,
Patrick Mair [aut] ,
Kurt Hornik [ctb] | Title: | Structure Optimized Proximity Scaling |
|---|---|
| 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. |
| Authors: | Thomas Rusch [aut, cre] ,
Patrick Mair [aut] ,
Kurt Hornik [ctb] |
| Maintainer: | Thomas Rusch <[email protected]> |
| License: | GPL-2 | GPL-3 |
| Version: | 1.8-2 |
| Built: | 2024-11-21 05:52:49 UTC |
| Source: | https://github.com/r-forge/stops |
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).
A 69 x 70 matrix.
data(bankingCrises) in library(Ecdat)
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
c_association( confs, aggr = NULL, alpha = 0.6, C = 15, var.thr = 1e-05, zeta = NULL )c_association( confs, aggr = NULL, alpha = 0.6, C = 15, var.thr = 1e-05, zeta = NULL )
confs |
a numeric matrix or data frame |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
alpha |
an optional number of cells allowed in the X-by-Y search-grid. Default value is 0.6 |
C |
an optional number determining the starting point of the X-by-Y search-grid. When trying to partition the x-axis into X columns, the algorithm will start with at most C X clumps. Default value is 15. |
var.thr |
minimum value allowed for the variance of the input variables, since mine can not be computed in case of variance close to 0. Default value is 1e-5. |
zeta |
integer in [0,1] (?). If NULL (default) it is set to 1-MIC. It can be set to zero for noiseless functions, but the default choice is the most appropriate parametrization for general cases (as stated in Reshef et al). It provides robustness. |
a numeric value; association (aggregated maximal information coefficient MIC, see mine)
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)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)
Measures the c-clumpiness structure
c_clumpiness(conf, aggr = NULL)c_clumpiness(conf, aggr = NULL)
conf |
A numeric matrix. |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
a numeric value; clumpiness (see scagnostics)
delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_clumpiness(conf)delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_clumpiness(conf)
c-clusteredness calculates c-clusteredness as the OPTICS cordillera. The higher the more clustered.
c_clusteredness( confs, voidarg = NULL, minpts = 2, q = 2, epsilon = 2 * max(dist(confs)), distmeth = "euclidean", dmax = NULL, digits = 10, scale = 0, ... )c_clusteredness( confs, voidarg = NULL, minpts = 2, q = 2, epsilon = 2 * max(dist(confs)), distmeth = "euclidean", dmax = NULL, digits = 10, scale = 0, ... )
confs |
a numeric matrix or a dist object |
voidarg |
a placeholder to allow to pass NULL as strucpar and not interfere with the other arguments |
minpts |
The minimum number of points that must make up a cluster in OPTICS (corresponds to k in the paper). It is passed to |
q |
The norm used for the Cordillera. Defaults to 2. |
epsilon |
The epsilon parameter for OPTICS (called epsilon_max in the paper). Defaults to 2 times the maximum distance between any two points. |
distmeth |
The distance to be computed if X is not a symmetric matrix or a dist object (otherwise ignored). Defaults to Euclidean distance. |
dmax |
The winsorization value for the highest allowed reachability. If used for comparisons between different configurations this should be supplied. If no value is supplied, it is NULL (default); then dmax is taken from the data as the either epsilon or the largest reachability, whatever is smaller. |
digits |
The precision to round the raw Cordillera and the norm factor. Defaults to 10. |
scale |
Should X be scaled if it is an asymmetric matrix or data frame? Can take values TRUE or FALSE or a numeric value. If TRUE or 1, standardisation is to mean=0 and sd=1. If 2, no centering is applied and scaling of each column is done with the root mean square of each column. If 3, no centering is applied and scaling of all columns is done as X/max(standard deviation(allcolumns)). If 4, no centering is applied and scaling of all columns is done as X/max(rmsq(allcolumns)). If FALSE, 0 or any other numeric value, no standardisation is applied. Defaults to 0. |
... |
Additional arguments to be passed to |
a numeric value; clusteredness (see cordillera)
delts<-smacof::kinshipdelta dis<-smacofSym(delts)$confdist c_clusteredness(dis,minpts=3)delts<-smacof::kinshipdelta dis<-smacofSym(delts)$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
c_complexity( confs, aggr = NULL, alpha = 1, C = 15, var.thr = 1e-05, zeta = NULL )c_complexity( confs, aggr = NULL, alpha = 1, C = 15, var.thr = 1e-05, zeta = NULL )
confs |
a numeric matrix or data frame |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to min. |
alpha |
an optional number of cells allowed in the X-by-Y search-grid. Default value is 1 |
