Title:	Structure Optimized Proximity Scaling
Version:	1.9-1
Maintainer:	Thomas Rusch <thomas.rusch@wu.ac.at>
Description:	Methods that use flexible variants of multidimensional scaling (MDS) which incorporate parametric nonlinear distance transformations and trade-off the goodness-of-fit fit with structure considerations to find optimal hyperparameters, also known as structure optimized proximity scaling (STOPS) (Rusch, Mair & Hornik, 2023,<doi:10.1007/s11222-022-10197-w>). The package contains various functions, wrappers, methods and classes for fitting, plotting and displaying different 1-way MDS models with ratio, interval, ordinal optimal scaling in a STOPS framework. These cover essentially the functionality of the package smacofx, including Torgerson (classical) scaling with power transformations of dissimilarities, SMACOF MDS with powers of dissimilarities, Sammon mapping with powers of dissimilarities, elastic scaling with powers of dissimilarities, spherical SMACOF with powers of dissimilarities, (ALSCAL) s-stress MDS with powers of dissimilarities, r-stress MDS, MDS with powers of dissimilarities and configuration distances, elastic scaling powers of dissimilarities and configuration distances, Sammon mapping powers of dissimilarities and configuration distances, power stress MDS (POST-MDS), approximate power stress, Box-Cox MDS, local MDS, Isomap, curvilinear component analysis (CLCA), curvilinear distance analysis (CLDA) and sparsified (power) multidimensional scaling and (power) multidimensional distance analysis (experimental models from smacofx influenced by CLCA). All of these models can also be fit by optimizing over hyperparameters based on goodness-of-fit fit only (i.e., no structure considerations). The package further contains functions for optimization, specifically the adaptive Luus-Jaakola algorithm and a wrapper for Bayesian optimization with treed Gaussian process with jumps to linear models, and functions for various c-structuredness indices. Hyperparameter optimization can be done with a number of techniques but we recommend either Bayesian optimization or particle swarm. For using "Kriging", users need to install a version of the archived 'DiceOptim' R package.
Depends:	R (≥ 3.5.0), smacofx
Imports:	acepack, clue, cmaes, cordillera, dfoptim, energy, minerva, nloptr, pomp, pso, registry, scagnostics, smacof, tgp, vegan
Enhances:	stats
Suggests:	R.rsp, DiceOptim, DiceKriging
License:	GPL-2 | GPL-3
LazyData:	true
URL:	https://r-forge.r-project.org/projects/stops/
VignetteBuilder:	R.rsp
Encoding:	UTF-8
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2025-04-28 08:44:54 UTC; trusch
Author:	Thomas Rusch [aut, cre], Patrick Mair [aut], Kurt Hornik [ctb]
Repository:	CRAN
Date/Publication:	2025-04-28 09:10:02 UTC

stops: Structure Optimized Proximity Scaling

Description

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

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

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]

See Also

Useful links:

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

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)

Banking Crises Distances

Description

Matrix of Jaccard distances between 70 countries (Hungary and Greece were combined to be the same observation) based on their binary time series of having had a banking crises in a year from 1800 to 2010 or not. See data(bankingCrises) in package Ecdat for more info. The last column is Reinhart & Rogoffs classification as a low (3), middle- (2) or high-income country (1).

Format

A 69 x 70 matrix.

Source

data(bankingCrises) in library(Ecdat)

Pen digits

Description

These data are a random sample of 500 of the 10992 pendigits data from Alimoglu (1996). The original data were from 44 writers who handwrote 250 times the digits 0,...,9. The digits were written inside a rectangular box with a resolution of 500 x 500 pixels and the first 10 per writer were ignored for further analysis. This led to 10992 digits. They were recorded in small time intervals by following the trajectory of the pen on the 500 x 500 grid and then normalized. From the normalized trajectory 8 points (x and y axis position) were randomly selected for each handwritten digit, leading to 16 predictors variables. We extarcted a random sample of 500 of them.

Usage

data(Pendigits500)

Format

A data frame with 500 rows and 17 variables

Details

The variables are

• The rownames of Pendigits500 refer to the data point of the 10992 original data

• V1-V16: trajectory points (x, y coordinate) of the grid

• digits: The digit actually written (the label)

Source

From A. Izenman (2010) Modern multivariate statistical techniques. Springer.

Swiss roll

Description

A swiss roll data example where 150 data points are arranged on a swiss roll embedded in a 3D space.

Usage

data(Swissroll)

Format

A data frame with 150 rows and 4 columns

Details

A data frame with the variables (columns)

• x The x axis coordinate for each point

• y The y axis coordinate for each point

• z The z axis coordinate for each point

• col a color code for each point with points along the y axis having the same color (based on the viridis palette)

S3 method for stops objects

Description

S3 method for stops objects

Usage

## S3 method for class 'stops'
biplotmds(object, extvar, scale = TRUE)

Arguments

Details

If a model for individual differences is provided, the external variables are regressed on the group stimulus space configurations. For objects returned from 'biplotmds' we use the plot method in biplotmds. In the biplot called with plot() only the relative length of the vectors and their direction matters. Using the vecscale argument in plot() the user can control for the relative length of the vectors. If 'vecscale = NULL', the 'vecscale()' function from the 'candisc' package is used which tries to automatically calculate the scale factor so that the vectors approximately fill the same space as the configuration. In this method vecscale should usually be smaller than the one used in smacof by a factor of 0.1.

