MDS class — MDS-class • CytoMDS

Class representing Multi Dimensional Scaling (MDS) projection.

returns the value of the stress criterion, minimized by the SMACOF algorithm.

returns a vector of nPoints dimension, containing the stress indicator per point. The stress minimization criterion can indeed be allocated per represented point. The more the stress of a particular point, the less accurate its distances w.r.t. the other points.

Usage

# S4 method for class 'MDS'
show(object)

nDim(x)

nPoints(x)

pwDist(x)

projections(x)

projDist(x)

stress(x)

spp(x)

eigenVals(x)

pctvar(x)

RSq(x)

RSqVec(x)

GoF(x)

smacofRes(x)

Arguments

object: a MDS object
x: a MDS object

Value

nothing

Slots

nDim

numeric, nb of dimensions of the projection

pwDist

An object of class dist storing the triangular relevant part of the symmetric, zero diagonal pairwise distance matrix (nPoints * nPoints), BEFORE projection.

proj

The projection matrix, resulting from MDS

projDist

An object of class dist storing the triangular relevant part of the symmetric, zero diagonal pairwise distance matrix (nPoints * nPoints), AFTER projection.

eigen

numeric, vector of nDim length, containing the eigen values of the PCA that is applied after the Smacof algorithm.

pctvar

numeric, vector of nDim length, containing the percentage of explained variance per axis.

RSq

numeric, vector of pseudo R square indicators, as a function of number of dimensions. RSq[nDim] is the global pseudo R square, as displayed on plots.

GoF

numeric, vector of goodness of fit indicators, as a function of number of dimensions. GoF[nDim] is the global goodness of fit.

Note pseudo R square and goodness of fit indicators are essentially the same indicator, only the definition of total sum of squares differ:

for pseudo RSq: TSS is calculated using the mean pairwise distance as minimum
for goodness of fit: TSS is calculated using 0 as minimum

smacofRes

an object of class 'smacofB' containing the algorithmic optimization results, for example stress and stress per point, as returned by smacof::smacofSym() method.

Examples



nHD <- 10
nLD <- 2
nPoints <- 20 

# generate uniformly distributed points in 10 dimensions
points <- matrix(
    data = runif(n = nPoints * nHD),
    nrow = nPoints)
    
# calculate euclidian distances     
pwDist  <- dist(points)

# compute Metric MDS object by reaching a target pseudo RSquare
mdsObj <- computeMetricMDS(pwDist, targetPseudoRSq = 0.95)

show(mdsObj)
#> MDS object containing MDS projection (using Smacof algorithm)  data:
#> Nb of dimensions:  7 
#> Nb of points:  20 
#> Stress:  0.035678 
#> Pseudo RSquare:  0.964146 
#> Goodness of fit:  0.998727