C |
an optional number determining the starting point of the X-by-Y search-grid. When trying to partition the x-axis into X columns, the algorithm will start with at most C X clumps. Default value is 15. |
var.thr |
minimum value allowed for the variance of the input variables, since mine can not be computed in case of variance close to 0. Default value is 1e-5. |
zeta |
integer in [0,1] (?). If NULL (default) it is set to 1-MIC. It can be set to zero for noiseless functions, but the default choice is the most appropriate parametrization for general cases (as stated in Reshef et al.). It provides robustness. |
a numeric value; complexity (aggregated minimum cell number MCN, see mine)
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)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)
Measures the c-convexity structure
c_convexity(conf, aggr = NULL)c_convexity(conf, aggr = NULL)
conf |
A numeric matrix. |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
a numeric value; convexity (see scagnostics)
delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_convexity(conf)delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$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
c_dependence(confs, aggr = NULL, index = 1)c_dependence(confs, aggr = NULL, index = 1)
confs |
a numeric matrix or data frame |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
index |
exponent on Euclidean distance, in (0,2] |
a numeric value; dependence (aggregated distance correlation)
x<-1:10 y<-2+3*x+rnorm(10) confs<-cbind(x,y) c_dependence(confs,1.5)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
c_faithfulness(confs, obsdiss, k = 3, ...)c_faithfulness(confs, obsdiss, k = 3, ...)
confs |
a numeric matrix or a dist object |
obsdiss |
a symmetric numeric matrix or a dist object. Must be supplied. |
k |
the number of nearest neighbours to be looked at |
... |
additional arguments passed to dist() |
a numeric value; faithfulness
delts<-smacof::kinshipdelta dis<-smacofSym(delts)$confdist c_faithfulness(dis,obsdiss=delts,k=3)delts<-smacof::kinshipdelta dis<-smacofSym(delts)$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
c_functionality( confs, aggr = NULL, alpha = 1, C = 15, var.thr = 1e-05, zeta = NULL )c_functionality( confs, aggr = NULL, alpha = 1, C = 15, var.thr = 1e-05, zeta = NULL )
confs |
a numeric matrix or data frame |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to mean |
alpha |
an optional number of cells allowed in the X-by-Y search-grid. Default value is 1 |
C |
an optional number determining the starting point of the X-by-Y search-grid. When trying to partition the x-axis into X columns, the algorithm will start with at most C X clumps. Default value is 15. |
var.thr |
minimum value allowed for the variance of the input variables, since mine can not be computed in case of variance close to 0. Default value is 1e-5. |
zeta |
integer in [0,1] (?). If NULL (default) it is set to 1-MIC. It can be set to zero for noiseless functions, but the default choice is the most appropriate parametrization for general cases (as stated in Reshef et al.). It provides robustness. |
a numeric value; functionality (aggregated maximaum edge value MEV, see mine)
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)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.
c_hierarchy(confs, voidarg = NULL, p = 2, agglmethod = "complete")c_hierarchy(confs, voidarg = NULL, p = 2, agglmethod = "complete")
confs |
a numeric matrix |
voidarg |
a placeholder to allow to pass NULL as strucpar and not interfere with the other arguments |
p |
the parameter of the Minokwski distances (p=2 euclidean and p=1 is manhattan) |
agglmethod |
the method used for creating the clustering, see |
a numeric value; hierarchy (see cl_validity)
delts<-smacof::kinshipdelta conf<-smacofSym(delts)$conf c_hierarchy(conf,p=2,agglmethod="single")delts<-smacof::kinshipdelta conf<-smacofSym(delts)$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.
c_inequality(confs, ...)c_inequality(confs, ...)
confs |
a numeric matrix or data frame |
... |
additional arguments (don't do anything) |
a numeric value; inequality (Pearsons coefficient of variation of the fitted distance matrix)
x<-1:10 y<-2+3*x+rnorm(10) z<- sin(y-x) confs<-cbind(z,y,x) c_inequality(confs)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.
c_linearity(confs, aggr = NULL)c_linearity(confs, aggr = NULL)
confs |
a numeric matrix or data frame |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
a numeric value; linearity (aggregated multiple correlation of all columns of the configuration)
x<-1:10 y<-2+3*x+rnorm(10) z<- sin(y-x) confs<-cbind(z,y,x) c_linearity(confs)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.