Value

Returns an object belonging to classes 'mlm' and 'mdsbi'. See 'lm' for details. R2vec: Vector containing the R2 values. See also biplotmds for the plot method.

MDS Bootstrap for stops objects

Description

Performs a bootstrap on an MDS solution. It works for derived dissimilarities only, i.e. generated by the call dist(data). The original data matrix needs to be provided, as well as the type of dissimilarity measure used to compute the input dissimilarities (note we cannot as of yet have any dissimilarity matrix).

Usage

## S3 method for class 'stops'
bootmds(
  object,
  data,
  method.dat = "pearson",
  nrep = 100,
  alpha = 0.05,
  verbose = FALSE,
  ...
)

Arguments

Details

In order to examine the stability solution of an MDS, a bootstrap on the raw data can be performed. This results in confidence ellipses in the configuration plot. The ellipses are returned as list which allows users to produce (and further customize) the plot by hand. See bootmds for more.

Value

An object of class 'smacofboot', see bootmds. With values

• cov: Covariances for ellipse computation

• bootconf: Configurations bootstrap samples

• stressvec: Bootstrap stress values

• bootci: Stress bootstrap percentile confidence interval

• spp: Stress per point (based on stress.en)

• stab: Stability coefficient

Examples

dats <- na.omit(PVQ40[,1:5])
diss <- dist(t(dats))   ## Euclidean distances 
fit <- stops(diss,loss="rstress",itmax=5,lower=0.2,upper=3)       
set.seed(123)
resboot <- bootmds(fit, dats, method.dat = "euclidean", nrep = 2)
resboot

c-association calculates the c-association based on the maximal information coefficient We define c-association as the aggregated association between any two columns in confs

Description

c-association calculates the c-association based on the maximal information coefficient We define c-association as the aggregated association between any two columns in confs

Usage

c_association(
  confs,
  aggr = NULL,
  alpha = 0.6,
  C = 15,
  var.thr = 1e-05,
  zeta = NULL
)

Arguments

Value

a numeric value; association (aggregated maximal information coefficient MIC, see mine)

Examples

x<-seq(-3,3,length.out=200)
y<-sqrt(3^2-x^2)
z<- sin(y-x)
confs<-cbind(x,y,z)
c_association(confs)

c-clumpiness

Description

Measures the c-clumpiness structure

Usage

c_clumpiness(conf, aggr = NULL)

Arguments

Value

a numeric value; clumpiness (see scagnostics)

Examples

delts<-smacof::kinshipdelta
conf<-smacof::smacofSym(delts)$conf
plot(conf,pch=19,asp=1)
c_clumpiness(conf)

c-clusteredness calculates c-clusteredness as the OPTICS cordillera. The higher the more clustered.

Description

c-clusteredness calculates c-clusteredness as the OPTICS cordillera. The higher the more clustered.

Usage

c_clusteredness(
  confs,
  voidarg = NULL,
  minpts = 2,
  q = 2,
  epsilon = 2 * max(dist(confs)),
  distmeth = "euclidean",
  dmax = NULL,
  digits = 10,
  scale = 0,
  ...
)

Arguments

Value

a numeric value; clusteredness (see cordillera)

Examples

delts<-smacof::kinshipdelta
dis<-smacofSym(delts)$confdist
c_clusteredness(dis,minpts=3)

c-complexity Calculates the c-complexity based on the minimum cell number We define c-complexity as the aggregated minimum cell number between any two columns in confs This is one of few c-structuredness indices not between 0 and 1, but can be between 0 and (theoretically) infinity

Description

c-complexity Calculates the c-complexity based on the minimum cell number We define c-complexity as the aggregated minimum cell number between any two columns in confs This is one of few c-structuredness indices not between 0 and 1, but can be between 0 and (theoretically) infinity

Usage

c_complexity(
  confs,
  aggr = NULL,
  alpha = 1,
  C = 15,
  var.thr = 1e-05,
  zeta = NULL
)

Arguments

Value

a numeric value; complexity (aggregated minimum cell number MCN, see mine)

Examples

x<-seq(-3,3,length.out=200)
y<-sqrt(3^2-x^2)
z<- sin(y-x)
confs<-cbind(x,y,z)
c_complexity(confs)

c-convexity

Description

Measures the c-convexity structure

Usage

c_convexity(conf, aggr = NULL)

Arguments

Value

a numeric value; convexity (see scagnostics)

Examples

delts<-smacof::kinshipdelta
conf<-smacof::smacofSym(delts)$conf
plot(conf,pch=19,asp=1)
c_convexity(conf)

c-dependence calculates c-dependence as the aggregated distance correlation of each pair if nonidentical columns

Description

c-dependence calculates c-dependence as the aggregated distance correlation of each pair if nonidentical columns

Usage

c_dependence(confs, aggr = NULL, index = 1)

Arguments

Value

a numeric value; dependence (aggregated distance correlation)

Examples

x<-1:10
y<-2+3*x+rnorm(10)
confs<-cbind(x,y)
c_dependence(confs,1.5)

c-faithfulness calculates the c-faithfulness based on the index by Chen and Buja 2013 (M_adj) with equal input neigbourhoods

Description

c-faithfulness calculates the c-faithfulness based on the index by Chen and Buja 2013 (M_adj) with equal input neigbourhoods

Usage

c_faithfulness(confs, obsdiss, k = 3, ...)

