smacofSym: Symmetric smacof

Description

Multidimensional scaling on a symmetric dissimilarity matrix using SMACOF.

Usage

smacofSym(delta, ndim = 2, type = c("ratio", "interval", "ordinal", "mspline"),  weightmat = NULL, init = "torgerson", ties = "primary", verbose = FALSE,  relax = FALSE, modulus = 1, itmax = 1000, eps = 1e-06,  spline.degree = 2, spline.intKnots = 2)
mds(delta, ndim = 2, type = c("ratio", "interval", "ordinal", "mspline"),  weightmat = NULL, init = "torgerson", ties = "primary", verbose = FALSE,  relax = FALSE, modulus = 1, itmax = 1000, eps = 1e-06,  spline.degree = 2, spline.intKnots = 2)

Arguments

delta

Either a symmetric dissimilarity matrix or an object of class "dist"

ndim

Number of dimensions

weightmat

Optional matrix with dissimilarity weights

init

Either "torgerson" (classical scaling starting solution), "random" (random configuration), or a user-defined matrix

type

MDS type: "interval", "ratio", "ordinal" (nonmetric MDS), or "mspline"

ties

Tie specification (ordinal MDS only): "primary", "secondary", or "tertiary"

verbose

If TRUE, intermediate stress is printed out

relax

If TRUE, block relaxation is used for majorization

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

Value

delta: Observed dissimilarities, not normalized
dhat: Disparities (transformed proximities, approximated distances, d-hats)
confdiss: Configuration distances
conf: Matrix of fitted configurations
stress: Stress-1 value
spp: Stress per point (stress contribution in percentages)
resmat: Matrix with squared residuals
rss: Residual sum-of-squares
weightmat: Weight matrix
ndim: Number of dimensions
init: Starting configuration
model: Name of smacof model
niter: Number of iterations
nobj: Number of objects
type: Type of MDS model

Details

This is the simplest MDS-SMACOF version of the package. It solves the stress target function for symmetric dissimiliarities by means of the majorization approach (SMACOF) and reports the Stress-1 value (normalized). The main output are the coordinates in the low-dimensional space (configurations; conf).

The function mds() is a wrapper function and can be used instead of smacofSym()

This function allows for fitting three basic types of MDS: ratio MDS (default), interval MDS (polynomial transformation), and ordinal MDS (aka nonmetric MDS). It also returns the point stress, i.e. the larger the contribution of a point to the total stress, the worse the fit (see also plot.smacof.

References

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.

Examples

Run this code


## simple SMACOF solution for kinship data
res <- mds(kinshipdelta)
res
summary(res)
plot(res)
plot(res, type = "p", label.conf = list(label = TRUE, col = "darkgray"), pch = 25, col = "red")

## interval MDS, random starts
res <- smacofSym(kinshipdelta, type = "interval", init = "random")
res

## 3D ordinal SMACOF solution for trading data (secondary approach to ties)
data(trading)
res <- smacofSym(trading, ndim = 3, type = "ordinal", ties = "secondary")
res

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