c_manifoldness(confs, aggr = NULL)c_manifoldness(confs, aggr = NULL)
confs |
a numeric matrix or data frame |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
a numeric value; manifoldness (aggregated maximal correlation, correlation of ACE tranformed x and y, see ace)
x<--100:100 y<-sqrt(100^2-x^2) confs<-cbind(x,y) c_manifoldness(confs)x<--100:100 y<-sqrt(100^2-x^2) confs<-cbind(x,y) c_manifoldness(confs)
wrapper for getting the mine coefficients
c_mine(confs, master = NULL, alpha = 0.6, C = 15, var.thr = 1e-05, zeta = NULL)c_mine(confs, master = NULL, alpha = 0.6, C = 15, var.thr = 1e-05, zeta = NULL)
confs |
a numeric matrix or data frame with two columns |
master |
the master column |
alpha |
an optional number of cells allowed in the X-by-Y search-grid. Default value is 0.6 |
C |
an optional number determining the starting point of the X-by-Y search-grid. When trying to partition the x-axis into X columns, the algorithm will start with at most C X clumps. Default value is 15. |
var.thr |
minimum value allowed for the variance of the input variables, since mine can not be computed in case of variance close to 0. Default value is 1e-5. |
zeta |
integer in [0,1] (?). If NULL (default) it is set to 1-MIC. It can be set to zero for noiseless functions, but the default choice is the most appropriate parametrization for general cases (as stated in Reshef et al. SOM; they call it epsilon in the paper). It provides robustness. |
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
c_nonmonotonicity( confs, aggr = NULL, alpha = 1, C = 15, var.thr = 1e-05, zeta = NULL )c_nonmonotonicity( confs, aggr = NULL, alpha = 1, C = 15, var.thr = 1e-05, zeta = NULL )
confs |
a numeric matrix or data frame |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
alpha |
an optional number of cells allowed in the X-by-Y search-grid. Default value is 1 |
C |
an optional number determining the starting point of the X-by-Y search-grid. When trying to partition the x-axis into X columns, the algorithm will start with at most C X clumps. Default value is 15. |
var.thr |
minimum value allowed for the variance of the input variables, since mine can not be computed in case of variance close to 0. Default value is 1e-5. |
zeta |
integer in [0,1] (?). If NULL (default) it is set to 1-MIC. It can be set to zero for noiseless functions, but the default choice is the most appropriate parametrization for general cases (as stated in Reshef et al. SOM). It provides robustness. |
a numeric value; nonmonotonicity (aggregated maximal asymmetric score MAS, see mine)
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)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)
Measures the c-outlying structure
c_outlying(conf, aggr = NULL)c_outlying(conf, aggr = NULL)
conf |
A numeric matrix. |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
a numeric value; outlying (see scagnostics)
delts<-smacof::kinshipdelta conf3<-smacof::smacofSym(delts,ndim=3)$conf c_outlying(conf3)delts<-smacof::kinshipdelta conf3<-smacof::smacofSym(delts,ndim=3)$conf c_outlying(conf3)
c-regularity calculates c-regularity as 1 - OPTICS cordillera for k=2. The higher the more regular.
c_regularity( confs, voidarg = NULL, q = 1, epsilon = 2 * max(dist(confs)), distmeth = "euclidean", dmax = NULL, digits = 10, scale = 0, ... )c_regularity( confs, voidarg = NULL, q = 1, epsilon = 2 * max(dist(confs)), distmeth = "euclidean", dmax = NULL, digits = 10, scale = 0, ... )
confs |
a numeric matrix or a dist object |
voidarg |
a placeholder to allow to pass NULL as strucpar and not interfere with the other arguments |
q |
The norm used for the Cordillera. Defaults to 1 (and should always be 1 imo). |
epsilon |
The epsilon parameter for OPTICS (called epsilon_max in the paper). Defaults to 2 times the maximum distance between any two points. |
distmeth |
The distance to be computed if X is not a symmetric matrix or a dist object (otherwise ignored). Defaults to Euclidean distance. |
dmax |
The winsorization value for the highest allowed reachability. If used for comparisons this should be supplied. If no value is supplied, it is NULL (default), then dmax is taken from the data as minimum of epsilon or the largest reachability. |
digits |
The precision to round the raw Cordillera and the norm factor. Defaults to 10. |
scale |