Arguments

Value

a numeric value; faithfulness

Examples

delts<-smacof::kinshipdelta
dis<-smacofSym(delts)$confdist
c_faithfulness(dis,obsdiss=delts,k=3)

c-functionality calculates the c-functionality based on the maximum edge value We define c-functionality as the aggregated functionality between any two columns of confs

Description

c-functionality calculates the c-functionality based on the maximum edge value We define c-functionality as the aggregated functionality between any two columns of confs

Usage

c_functionality(
  confs,
  aggr = NULL,
  alpha = 1,
  C = 15,
  var.thr = 1e-05,
  zeta = NULL
)

Arguments

Value

a numeric value; functionality (aggregated maximaum edge value MEV, see mine)

Examples

x<-seq(-3,3,length.out=200)
y<-sqrt(3^2-x^2)
z<- sin(y-x)
confs<-cbind(x,y,z)
c_functionality(confs)

c-hierarchy captures how well a partition/ultrametric (obtained by hclust) explains the configuration distances. Uses variance explained for euclidean distances and deviance explained for everything else.

Description

c-hierarchy captures how well a partition/ultrametric (obtained by hclust) explains the configuration distances. Uses variance explained for euclidean distances and deviance explained for everything else.

Usage

c_hierarchy(confs, voidarg = NULL, p = 2, agglmethod = "complete")

Arguments

Value

a numeric value; hierarchy (see cl_validity)

Examples

delts<-smacof::kinshipdelta
conf<-smacofSym(delts)$conf
c_hierarchy(conf,p=2,agglmethod="single")

c-inequality Calculates c-inequality (as in an economic measure of inequality) as Pearsons coefficient of variation of the fitted distance matrix. This can help with avoiding degenerate solutions. This is one of few c-structuredness indices not between 0 and 1, but 0 and infinity.

Description

c-inequality Calculates c-inequality (as in an economic measure of inequality) as Pearsons coefficient of variation of the fitted distance matrix. This can help with avoiding degenerate solutions. This is one of few c-structuredness indices not between 0 and 1, but 0 and infinity.

Usage

c_inequality(confs, ...)

Arguments

Value

a numeric value; inequality (Pearsons coefficient of variation of the fitted distance matrix)

Examples

x<-1:10
y<-2+3*x+rnorm(10)
z<- sin(y-x)
confs<-cbind(z,y,x)
c_inequality(confs)

c-linearity calculates c-linearity as the aggregated multiple correlation of all columns of the configuration.

Description

c-linearity calculates c-linearity as the aggregated multiple correlation of all columns of the configuration.

Usage

c_linearity(confs, aggr = NULL)

Arguments

Value

a numeric value; linearity (aggregated multiple correlation of all columns of the configuration)

Examples

x<-1:10
y<-2+3*x+rnorm(10)
z<- sin(y-x)
confs<-cbind(z,y,x)
c_linearity(confs)

c-manifoldness calculates c-manifoldness as the aggregated maximal correlation coefficient (i.e., Pearson correlation of the ACE transformed variables) of all pairwise combinations of two different columns in confs. If there is an NA (happens usually when the optimal transformation of any variable is a constant and therefore the covariance is 0 but also one of the sds in the denominator), it gets skipped.

Description

c-manifoldness calculates c-manifoldness as the aggregated maximal correlation coefficient (i.e., Pearson correlation of the ACE transformed variables) of all pairwise combinations of two different columns in confs. If there is an NA (happens usually when the optimal transformation of any variable is a constant and therefore the covariance is 0 but also one of the sds in the denominator), it gets skipped.

