point
resmat	Matrix with squared residuals
rss	Residual sum-of-squares
stress	Stress-1 value
init	Starting configurations
ndim	Number of dimensions
dummyvec	Dummy vector of restriction matrix
model	Type of smacof model
niter	Number of iterations
nobj	Number of objects

Author(s)

Jan de Leeuw and Patrick Mair

References

De Leeuw, J. & Mair, P. (2009). Multidimensional scaling using majorization: The R package smacof. Journal of Statistical Software, 31(3), 1-30, doi: 10.18637/jss.v031.i03

See Also

smacofRect, smacofIndDiff, smacofSym,smacofConstraint

Examples

## spherical SMACOF solution for trading data
## dual algorithm
res <- smacofSphere(trading, type = "ordinal")  
res
plot(res)

## lower penalty
res <- smacofSphere(trading, penalty = 20, type = "ordinal")  
res
plot(res)

## primal algorithm, interval
res <- smacofSphere(trading, type = "interval", algorithm = "primal")  
res

smacof documentation built on May 6, 2022, 9:05 a.m.