Should X be scaled if it is an asymmetric matrix or data frame? Can take values TRUE or FALSE or a numeric value. If TRUE or 1, standardisation is to mean=0 and sd=1. If 2, no centering is applied and scaling of each column is done with the root mean square of each column. If 3, no centering is applied and scaling of all columns is done as X/max(standard deviation(allcolumns)). If 4, no centering is applied and scaling of all columns is done as X/max(rmsq(allcolumns)). If FALSE, 0 or any other numeric value, no standardisation is applied. Defaults to 0. |
... |
Additional arguments to be passed to |
a numeric value; regularity
hpts<-expand.grid(seq(-5,5),seq(-5,5)) c_regularity(hpts) hpts2<-cbind(jitter(hpts[,1]),jitter(hpts[,2])) c_regularity(hpts2)hpts<-expand.grid(seq(-5,5),seq(-5,5)) c_regularity(hpts) hpts2<-cbind(jitter(hpts[,1]),jitter(hpts[,2])) c_regularity(hpts2)
Measures the c-skinniness structure
c_skinniness(conf, aggr = NULL)c_skinniness(conf, aggr = NULL)
conf |
A numeric matrix. |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
a numeric value; skinniness (see scagnostics)
delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_skinniness(conf)delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_skinniness(conf)
Measures the c-sparsity structure
c_sparsity(conf, aggr = NULL)c_sparsity(conf, aggr = NULL)
conf |
A numeric matrix. |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
a numeric value; sparsity (see scagnostics)
delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_sparsity(conf)delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_sparsity(conf)
Measures the c-striatedness structure
c_striatedness(conf, aggr = NULL)c_striatedness(conf, aggr = NULL)
conf |
A numeric matrix. |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
a numeric value; striatedness (see scagnostics)
delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_striatedness(conf)delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_striatedness(conf)
Measures the c-stringiness structure
c_stringiness(conf, aggr = NULL)c_stringiness(conf, aggr = NULL)
conf |
A numeric matrix. |
aggr |
the aggregation function for configurations of more than two dimensions. Defaults to max. |
a numeric value; stringiness (see scagnostics)
delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_stringiness(conf)delts<-smacof::kinshipdelta conf<-smacof::smacofSym(delts)$conf plot(conf,pch=19,asp=1) c_stringiness(conf)
calculate k nearest neighbours from a distance matrix
knn_dist(dis, k)knn_dist(dis, k)
dis |
distance matrix |
k |
number of nearest neighbours (Note that with a tie, the function returns the alphanumerically first one!) |
Adaptive means that the search space reduction factors in the number of iterations; makes convergence faster at about 100 iterations
ljoptim( x, fun, ..., red = ifelse(adaptive, 0.99, 0.95), lower, upper, acc = 1e-06, accd = 1e-04, itmax = 1000, verbose = 0, adaptive = TRUE )ljoptim( x, fun, ..., red = ifelse(adaptive, 0.99, 0.95), lower, upper, acc = 1e-06, accd = 1e-04, itmax = 1000, verbose = 0, adaptive = TRUE )
x |
optional starting values |
fun |
function to minimize |
... |
additional arguments to be passed to the function to be optimized |
red |
value of the reduction of the search region |
lower |
The lower contraints of the search region |
upper |
The upper contraints of the search region |
acc |
if the numerical accuracy of two successive target function values is below this, stop the optimization; defaults to 1e-6 |
accd |
if the width of the search space is below this, stop the optimization; defaults to 1e-4 |
itmax |
maximum number of iterations |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
adaptive |
should the adaptive version be used? defaults to TRUE. |
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)
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) res2fbana <- 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
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.
data(Pendigits500)data(Pendigits500)
A data frame with 500 rows and 17 variables
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)
From A. Izenman (2010) Modern multivariate statistical techniques. Springer.
S3 plot method for stops objects
## S3 method for class 'stops' plot(x, plot.type = "confplot", main, asp = 1, ...)## S3 method for class 'stops' plot(x, plot.type = "confplot", main, asp = 1, ...)