Usage

c_manifoldness(confs, aggr = NULL)

Arguments

Value

a numeric value; manifoldness (aggregated maximal correlation, correlation of ACE tranformed x and y, see ace)

Examples

x<--100:100
y<-sqrt(100^2-x^2)
confs<-cbind(x,y)
c_manifoldness(confs)

wrapper for getting the mine coefficients

Description

wrapper for getting the mine coefficients

Usage

c_mine(confs, master = NULL, alpha = 0.6, C = 15, var.thr = 1e-05, zeta = NULL)

Arguments

c-nonmonotonicity calculates the c-nonmonotonicity based on the maximum asymmetric score We define c-nonmonotonicity as the aggregated nonmonotonicity between any two columns in confs this is one of few c-structuredness indices not between 0 and 1

Description

c-nonmonotonicity calculates the c-nonmonotonicity based on the maximum asymmetric score We define c-nonmonotonicity as the aggregated nonmonotonicity between any two columns in confs this is one of few c-structuredness indices not between 0 and 1

Usage

c_nonmonotonicity(
  confs,
  aggr = NULL,
  alpha = 1,
  C = 15,
  var.thr = 1e-05,
  zeta = NULL
)

Arguments

Value

a numeric value; nonmonotonicity (aggregated maximal asymmetric score MAS, see mine)

Examples

x<-seq(-3,3,length.out=200)
y<-sqrt(3^2-x^2)
z<- sin(y-x)
confs<-cbind(x,y,z)
c_nonmonotonicity(confs)

c-outlying

Description

Measures the c-outlying structure

Usage

c_outlying(conf, aggr = NULL)

Arguments

Value

a numeric value; outlying (see scagnostics)

Examples

delts<-smacof::kinshipdelta
conf3<-smacof::smacofSym(delts,ndim=3)$conf
c_outlying(conf3)

c-regularity calculates c-regularity as 1 - OPTICS cordillera for k=2. The higher the more regular.

Description

c-regularity calculates c-regularity as 1 - OPTICS cordillera for k=2. The higher the more regular.

Usage

c_regularity(
  confs,
  voidarg = NULL,
  q = 1,
  epsilon = 2 * max(dist(confs)),
  distmeth = "euclidean",
  dmax = NULL,
  digits = 10,
  scale = 0,
  ...
)

Arguments

Value

a numeric value; regularity

Examples

hpts<-expand.grid(seq(-5,5),seq(-5,5))
c_regularity(hpts)
hpts2<-cbind(jitter(hpts[,1]),jitter(hpts[,2]))
c_regularity(hpts2)

c-shepardness calculates the c-shepardness as the correlation between a loess smoother of the transformed distances and the transformed dissimilarities

Description

c-shepardness calculates the c-shepardness as the correlation between a loess smoother of the transformed distances and the transformed dissimilarities

Usage

c_shepardness(object, voidarg = NULL)

Arguments

Value

a numeric value

Examples

delts<-smacof::kinshipdelta
res<-smacofx::postmds(delts)
c_shepardness(res)

c-skinniness

Description

Measures the c-skinniness structure

Usage

c_skinniness(conf, aggr = NULL)

Arguments

Value

a numeric value; skinniness (see scagnostics)

Examples

delts<-smacof::kinshipdelta
conf<-smacof::smacofSym(delts)$conf
plot(conf,pch=19,asp=1)
c_skinniness(conf)

c-sparsity

Description

Measures the c-sparsity structure

Usage

c_sparsity(conf, aggr = NULL)

Arguments

Value

a numeric value; sparsity (see scagnostics)

Examples

delts<-smacof::kinshipdelta
conf<-smacof::smacofSym(delts)$conf
plot(conf,pch=19,asp=1)
c_sparsity(conf)

c-striatedness

Description

Measures the c-striatedness structure

Usage

c_striatedness(conf, aggr = NULL)

Arguments

Value

a numeric value; striatedness (see scagnostics)

Examples

delts<-smacof::kinshipdelta
conf<-smacof::smacofSym(delts)$conf
plot(conf,pch=19,asp=1)
c_striatedness(conf)

c-stringiness

Description

Measures the c-stringiness structure

Usage

c_stringiness(conf, aggr = NULL)

Arguments

Value

a numeric value; stringiness (see scagnostics)

Examples

delts<-smacof::kinshipdelta
conf<-smacof::smacofSym(delts)$conf
plot(conf,pch=19,asp=1)
c_stringiness(conf)

S3 coef method for stops objects

Description

S3 coef method for stops objects

Usage

## S3 method for class 'stops'
coef(object, ...)

Arguments

Value

a vector of hyperparmeters theta

MDS Jackknife for stops objects

Description

These functions perform an MDS Jackknife and plot the corresponding solution.

Usage

## S3 method for class 'stops'
jackmds(object, eps = 1e-06, itmax = 5000, verbose = FALSE)

Arguments

Details

In order to examine the stability solution of an MDS, a Jackknife on the configurations can be performed (see de Leeuw & Meulman, 1986) and plotted. The plot shows the jackknife configurations which are connected to their centroid. In addition, the original configuration (transformed through Procrustes) is plotted. The Jackknife function itself returns also a stability measure (as ratio of between and total variance), a measure for cross validity, and the dispersion around the original smacof solution.

Note that this jackknife only resamples the configuration given the selected hyperparameters, so uncertainty with respect to the hyperparameter selection is not incorporated.

