stops-package

stops: Structure Optimized Proximity Scaling

A package for "structure optimized proximity scaling" (STOPS), a collection of methods that fit nonlinear distance transformations in multidimensional scaling (MDS) and trade-off the fit with structure considerations to find optimal parameters or optimal configurations. The package contains various functions, wrappers, methods and classes for fitting, plotting and displaying different MDS models in a STOPS framework like Torgerson scaling, SMACOF, Sammon mapping, elastic scaling, symmetric SMACOF, spherical SMACOF, sstress, rstress, powermds, power elastic scaling, power sammon mapping, power stress, Isomap, approximate power stress, restricted power stress. All of these models can also be fit as MDS variants (i.e., no structuredness). The package further contains functions for optimization (Adaptive Luus-Jaakola and for Bayesian optimization with treed Gaussian process with jump to linear models) and functions for various structuredness indices package

Details

The stops package provides five categories of important functions:

Models:

• stops ... which fits STOPS models as described in Rusch et al. (2023) via argument loss with ratio, interval or ordinal optimal scaling (not all optimal scalings can be used with all loss arguments). By setting cordweight or strucweight to zero they can also be used to fit MDS for many different models:

  • loss="stress": One parameter theta, power transformations of dissimilarities. Via stop_smacofSym.
  • loss="sammon": One parameter theta, power transformations of dissimilarities. Via stop_sammon.
  • loss="strain": One parameter theta, power transformations of dissimilarities. Via stop_cmdscale.
  • loss="rstress": One parameter theta, power transformations of fitted distances. Via stop_rstress.
  • loss="smacofSphere": One parameter theta, power transformations of dissimilarities. Via stop_smacofSphere.
  • loss="sammon2": One parameter theta, power transformations of dissimilarities. Via stop_sammon2.
  • loss="elastic": One parameter theta, power transformations of dissimilarities. Via stop_elastic.
  • loss="sstress": One parameter theta, power transformations of dissimilarities. Via stop_sstress.
  • loss="isomap_k": One parameter theta, k neighborhood for geodesic distances. Via stop_isomap1.
  • loss="isomap_eps": One parameter theta, epsilon neighborhood for geodesic distances. Via stop_isomap2.
  • loss="smds": One parameter theta, neighborhood parameter tau. Via stop_smds.
  • loss="clca": One parameter theta, neighborhood parameters lambda0. Via stop_clca.
  • loss="powerelastic": Two parameter theta, power transformations of dissimilarities and fitted distances. Via stop_powerelastic.
  • loss="powersammon": Two parameter theta, power transformations of dissimilarities and fitted distances. Via stop_powersammon.
  • loss="powermds": Two parameter theta, power transformations of dissimilarities and fitted distances. Via stop_powermds.
  • loss="rpstress": Two parameter theta, power transformations of dissimilarities/fitted distances and weights. Via stop_rpowerstress.
  • loss="smdda_k": Two parameter theta, neighborhood parameters k (geodesic distance) and tau. Via stop_smmdak.
  • loss="smdda_eps": Two parameter theta, neighborhood parameters eps (geodesic distance) and tau. stop_smddae.
  • loss="lmds": Two parameter theta, neighbourhood parameters tau and k. Via stop_lmds.
  • loss="clda_eps": Two parameter theta, neighborhood parameters lambda0 and epsilon (geodesic distance). Via stop_cldae.
  • loss="clda_k": Two parameter theta, neighborhood parameters lambda0 and k (geodesic distance). Via stop_cldak.
  • loss="powerstress": Three parameter theta, power transformations of dissimilarities, fitted distances and weights. Via stop_powerstress.
  • loss="bcmds": Three parameter theta, Box-Cox transformations of dissimilarities, fitted distances and weights. Via stop_bcmds.
  • loss="apstress": Three parameter theta, power transformations of dissimilarities, fitted distances and weights. Via stop_apstress.
  • loss="spmds": Four parameter theta, power transformations of dissimilarities, fitted distances and weights and neighborhood parametr tau. Via stop_spmds.
  • loss="spmdda_k": Five parameter theta, power transformations for dissimilarities, fitted distances and weights and neighborhood parameters k (geodesic distance) and tau. Via stop_spmddak.
  • loss="spmdda_eps": Five parameter theta, power transformations for dissimilarities, fitted distances and weights and neighborhood parameters eps (geodesic distance) and tau. Via stop_spmddae.

Structuredness Indices: Various c-structuredness as c_foo(), where foo is the name of the structuredness. See Rusch et al. (2023).

Optimization functions:

• ljoptim() ... An (adaptive) version of the Luus-Jakola random search

Methods: For most of the objects returned by the high-level functions S3 classes and methods for standard generics were implemented, including print, summary, plot, coef (extracting the hyperparameetrs).

