SMACOF: SMACOF

In MultBiplotR: Multivariate Analysis Using Biplots in R

SMACOF

Description

SMACOF algorithm for symmetric proximity matrices

Usage

SMACOF(P, X = NULL, W = NULL, 
Model = c("Identity", "Ratio", "Interval", "Ordinal"), 
dimsol = 2, maxiter = 100, maxerror = 1e-06, 
StandardizeDisparities = TRUE, ShowIter = FALSE)

Arguments

P	A matrix of proximities
X	Inial configuration
W	A matrix of weights~
Model	MDS model.
dimsol	Dimension of the solution
maxiter	Maximum number of iterations of the algorithm
maxerror	Tolerance for convergence of the algorithm
StandardizeDisparities	Should the disparities be standardized
ShowIter	Show the iteration proccess

Details

SMACOF performs multidimensional scaling of proximity data to find a least- squares representation of the objects in a low-dimensional space. A majorization algorithm guarantees monotone convergence for optionally transformed, metric and nonmetric data under a variety of models.

Value

An object of class Principal.Coordinates and MDS. The function adds the information of the MDS to the object of class proximities. Together with the information about the proximities the object has:

Analysis	The type of analysis performed, "MDS" in this case
X	Coordinates for the objects
D	Distances
Dh	Disparities
stress	Raw Stress
stress1	stress formula 1
stress2	stress formula 2
sstress1	sstress formula 1
sstress2	sstress formula 2
rsq	Squared correlation between disparities and distances
rho	Spearman correlation between disparities and distances
tau	Kendall correlation between disparities and distances

Author(s)

Jose Luis Vicente-Villardon

References

Commandeur, J. J. F. and Heiser, W. J. (1993). Mathematical derivations in the proximity scaling (PROXSCAL) of symmetric data matrices (Tech. Rep. No. RR- 93-03). Leiden, The Netherlands: Department of Data Theory, Leiden University.

Kruskal, J. B. (1964). Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 28-42.

De Leeuw, J. & Mair, P. (2009). Multidimensional scaling using majorization: The R package smacof. Journal of Statistical Software, 31(3), 1-30, http://www.jstatsoft.org/v31/i03/

Borg, I., & Groenen, P. J. F. (2005). Modern Multidimensional Scaling (2nd ed.). Springer.

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

Groenen, P. J. F., Heiser, W. J. and Meulman, J. J. (1999). Global optimization in least squares multidimensional scaling by distance smoothing. Journal of Classification, 16, 225-254.

Groenen, P. J. F., van Os, B. and Meulman, J. J. (2000). Optimal scaling by alternating length-constained nonnegative least squares, with application to distance-based analysis. Psychometrika, 65, 511-524.

See Also

MDS, PrincipalCoordinates

Examples

data(spiders)
Dis=BinaryProximities(spiders)
MDSSol=SMACOF(Dis$Proximities)

MultBiplotR documentation built on Nov. 21, 2023, 5:08 p.m.