x |
an object of class stops |
plot.type |
String indicating which type of plot to be produced: "confplot", "resplot", "Shepard", "stressplot", "bubbleplot" (see details) |
main |
the main title of the plot |
asp |
aspect ratio of x/y axis; defaults to 1; setting to 1 will lead to an accurate represenation of the fitted distances. |
... |
Further plot arguments passed: see 'plot.smacof' and 'plot' for detailed information. Details: See plot.smacofP |
no return value, just plots
This uses an approximation to power stress that can make use of smacof as workhorse. Free parameters are kappa, lambda and nu.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of parameters to optimize over. Must be of length three, with the first the kappa argument, the second the lambda argument and the third the nu argument. One cannot supply upsilon and tau as of yet. Defaults to 1 1 1. |
type |
MDS type. |
ndim |
number of dimensions of the target space |
weightmat |
(optional) a binary matrix of nonnegative weights |
init |
(optional) initial configuration |
itmaxi |
number of iterations. default is 1000. |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
a character vector listing the structure indices to use. They always are called "cfoo" with foo being the structure. |
strucweight |
weight to be used for the structures; defaults to 1/number of structures |
strucpars |
a list of list of parameters for the structuredness indices; each list element corresponds to one index in the order of the appearance in structures vector. See examples. |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
which weighting to be used in the multi-objective optimization? Either 'additive' (default) or 'multiplicative'. |
registry |
registry object with c-structuredness indices. |
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
The free parameter is lambda for power transformations of the observed proximities.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; this must be a scalar of the lambda transformation for the observed proximities. |
type |
MDS type. Ignored here. |
weightmat |
(optional) a matrix of nonnegative weights. Not used. |
ndim |
number of dimensions of the target space |
init |
(optional) initial configuration |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structuredness indices to be included in the loss |
strucweight |
weight to be used for the structuredness indices; ; defaults to 1/#number of structures |
strucpars |
the parameters for the structuredness indices |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
How to construct the target function for the multi objective optimization? Either 'additive' (default) or 'multiplicative' |
itmaxi |
number of iterations. No effect here. |
add |
if TRUE dis is made to Euclidean distances |
registry |
registry object with c-structuredness indices. |
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
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.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; this must be a scalar of the lambda transformation for the observed proximities. Defaults to 1. |
type |
MDS type. Defaults ot 'ratio'. |
ndim |
number of dimensions of the target space |
weightmat |
(optional) a matrix of nonnegative weights (NOT the elscal weights) |
init |
(optional) initial configuration |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structuredness indices to be included in the loss |
strucweight |
weight to be used for the structuredness indices; ; defaults to 1/#number of structures |
strucpars |
the parameters for the structuredness indices |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
How to construct the target function for the multi objective optimization? Either 'additive' (default) or 'multiplicative' |
registry |
registry object with c-structuredness indices. |
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
Free parameter is k.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the number of shortest dissimilarities retained for a point (nearest neighbours), the isomap parameter. Must be a numeric scalar. Defaults to 3. |
type |
MDS type. Is "ratio". |
weightmat |
(optional) a matrix of nonnegative weights |
ndim |
number of dimensions of the target space |
init |
(optional) initial configuration |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structuredness indices to be included in the loss |
strucweight |
weight to be used for the structuredness indices; ; defaults to 1/#number of structures |
strucpars |
the parameters for the structuredness indices |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
How to construct the target function for the multi objective optimization? Either 'additive' (default) or 'multiplicative' |
itmaxi |
placeholder for compatibility in stops call; not used |
registry |
registry object with c-structuredness indices. |
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.
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
Free parameter is eps.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the number of shortest dissimilarities retained for a point (neighbourhood region), the isomap parameter. Defaults to the 0.1 quantile of the empirical distribution of dis. |
type |
MDS type. Is "ratio". |
weightmat |
(optional) a matrix of nonnegative weights |
ndim |
number of dimensions of the target space |
init |
(optional) initial configuration |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structuredness indices to be included in the loss |
strucweight |
weight to be used for the structuredness indices; ; defaults to 1/#number of structures |
strucpars |
the parameters for the structuredness indices |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
How to construct the target function for the multi objective optimization? Either 'additive' (default) or 'multiplicative' |
itmaxi |
placeholder for compatibility in stops call; not used |
registry |
registry object with c-structuredness indices. |
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.