Value

An object of class 'smacofJK', see jackmds. With values

• smacof.conf: Original configuration

• jackknife.confboot: An array of n-1 configuration matrices for each Jackknife MDS solution

• comparison.conf: Centroid Jackknife configurations (comparison matrix)

• cross: Cross validity

• stab: Stability coefficient

• disp: Dispersion

• loss: Value of the loss function (just used internally)

• ndim: Number of dimensions

• call: Model call

• niter: Number of iterations

• nobj: Number of objects

Examples

diso<-kinshipdelta
fit <- stops(diso,loss="stress",lower=1,upper=5)
res.jk <- jackmds(fit) 
plot(res.jk)

calculate k nearest neighbours from a distance matrix

Description

calculate k nearest neighbours from a distance matrix

Usage

knn_dist(dis, k)

Arguments

(Adaptive) Version of Luus-Jaakola Optimization

Description

Adaptive means that the search space reduction factors in the number of iterations; makes convergence faster at about 100 iterations

Usage

ljoptim(
  x,
  fun,
  ...,
  red = ifelse(adaptive, 0.99, 0.95),
  lower,
  upper,
  acc = 1e-06,
  accd = 1e-04,
  itmax = 1000,
  verbose = 0,
  adaptive = TRUE
)

Arguments

Value

A list with the components (optim)

• par The position of the optimimum in the search space (parameters that minimize the function; argmin fun)

• value The value of the objective function at the optimum (min fun)

• counts The number of iterations performed at convergence with entries fnction for the number of iterations and gradient which is always NA at the moment

• convergence 0 successful completion by the accd or acc criterion, 1 indicate iteration limit was reached, 99 is a problem

• message is NULL (only for compatibility or future use)

Examples

fbana <- function(x) {
x1 <- x[1]
x2 <- x[2]
100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
res1<-ljoptim(c(-1.2,1),fbana,lower=-5,upper=5,accd=1e-16,acc=1e-16)
res1

set.seed(210485)
fwild <- function (x) 10*sin(0.3*x)*sin(1.3*x^2) + 0.00001*x^4 + 0.2*x+80
plot(fwild, -50, 50, n = 1000, main = "ljoptim() minimising 'wild function'")
res2<-ljoptim(50, fwild,lower=-50,upper=50,adaptive=FALSE,accd=1e-16,acc=1e-16)
points(res2$par,res2$value,col="red",pch=19)
res2

function for lookup that partially matched and ignores cases and punctuation

Description

function for lookup that partially matched and ignores cases and punctuation

Usage

match_partial_ignorecase_nopunct(lookup, entry, ...)

Arguments

S3 plot method for stops objects

Description

S3 plot method for stops objects

Usage

## S3 method for class 'stops'
plot(x, plot.type = "confplot", main, asp = 1, ...)

Arguments

Value

no return value, just plots

S3 print method for stops objects

Description

S3 print method for stops objects

Usage

## S3 method for class 'stops'
print(x, ...)

Arguments

Value

no return value, just prints

S3 print method for summary.stops

Description

S3 print method for summary.stops

Usage

## S3 method for class 'summary.stops'
print(x, ...)

Arguments

Value

no return value, just prints

S3 residuals method for stops

Description

S3 residuals method for stops

Usage

## S3 method for class 'stops'
residuals(object, ...)

Arguments

Value

a vector of residuals (observed minus fitted distances)

STOPS version of approximated power stress models.

Description

This uses an approximation to power stress that can make use of smacof as workhorse. Free parameters are kappa, lambda and nu.

Usage

stop_apstress(
  dis,
  theta = c(1, 1, 1),
  type = "ratio",
  ndim = 2,
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  itmaxi = 1000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value (sqrt stress.m)

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa, lambda, nu)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of Box Cox Stress

Description

STOPS version of Box Cox Stress

Usage

stop_bcmds(
  dis,
  theta = c(1, 1, 0),
  type = "ratio",
  weightmat = NULL,
  init = NULL,
  ndim = 2,
  itmaxi = 5000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa, lambda)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of CLCA.

Description

CLCA with free lambda0 and 20 epochs. Should we add alpha0?

Usage

stop_clca(
  dis,
  theta = 3 * max(sd(dis)),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (tau)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of CLDA with free epsilon.

Description

CLDA with free lambda0 and epsilon and 20 epochs. Should we add alpha0?

Usage

stop_cldae(
  dis,
  theta = rep(3 * max(sd(dis)), 2),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (tau)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of CLDA with free k.

Description

CLDA with free lambda0 and k and 20 epochs. Should we add alpha0?

Usage

stop_cldak(
  dis,
  theta = c(3 * max(sd(dis)), nrow(dis)/4),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (tau)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of strain

Description

The free parameter is lambda for power transformations of the observed proximities.

Usage

stop_cmdscale(
  dis,
  theta = 1,
  type = "ratio",
  weightmat = NULL,
  ndim = 2,
  init = NULL,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  itmaxi = 1000,
  add = TRUE,
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the badness-of-fit value (this isn't stress here but 1-(sum_ndim(max(eigenvalues,0))/sum_n(max(eigenvalues,0)), 1-GOF[2])

• stress.m: explictly normalized stress (manually calculated)

• stoploss: the weighted loss value

• indices: the values of the structuredness indices

• parameters: the parameters used for fitting (lambda)

• fit: the returned object of the fitting procedure, which is cmdscalex object with some extra slots for the parameters and stresses

• stopobj: the stopobj object

STOPS versions of elastic scaling models (via smacofSym)

Description

The free parameter is lambda for power transformations the observed proximities. The fitted distances power is internally fixed to 1 and the power for the weights=delta is -2. Allows for a weight matrix because of smacof.