References:

• Rusch, T., Mair, P., & Hornik, K. (2023). Structure-based hyperparameter selection with Bayesian optimization in multidimensional scaling. Statistics & Computing, 33, [28]. https://doi.org/10.1007/s11222-022-10197-w

Examples

#data(Swissroll)
#dissm<-as.matrix(dist(Swissroll[,1:3]))
#cols<-Swissroll[,4]
#structures<-c("cregularity","cdependence")
#strucweight<-c(-0.5,0.5)
#strucpars<-list(list(epsilon=10,minpts=2,scale=3),list(NULL))

dissm<-as.matrix(smacof::morse)

#Setting up structurenedness parameters
strucpars<-list(list(epsilon=10,scale=3),list(NULL))
structures<-c("cclusteredness","cdependence")

#STOPS with strain
resstrain<-stops(dissm,loss="strain",theta=1,structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=0.5,upper=5,itmax=10)
resstrain
summary(resstrain)
plot(resstrain)
#Fun fact: With strain clinearity must be 0 as the
#two principal axes are orthogonal
#and this can't be changed by taking
#the dissimilarities to a power

resstressm<-stops(dissm,loss="stress",theta=1,structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=0.5,upper=5,itmax=10,stoptype="multiplicative")
resstressm
plot(resstressm)

#STOPS with stress or smacofSym
im<-2 #this is the itmax argument used for testing; use higher itmax in practice 
resstress<-stops(dissm,loss="stress",theta=1,
structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=0.5,upper=5,itmax=im)
resstress
summary(resstress)
plot(resstress)
plot(resstress,"Shepard")

#STOPS with smacofSphere
ressph<-stops(dissm,loss="smacofSphere",theta=1,
structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=0.5,upper=5,itmax=im)
ressph
summary(ressph)
plot(ressph)

#STOPS with sammon
ressam<-stops(dissm,loss="sammon",theta=1,
structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=0.5,upper=5,itmax=im)
ressam
summary(ressam)
plot(ressam)
plot(ressam,"transplot")

#STOPS with sammon2
ressam<-stops(dissm,loss="sammon2",theta=1,
structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=0.5,upper=5,itmax=im)
ressam
summary(ressam)
plot(ressam)
plot(ressam,"Shepard")

#STOPS with elastic 
ressam<-stops(dissm,loss="elastic",theta=1,
structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=0.5,upper=5,itmax=im)
ressam
summary(ressam)
plot(ressam)
plot(ressam,"transplot")

#STOPS with sstress
resss<-stops(dissm,loss="sstress",theta=1,
structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=0.5,upper=5,itmax=im)
resss
summary(resss)
plot(resss)
plot(resss,"Shepard")
plot(resss,"transplot")

#STOPS with powerstress
respstress<-stops(dissm,loss="powerstress",
structures=structures,theta=c(1,1,1),
strucpars=strucpars,weightmat=dissm,
itmaxps=1000,optimmethod="ALJ",lower=c(0.5,0.5,1),upper=c(5,5,5),itmax=im)
respstress
summary(respstress)
plot(respstress)

#STOPS with restricted powerstress
respstressr<-stops(dissm,loss="powerstress",theta=c(1,1),
structures=structures,
strucpars=strucpars,weightmat=dissm,
itmaxps=1000,optimmethod="ALJ",lower=c(0.5,0.5),upper=c(5,5),itmax=im)
respstressr
summary(respstressr)
plot(respstressr)

#STOPS with powermds
respmds<-stops(dissm,loss="powermds",
structures=structures,theta=c(1,1),
strucpars=strucpars,weightmat=dissm,
itmaxps=1000,optimmethod="ALJ",lower=c(0.5,0.5),upper=c(5,5),itmax=im)
respmds
summary(respmds)
plot(respmds)

#STOPS with powersammon
respmds<-stops(dissm,loss="powersammon",theta=c(1,1),
structures=structures,
strucpars=strucpars,weightmat=dissm,
itmaxps=1000,optimmethod="ALJ",lower=c(0.5,0.5),upper=c(5,5),itmax=im)
respmds
summary(respmds)
plot(respmds)

#STOPS with powerelastic
respmds<-stops(dissm,loss="powerelastic",theta=c(1,1),
structures=structures,
strucpars=strucpars,weightmat=dissm,
itmaxps=1000,optimmethod="ALJ",lower=c(0.5,0.5,1),upper=c(5,5,5),itmax=im)
respmds
summary(respmds)
plot(respmds)

#STOPS with ordinal rstress 
resr<-stops(dissm,loss="rstress",type="ordinal",theta=1,
structures=structures,
strucpars=strucpars,weightmat=dissm,
itmaxps=1000,optimmethod="ALJ",lower=0.5,upper=5,itmax=im)
resr
summary(resr)
plot(resr)