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
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; the first is k (for the neighbourhood), the second tau (for the penalty) . If a scalar is given it is recycled. Defaults to 2 and 0.5. |
type |
MDS type. Ignored. |
weightmat |
(not used) |
init |
(optional) initial configuration |
ndim |
number of dimensions of the target space |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structures to look for |
strucweight |
weight to be used for the structures; defaults to 0.5 |
strucpars |
a list of parameters for the structuredness indices; each list element corresponds to one index in the order of the appeacrance in structure |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
which weighting to be used in the multi-objective optimization? Either 'additive' (default) or 'multiplicative'. |
registry |
registry object with c-structuredness indices. |
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
This is power stress with free kappa and lambda but rho is fixed to -2 and the weights are delta.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; a vector of length two where the first element is kappa (for the fitted distances), the second lambda (for the observed proximities). If a scalar for the free parameters is given it is recycled. Defaults to 1 1. |
type |
MDS type. Defaults to "ratio". |
weightmat |
(optional) a matrix of nonnegative weights |
init |
(optional) initial configuration |
ndim |
number of dimensions of the target space |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which strcutures to look for |
strucweight |
weight to be used for the structures; defaults to 0.5 |
strucpars |
a list of parameters for the structuredness indices; each list element corresponds to one index in the order of the appeacrance in structures |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
which weighting to be used in the multi-objective optimization? Either 'additive' (default) or 'multiplicative'. |
registry |
registry object with c-structuredness indices. |
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
This is power stress with free kappa and lambda but rho is fixed to 1, so no weight transformation.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; a vector of length 2 where the first element is kappa (for the fitted distances), the second lambda (for the observed proximities). If a scalar is given it is recycled. Defaults to 1,1. |
type |
MDS type. Defaults to "ratio". |
weightmat |
(optional) a matrix of nonnegative weights |
init |
(optional) initial configuration |
ndim |
number of dimensions of the target space |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structures to look for |
strucweight |
weight to be used for the structures; defaults to 0.5 |
strucpars |
a list of parameters for the structuredness indices; each list element corresponds to one index in the order of the appeacrance in structures |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
which weighting to be used in the multi-objective optimization? Either 'additive' (default) or 'multiplicative'. |
registry |
registry object with c-structuredness indices. |
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
This is power stress with free kappa and lambda but rho is fixed to -1 and the weights are delta.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; a vector of length two where the first element is kappa (for the fitted distances), the second lambda (for the observed proximities). If a scalar is given it is recycled for the free parameters. Defaults to 1 1. |
type |
MDS type. Defaults to "ratio". |
weightmat |
(optional) a matrix of nonnegative weights |
init |
(optional) initial configuration |
ndim |
number of dimensions of the target space |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structures to look for |
strucweight |
weight to be used for the structures; defaults to 0.5 |
strucpars |
a list of parameters for the structuredness indices; each list element corresponds to one index in the order of the appeacrance in structures |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
which weighting to be used in the multi-objective optimization? Either 'additive' (default) or 'multiplicative'. |
registry |
registry object with c-structuredness indices. |
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
Power stress with free kappa and lambda and rho.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; the first is kappa (for the fitted distances), the second lambda (for the observed proximities), the third nu (for the weights). If a scalar is given it is recycled. Defaults to 1 1 1. |
type |
MDS type. |
weightmat |
(optional) a matrix of nonnegative weights |
init |
(optional) initial configuration |
ndim |
number of dimensions of the target space |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
a character vector listing the structure indices to use. They always are called "cfoo" with foo being the structure. |
strucweight |
weight to be used for the structures; defaults to 1/number of structures |
strucpars |
a list of parameters for the structuredness indices; each list element corresponds to one index in the order of the appearance in structures |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
which weighting to be used in the multi-objective optimization? Either 'additive' (default) or 'multiplicative'. |
registry |
registry object with c-structuredness indices. |
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
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; the first two arguments are for kappa and lambda and should be equal (for the fitted distances and observed proximities), the third nu (for the weights). Internally the kappa and lambda are equated. If a scalar is given it is recycled (so all elements of theta are equal); if a vector of length 2 is given, it gets expanded to c(theta[1],theta[1],theta[2]). Defaults to 1 1 1. |
type |
MDS type. Defaults to "ratio". |
weightmat |
(optional) a matrix of nonnegative weights |
init |
(optional) initial configuration |
ndim |
number of dimensions of the target space |
itmaxi |
number of iterations. default is 10000. |
... |
additional arguments to be passed to the fitting procedure powerStressMin |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
a character vector listing the structure indices to use. They always are called "cfoo" with foo being the structure. |
strucweight |
weight to be used for the structures; defaults to 1/number of structures |
strucpars |
a list of list of parameters for the structuredness indices; each list element corresponds to one index in the order of the appearance in structures vector. See examples. |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
which weighting to be used in the multi-objective optimization? Either 'additive' (default) or 'multiplicative'. |
registry |
registry object with c-structuredness indices. |
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
Free parameter is kappa=2r for the fitted distances.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; this must be a scalar of the kappa=2*r transformation for the fitted distances proximities. Defaults to 1. Note that what is returned is r, not kappa. |
type |
MDS type. Default is "ratio" |
weightmat |
(optional) a matrix of nonnegative weights |
init |