Usage

stop_elastic(
  dis,
  theta = 1,
  type = "ratio",
  ndim = 2,
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  itmaxi = 1000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 (sqrt(stress.m))

• stress.m: default normalized stress (used for STOPS)

• stoploss: the weighted loss value

• indices: the values of the structuredness indices

• parameters: the parameters used for fitting (lambda)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj objects

STOPS version of isomap to optimize over integer k.

Description

Free parameter is k.

Usage

stop_isomap1(
  dis,
  theta = 3,
  type = "ratio",
  weightmat = NULL,
  ndim = 2,
  init = NULL,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  itmaxi = NULL,
  registry = struc_reg
)

Arguments

Details

Currently this version is a bit less flexible than the vegan one, as the only allowed parameter for isomap is the theta (k in isomap, no epsilon) and the shortest path is always estimated with argument "shortest". Also note that fragmentedOK is always set to TRUE which means that for theta that is too small only the largest conected group will be analyzed. If that's not wanted just set the theta higher.

Value

A list with the components

• stress: Not really stress but 1-GOF[2] where GOF is the second element returned from smacofx::cmdscale (the sum of the first ndim eigenvalues divided by the sum of all absolute eigenvalues).

• stress.m: default normalized stress (sqrt explicitly normalized stress; really the stress this time)

• stoploss: the weighted loss value

• indices: the values of the structuredness indices

• parameters: the parameters used for fitting

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of isomap over real epsilon.

Description

Free parameter is eps.

Usage

stop_isomap2(
  dis,
  theta = stats::quantile(dis, 0.1),
  type = "ratio",
  weightmat = NULL,
  ndim = 2,
  init = NULL,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  itmaxi = NULL,
  registry = struc_reg
)

Arguments

Details

Currently this version is a bit less flexible than the vegan one, as the only allowed parameter for isomap is the theta (epsilon in isomap) and the shortest path is always estimated with argument "shortest". Also note that fragmentedOK is always set to TRUE which means that for theta that is too small only the largest conected group will be analyzed. If that's not wanted just set the theta higher.

Value

A list with the components

• stress: Not really stress but 1-GOF[2] where GOF is the second element returned from cmdscale (the sum of the first ndim absolute eigenvalues divided by the sum of all absolute eigenvalues).

• stress.m: default normalized stress (sqrt explicitly normalized stress; really the stress this time)

• stoploss: the weighted loss value

• indices: the values of the structuredness indices

• parameters: the parameters used for fitting

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of lMDS

Description

STOPS version of lMDS

Usage

stop_lmds(
  dis,
  theta = c(2, 0.5),
  type = "ratio",
  weightmat = NULL,
  init = NULL,
  ndim = 2,
  itmaxi = 5000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa, lambda)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of elastic scaling with powers for proximities and distances

Description

This is power stress with free kappa and lambda but rho is fixed to -2 and the weights are delta.

Usage

stop_powerelastic(
  dis,
  theta = c(1, 1),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 1e+05,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa, lambda)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of powermds

Description

This is power stress with free kappa and lambda but rho is fixed to 1, so no weight transformation.

Usage

stop_powermds(
  dis,
  theta = c(1, 1),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa, lambda)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of sammon with powers

Description

This is power stress with free kappa and lambda but rho is fixed to -1 and the weights are delta.

Usage

stop_powersammon(
  dis,
  theta = c(1, 1),
  type = "ratio",
  weightmat = NULL,
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa, lambda)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of powerstress

Description

Power stress with free kappa and lambda and rho.

Usage

stop_powerstress(
  dis,
  theta = c(1, 1, 1),
  type = "ratio",
  weightmat = NULL,
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa, lambda, nu)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of restricted powerstress

Description

STOPS version of restricted powerstress

Usage

stop_rpowerstress(
  dis,
  theta = c(1, 1, 1),
  type = "ratio",
  weightmat = NULL,
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa=lambda, nu)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of rstress

Description

Free parameter is kappa=2r for the fitted distances.

Usage

stop_rstress(
  dis,
  theta = 1,
  type = "ratio",
  weightmat = NULL,
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• indices: the values of the structuredness indices

• parameters: the parameters used for fitting

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of Sammon mapping

Description

Uses smacofx::sammon. The free parameter is lambda for power transformations of the observed proximities.

