smacofSphere: 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)

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

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

Author

Jan de Leeuw and Patrick Mair

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).

References

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

Examples

Run this code


## 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

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