#STOPS with approximated powerstress
respstressa<-stops(dissm,loss="powerstress",
structures=structures,
strucpars=strucpars,weightmat=dissm,theta=c(1,1,1),
itmaxps=1000,optimmethod="ALJ",lower=c(0.5,0.5,1),upper=c(5,5,5),itmax=im)
respstressa
summary(respstressa)
plot(respstressa,"transplot")

#STOPS with bcmds
resbcstress<-stops(dissm,loss="bcmds",
structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=c(0.5,1,0.5),upper=c(5,5,5),itmax=im)
resbcstress
summary(resbcstress)
plot(resbcstress)

#STOPS with lmds
reslmds<-stops(dissm,loss="lmds",theta=c(1,1),
structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=c(2,0),upper=c(5,1),itmax=im)
reslmds
summary(reslmds)
plot(reslmds)

#STOPS with Isomap (the k version)
resiso2<-stops(dissm,loss="isomap",theta=5,
structures=structures,
strucpars=strucpars,optimmethod="ALJ",lower=3,upper=10,itmax=im)
resiso2
summary(resiso2)
plot(resiso2)

#STOPS with Isomap (the eps version)
resiso<-stops(dissm,loss="isomapeps",
structures=structures,
theta=40,
strucpars=strucpars,optimmethod="ALJ",lower=50,upper=120,itmax=im)
resiso
summary(resiso)
plot(resiso)

strucweight<-c(-0.5,-0.5)

#STOPS with smds
resclca<-stops(dissm,loss="smds",theta=0.3,
structures=structures, strucpars=strucpars,
strucweight=strucweight,lower=0.1,upper=5,
optimmethod="pso",itmax=im*4)
resclca
summary(resclca)
plot(resclca)

#STOPS with spmds
respclca<-stops(dissm,loss="spmds",theta=c(1,1,1,1),
structures=structures,strucpars=strucpars,
strucweight=strucweight,lower=c(0.1,0.1,0.1,0.1),upper=c(5,5,5,5),
optimmethod="ALJ",itmax=im)
respclca
coef(respclca)
summary(respclca)
plot(respclca)

#STOPS with smdda and k 
rescldak<-stops(dissm,loss="smdda_k",theta=c(1,5),
structures=structures,strucpars=strucpars,
strucweight=strucweight,lower=c(0.2,4),upper=c(4,20),
optimmethod="pso",itmax=im*4)
rescldak
summary(rescldak)
plot(rescldak)

#STOPS with smdda in eps
set.seed(123)
rescldae<-stops(dissm,loss="smdda_eps",theta=c(1,2),
structures=structures,strucpars=strucpars,
strucweight=strucweight,lower=c(0.2,1),upper=c(4,10),
optimmethod="SANN",itmax=10*im,stoptype="multiplicative")
rescldae
summary(rescldae)
plot(rescldae)

#STOPS with spmdda with k (five parameters already..)
respcldak<-stops(dissm,loss="spmdda_k",theta=c(1,1,1,1,5),
structures=structures,strucpars=strucpars,
strucweight=strucweight,lower=c(0.8,0.8,0.8,0.8,4),upper=c(5,5,5,5,20),
optimmethod="tgp",itmax=im)
respcldak
summary(respcldak)
plot(respcldak)

#STOPS with spmdda with eps (five parameter already..)
set.seed(123)
respcldae<-stops(dissm,loss="spmdda_eps",theta=c(1,1,1,1,2),
structures=structures,strucpars=strucpars,
strucweight=strucweight,lower=c(0.8,0.8,0.8,0.8,1),upper=c(5,5,5,5,10),
optimmethod="tgp",itmax=im)
respcldae
summary(respcldae)
plot(respcldae)

#STOPS with clca 
set.seed(123)
resclca<-stops(dissm,loss="clca",theta=c(1),
structures=structures,strucpars=strucpars,
strucweight=strucweight,lower=0.1,upper=5,itmax=im)
resclca
summary(resclca)
plot(resclca)

#STOPS with clda with eps 
set.seed(123)
respcldae<-stops(dissm,loss="spmdda_eps",theta=c(1,1,1,1,2),
structures=structures,strucpars=strucpars,
strucweight=strucweight,lower=c(0.1,0.1,0.1,0.1,1),upper=c(5,5,5,5,10),
optimmethod="tgp",itmax=im)
respcldae
summary(respcldae)
plot(respcldae)

See Also

Useful links:

• https://r-forge.r-project.org/projects/stops/

Author(s)

Maintainer : Thomas Rusch thomas.rusch@wu.ac.at (ORCID)

Authors:

• Patrick Mair (ORCID)

Other contributors:

• Kurt Hornik Kurt.Hornik@R-project.org (ORCID) [contributor]