(optional) initial configuration |
ndim |
number of dimensions of the target space |
itmaxi |
number of iterations. |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structuredness indices to be included in the loss |
strucweight |
weight to be used for the structuredness indices; ; defaults to 1/#number of structures |
strucpars |
the parameters for the structuredness indices |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
How to construct the target function for the multi objective optimization? Either 'additive' (default) or 'multiplicative' |
registry |
registry object with c-structuredness indices. |
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
Uses smacofx::sammon. The free parameter is lambda for power transformations of the observed proximities.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; this must be a scalar of the lambda transformation for the observed proximities. Defaults to 1. |
type |
MDS type. Ignored here. |
ndim |
number of dimensions of the target space |
init |
(optional) initial configuration |
weightmat |
a matrix of nonnegative weights. Has no effect here. |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structuredness indices to be included in the loss |
strucweight |
weight to be used for the structuredness indices; ; defaults to 1/#number of structures |
strucpars |
the parameters for the structuredness indices |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
How to construct the target function for the multi objective optimization? Either 'additive' (default) or 'multiplicative' |
registry |
registry object with c-structuredness indices. |
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
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.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; this must be a scalar of the lambda transformation for the observed proximities. Defaults to 1. |
type |
MDS type |
ndim |
number of dimensions of the target space |
weightmat |
(optional) a matrix of nonnegative weights |
init |
(optional) initial configuration |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structuredness indices to be included in the loss |
strucweight |
weight to be used for the structuredness indices; ; defaults to 1/#number of structures |
strucpars |
the parameters for the structuredness indices |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
How to construct the target function for the multi objective optimization? Either 'additive' (default) or 'multiplicative'. |
registry |
registry object with c-structuredness indices. |
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
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.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; this must be a scalar of the lambda transformation for the observed proximities. Defaults to 1. |
type |
MDS type. |
ndim |
number of dimensions of the target space |
weightmat |
(optional) a matrix of nonnegative weights |
init |
(optional) initial configuration |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structuredness indices to be included in the loss |
strucweight |
weight to be used for the structuredness indices; ; defaults to 1/#number of structures |
strucpars |
the parameters for the structuredness indices |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
How to construct the target function for the multi objective optimization? Either 'additive' (default) or 'multiplicative' |
registry |
registry object with c-structuredness indices. |
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
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.
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector; must be a scalar for the lambda (proximity) transformation. Defaults to 1. |
type |
MDS type. Defaults ot 'ratio'. |
ndim |
number of dimensions of the target space |
weightmat |
(optional) a matrix of nonnegative weights |
init |
(optional) initial configuration |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting |
structures |
which structuredness indices to be included in the loss |
stressweight |
weight to be used for the fit measure; defaults to 1 |
strucweight |
weight to be used for the structuredness indices; ; defaults to 1/#number of structures |
strucpars |
the parameters for the structuredness indices |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
How to construct the target function for the multi objective optimization? Either 'additive' (default) or 'multiplicative' |
registry |
registry object with c-structuredness indices. |
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
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)).
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 )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 )
dis |
numeric matrix or dist object of a matrix of proximities |
theta |
the theta vector of powers; this must be a scalar of the lambda transformation for the observed proximities. Defaults to 1. Note that the lambda here works as a multiplicator of 2 (as sstress has f(delta^2)). |
type |
MDS type. |
weightmat |
(optional) a matrix of nonnegative weights |
init |
(optional) initial configuration |
ndim |
the number of dimensions of the target space |
itmaxi |
number of iterations |
... |
additional arguments to be passed to the fitting procedure |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which structuredness indices to be included in the loss |
strucweight |
weight to be used for the structuredness indices; ; defaults to 1/#number of structures |
strucpars |
the parameters for the structuredness indices |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
stoptype |
How to construct the target function for the multi objective optimization? Either 'additive' (default) or 'multiplicative' |
registry |
registry object with c-structuredness indices. |
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
stoploss( obj, stressweight = 1, structures, strucweight = rep(-1/length(structures), length(structures)), strucpars, stoptype = c("additive", "multiplicative"), verbose = 0, registry = struc_reg )stoploss( obj, stressweight = 1, structures, strucweight = rep(-1/length(structures), length(structures)), strucpars, stoptype = c("additive", "multiplicative"), verbose = 0, registry = struc_reg )
obj |
object returned inside a stop_* function. Uses the stress.m slot for getting the stress. |
stressweight |
weight to be used for the fit measure; defaults to 1 |
structures |
which c-structuredness indices to be included in the loss |
strucweight |
the weights of the structuredness indices; defaults to -1/#number of structures |
strucpars |
a list of parameters to be passed to the c-structuredness indices in the same order as the values in structures. If the index has no parameters or you want to use the defaults, supply NULL. (alternatively a named list that has the structure name as the element name). |
stoptype |
what type of weighted combination should be used? Can be 'additive' or 'multiplicative'. |
verbose |
verbose output |
registry |
an object of class registry. This can be used to add additional c-structuredness indices. Defaults ot the registry created via .onLoad in zzz.R |
a list with calculated stoploss ($stoploss), structuredness indices ($strucinidices) and hyperparameters ($parameters and $theta)
This allows to fit STOPS models as described in Rusch, Mair, Hornik (2023).
