SMACOF function

SMACOF

SMACOF algorithm for symmetric proximity matrices

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.

Returns

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

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.

Author(s)

Jose Luis Vicente-Villardon

See Also

MDS, PrincipalCoordinates

Examples

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