Usage

stop_sammon(
  dis,
  theta = 1,
  type = "ratio",
  ndim = 2,
  init = NULL,
  weightmat = NULL,
  itmaxi = 1000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "chierarchy", "cconvexity", "cstriatedness", "coutlying", "cskinniness", "csparsity",
    "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress/1 *sqrt stress(

• stress.m: default normalized stress

• stoploss: the weighted loss value

• indices: the values of the structuredness indices

• parameters: the parameters used for fitting

• fit: the returned object of the fitting procedure smacofx::sammon

• stopobj: the stopobj object

Another STOPS version of Sammon mapping models (via smacofSym)

Description

Uses Smacof, so it can deal with a weight matrix too. The free parameter is lambda for power transformations of the observed proximities. The fitted distances power is internally fixed to 1 and the power for the weights=delta is -1.

Usage

stop_sammon2(
  dis,
  theta = 1,
  type = "ratio",
  ndim = 2,
  weightmat = NULL,
  init = NULL,
  itmaxi = 1000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 (sqrt(stress.m))

• stress.m: default normalized stress (used for STOPS)

• stoploss: the weighted loss value

• indices: the values of the structuredness indices

• parameters: the parameters used for fitting (lambda)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS versions of smacofSphere models

Description

The free parameter is lambda for power transformations the observed proximities. The fitted distances power is internally fixed to 1 and the power for the weights is 1.

Usage

stop_smacofSphere(
  dis,
  theta = 1,
  type = "ratio",
  ndim = 2,
  weightmat = NULL,
  init = NULL,
  itmaxi = 1000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• indices: the values of the structuredness indices

• parameters: the parameters used for fitting

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of smacofSym models

Description

The free parameter is lambda for power transformations the observed proximities. The fitted distances power is internally fixed to 1 and the power for the weights is 1.

Usage

stop_smacofSym(
  dis,
  theta = 1,
  type = "ratio",
  ndim = 2,
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  itmaxi = 1000,
  ...,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "chierarchy", "cconvexity", "cstriatedness", "coutlying", "cskinniness", "csparsity",
    "cstringiness", "cclumpiness", "cinequality"),
  stressweight = 1,
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 (sqrt(stress.m))

• stress.m: default normalized stress (used for STOPS)

• stoploss: the weighted loss value

• indices: the values of the structuredness indices

• parameters: the parameters used for fitting (lambda)

• fit: the returned object of the fitting procedure

• stopobj: the stops object

STOPS version of sparsified multidimensional distance analysis for fixed eps and tau

Description

smdda with free parameters tau and epsilon.

Usage

stop_smddae(
  dis,
  theta = c(100, 100),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (tau)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of sparsified multidimensional distance analysis for fixed k and tau

Description

smdda with free parameters tau and k.

Usage

stop_smddak(
  dis,
  theta = c(100, 10),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (tau)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of sparsified MDS.

Description

smds with free tau.

Usage

stop_smds(
  dis,
  theta = c(100),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (tau)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of sparsified post multidimensional distance analysis for fixed tau and epsilon.

Description

Sparsified POST MDDA with free kappa, lambda, rho, tau and epsilon. Phew.

Usage

stop_spmddae(
  dis,
  theta = c(1, 1, 1, 100, 100),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa, lambda, nu, tau)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of sparsified post multidimensional distance analysis for fixed tau and k.

Description

Sparsified Post MDDA with free kappa, lambda, rho, tau and k. Phew.

Usage

stop_spmddak(
  dis,
  theta = c(1, 1, 1, 100, 10),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa, lambda, nu, tau)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of sparsified POST-MDS for fixed tau

Description

Sparsified power stress with free kappa, lambda, rho and tau.

Usage

stop_spmds(
  dis,
  theta = c(1, 1, 1, 100),
  type = "ratio",
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 10000,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• struc: the structuredness indices

• parameters: the parameters used for fitting (kappa, lambda, nu, tau)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

STOPS version of sstress

Description

Free parameter is lambda for the observed proximities. Fitted distances are transformed with power 2, weights have exponent of 1. Note that the lambda here works as a multiplicator of 2 (as sstress has f(delta^2)).

Usage

stop_sstress(
  dis,
  theta = 1,
  type = type,
  weightmat = 1 - diag(nrow(dis)),
  init = NULL,
  ndim = 2,
  itmaxi = 1e+05,
  ...,
  stressweight = 1,
  structures = c("cclusteredness", "clinearity", "cdependence", "cmanifoldness",
    "cassociation", "cnonmonotonicity", "cfunctionality", "ccomplexity", "cfaithfulness",
    "cregularity", "chierarchy", "cconvexity", "cstriatedness", "coutlying",
    "cskinniness", "csparsity", "cstringiness", "cclumpiness", "cinequality"),
  strucweight = rep(1/length(structures), length(structures)),
  strucpars,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  registry = struc_reg
)

Arguments

Value

A list with the components

• stress: the stress-1 value

• stress.m: default normalized stress

• stoploss: the weighted loss value

• indices: the values of the structuredness indices

• parameters: the parameters used for fitting (lambda)

• fit: the returned object of the fitting procedure

• stopobj: the stopobj object

Calculate the weighted multiobjective loss function used in STOPS

Description

Calculate the weighted multiobjective loss function used in STOPS

Usage

stoploss(
  obj,
  stressweight = 1,
  structures,
  strucweight = rep(-1/length(structures), length(structures)),
  strucpars,
  stoptype = c("additive", "multiplicative"),
  verbose = 0,
  registry = struc_reg
)

Arguments

Value

a list with calculated stoploss ($stoploss), structuredness indices ($strucinidices) and hyperparameters ($parameters and $theta)

High Level STOPS Function

Description

This allows to fit STOPS models as described in Rusch, Mair, Hornik (2023).