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, ... )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, ... )
dis |
numeric matrix or dist object of a matrix of proximities |
loss |
which loss function to be used for fitting, defaults to stress. |
theta |
hyperparameter vector starting values for the transformation functions. If the length is smaller than the number of hyperparameters for the MDS version the vector gets recycled (see the corresponding stop_XXX function or the vignette for how theta must look like exactly for each loss). If larger than the number of hyperparameters for the MDS method, an error is thrown. If completely missing theta is set to 1 and recycled. |
type |
type of MDS optimal scaling (implicit transformation). One of "ratio", "interval" or "ordinal". Default is "ratio". Not every type can be used with every loss, only ratio works with all. |
structures |
character vector of which c-structuredness indices should be considered; if missing no structure is considered. |
ndim |
number of dimensions of the target space |
weightmat |
(optional) a matrix of nonnegative weights; defaults to 1 for all off diagonals |
init |
(optional) initial configuration |
stressweight |
weight to be used for the fit measure; defaults to 1 |
strucweight |
vector of weights to be used for the c-structuredness indices (in the same order as in structures); defaults to -1/length(structures) for each index |
strucpars |
(possibly named with the structure). Metaparameters for the structuredness indices (gamma in the article). It's safest for it be a list of lists with the named arguments for the structuredness indices and the order of the lists must be like the order of structures. So something like this |
optimmethod |
What solver to use. Currently supported are Bayesian optimization with Gaussian Process priors and Kriging ("Kriging", see |
lower |
The lower contraints of the search region. Needs to be a numeric vector of the same length as the parameter vector theta. |
upper |
The upper contraints of the search region. Needs to be a numeric vector of the same length as the parameter vector theta. |
verbose |
numeric value hat prints information on the fitting process; >2 is very verbose. |
stoptype |
which aggregation for the multi objective target function? Either 'additive' (default) or 'multiplicative' |
initpoints |
number of initial points to fit the surrogate model for Bayesian optimization; default is 10. |
itmax |
maximum number of iterations of the outer optimization (for theta) or number of steps of Bayesian optimization; default is 50. We recommend a higher number for ALJ (around 150). Note that due to the inner workings of some solvers, this may or may not correspond to the actual number of function evaluations performed (or PS models fitted). E.g., with tgp the actual number of function evaluation of the PS method is between itmax and 6*itmax as tgp samples 1-6 candidates from the posterior and uses the best candidate. For pso it is the number of particles s times itmax. For cmaes it is usually a bit higher than itmax. This currently may get overruled by a control argument if it is used (and then set to either ewhat is supplie dby control or to the default of the method). |
itmaxps |
maximum number of iterations of the inner optimization (to obtain the PS configuration) |
model |
a character specifying the surrogate model to use. For Kriging it specifies the covariance kernel for the GP prior; see |
control |
a control argument passed to the outer optimization procedure. Will override any other control arguents passed, especially verbose and itmax. For the effect of control, see the functions pomp::sannbox for SANN and pso::psoptim for pso, cmaes::cma_es for cmaes, dfoptim::hjkb for hjk and the nloptr docs for the algorithms direct, stogo, cobyla, crs2lm, isres, mlsl, neldermead, sbplx. |
registry |
an object of class registry containing the c-structuredness indices. Defaults to the what is created .onLoad. |
... |
additional arguments passed to the outer optimization procedures (not fully tested). |
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).
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
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) res1data(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
A swiss roll data example where 150 data points are arranged on a swiss roll embedded in a 3D space.
data(Swissroll)data(Swissroll)
A data frame with 150 rows and 4 columns
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)
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.
tgpoptim( x, fun, ..., initpoints = 10, lower, upper, acc = 1e-08, itmax = 10, verbose = 0, model = "bgp" )tgpoptim( x, fun, ..., initpoints = 10, lower, upper, acc = 1e-08, itmax = 10, verbose = 0, model = "bgp" )
x |
optional starting values |
fun |
function to minimize |
... |
additional arguments to be passed to the function to be optimized |
initpoints |
the number of points to sample initially to fit the surrogate model |
lower |
The lower contraints of the search region |
upper |
The upper contraints of the search region |
acc |
if the numerical accuracy of two successive target function values is below this, stop the optimization; defaults to 1e-8 |
itmax |
maximum number of iterations |
verbose |
numeric value hat prints information on the fitting process; >2 is extremely verbose |
model |
which surrogate model class to use (currently uses defaults only, will extend this to tweak the model) |
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
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) res2fbana <- 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