Usage

stops(
  dis,
  loss = "stress",
  theta = 1,
  type = "ratio",
  structures,
  ndim = 2,
  weightmat = NULL,
  init = NULL,
  stressweight = 1,
  strucweight,
  strucpars,
  optimmethod = c("SANN", "ALJ", "pso", "Kriging", "tgp", "direct", "stogo", "cobyla",
    "crs2lm", "isres", "mlsl", "neldermead", "sbplx", "hjk", "cmaes"),
  lower,
  upper,
  verbose = 0,
  stoptype = c("additive", "multiplicative"),
  initpoints = 10,
  itmax = 50,
  itmaxps = 10000,
  model,
  control,
  registry = struc_reg,
  ...
)

Arguments

Details

The combination of c-structurednes indices and stress uses the stress.m values, which are the explictly normalized stresses. Reported however is the stress-1 value which is sqrt(stress.m).

Value

A list with the components

• stoploss: the stoploss value

• optim: the object returned from the optimization procedure

• stressweight: the stressweight

• strucweight: the vector of structure weights

• call: the call

• optimmethod: The solver selected

• loss: The PS badness-of-fit function

• nobj: the number of objects in the configuration

• type: The type of stoploss scalacrisation (additive or multiplicative)

• fit: The fitted PS object (most importantly $fit$conf the fitted configuration)

• stoptype: Type of stoploss combinatio

Examples

data(kinshipdelta,package="smacof")
strucpar<-list(NULL,NULL) #parameters for indices
res1<-stops(kinshipdelta,loss="stress",
structures=c("cclumpiness","cassociation"),strucpars=strucpar,
lower=0,upper=10,itmax=10)
res1


#use higher itmax in general, we use 5 just to shorten the tests
data(BankingCrisesDistances)
strucpar<-list(c(epsilon=10,minpts=2),NULL) #parameters for indices
res1<-stops(BankingCrisesDistances[,1:69],loss="stress",verbose=0,
structures=c("cclusteredness","clinearity"),strucpars=strucpar,
lower=0,upper=10,itmax=5)
res1

strucpar<-list(list(alpha=0.6,C=15,var.thr=1e-5,zeta=NULL),
list(alpha=0.6,C=15,var.thr=1e-5,zeta=NULL))
res1<-stops(BankingCrisesDistances[,1:69],loss="stress",verbose=0,
structures=c("cfunctionality","ccomplexity"),strucpars=strucpar,
lower=0,upper=10,itmax=5)
res1

S3 summary method for stops

Description

S3 summary method for stops

Usage

## S3 method for class 'stops'
summary(object, ...)

Arguments

Value

object of class 'summary.stops'

Bayesian Optimization by a (treed) Bayesian Gaussian Process Prior (with jumps to linear models) surrogate model Essentially a wrapper for the functionality in tgp that has the same slots as optim with defaults for STOPS models.

Description

Bayesian Optimization by a (treed) Bayesian Gaussian Process Prior (with jumps to linear models) surrogate model Essentially a wrapper for the functionality in tgp that has the same slots as optim with defaults for STOPS models.

Usage

tgpoptim(
  x,
  fun,
  ...,
  initpoints = 10,
  lower,
  upper,
  acc = 1e-08,
  itmax = 10,
  verbose = 0,
  model = "bgp"
)

Arguments

Value

A list with the components (for compatibility with optim)

• par The position of the optimum in the search space (parameters that minimize the function; argmin fun).

• value The value of the objective function at the optimum (min fun). Note we do not use the last value in the candidate list but the best candidate (which can but need not coincide).

• svalue The value of the surrogate objective function at the optimal parameters

• counts The number of iterations performed at convergence with entries fnction for the number of iterations and gradient which is always NA at the moment

• convergence 0 successful completion by the accd or acc criterion, 1 indicate iteration limit was reached, 99 is a problem

• message is NULL (only for compatibility or future use)

• history the improvement history

• tgpout the output of the tgp model

Examples

fbana <- function(x) {
x1 <- x[1]
x2 <- x[2]
100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
res1<-tgpoptim(c(-1.2,1),fbana,lower=c(-5,-5),upper=c(5,5),acc=1e-16,itmax=20)
res1

fwild <- function (x) 10*sin(0.3*x)*sin(1.3*x^2) + 0.00001*x^4 + 0.2*x+80
plot(fwild, -50, 50, n = 1000, main = "Bayesian GP Optimization minimizing 'wild function'")
set.seed(210485)
res2<-tgpoptim(50, fwild,lower=-50,upper=50,acc=1e-16,itmax=20,model="btgpllm")
points(res2$par,res2$value,col="red",pch=19)
res2