opt.random.par: Optimizes a set of partitions based on the value of a criterion function.

Description

The function optimizes a set partitions based on the value of a criterion function (see crit.fun for details on the criterion function) for a given network and blockmodel for Generalized blockmodeling (Žiberna, 2006) based on other parameters (see below). The optimization is done through local optimization, where the neighborhood of a partition includes all partitions that can be obtained by moving one unit from one cluster to another or by exchanging two units (from different clusters). A list of paritions can be specified (opt.these.par) or the number of clusters and a number of partitions to generate (opt.random.par).

Usage

opt.random.par(M, k, n = NULL, rep, return.all = FALSE,
   return.err = TRUE, maxiter = 50, m = NULL, approach,
   trace.iter = FALSE, switch.names = NULL,
   save.initial.param = TRUE, skip.par = NULL,
   save.checked.par = TRUE,
   merge.save.skip.par = any(!is.null(skip.par), save.checked.par),
   skip.allready.checked.par = TRUE, check.skip = "iter",
   print.iter = FALSE, max.iden = 10, seed = NULL,
   parGenFun = genRandomPar, mingr = 1, maxgr = Inf,
   addParam = list(genPajekPar = TRUE, probGenMech = NULL),
   maxTriesToFindNewPar = rep * 10, ...)

opt.these.par(M, partitions, return.all = FALSE, return.err = TRUE,
   skip.allready.checked.par = TRUE, maxiter = 50, m = NULL,
   approach, trace.iter = FALSE, switch.names = TRUE,
   save.initial.param = TRUE, skip.par = NULL,
   save.checked.par = !is.null(skip.par),
   merge.save.skip.par = all(!is.null(skip.par), save.checked.par),
   check.skip = "never", print.iter = FALSE, ...)

Arguments

A matrix representing the (usually valued) network. For now, only one-relational networks are supported. The network can have one or more modes (diferent kinds of units with no ties among themselvs. If the network is not two-mode, the matrix must be squar

The number of clustrs used in generation of partitions.

The vector of the number of units in each mode (only necessary if mode is larger than 2.

rep

The number of repetitions/different starting partitions to check.

partitions

A list of partitions. Each unique value represents one cluster. If the nework is one-mode, than this should be a vector, else a list of vectors, one for each mode.

return.all

If FALSE, solution for only the best (one or more) partition/s is/are returned.

return.err

Should the error for each optimized partition be returned

maxiter

Maximum number of iterations

Suficient value for individual cells for valued approach. Can be a number or a character string giving the name of a function. Set to "max" for implicit approach.

approach

One of the approaches described in Žiberna (2007). Possible values are: "bin" - binary blockmodeling, "val" - valued blockmodeling, "imp" - implicit blockmodeling, "ss" - sum of squares homogenity blockmodeling, and "ad" - absolute deviations homogenity b

trace.iter

Should the result of each iteration (and not only of the best one) be saved

switch.names

Should partitions that differ only in diferent names of positions be treated as different. It should be set to TRUE only if a asymetric blockmodel via BLOCKS is specified.

save.initial.param

Should the inital parameters (approach,...) be saved

skip.par

The partitions that are not allowed or were already checked and should therfire be skiped.

save.checked.par

Should the checked partitions be saved. For example, so that they can be used in the next call as skip.par

merge.save.skip.par

Should the checked partitions be merged with skiped ones?

skip.allready.checked.par

If TRUE,the partitions that were already checked when runing opt.par form different statrting points will be skiped.

check.skip

When should the check be preformed: "all" - before every call to 'crit.fun' (Time demanding) "iter" - at the end of eack iteratiton "opt.par" - before every call to opt.par, when starting the optimization of a new partition. "never" - never

print.iter

Should the progress of each iteration be printed?

max.iden

The maximum number of results that should be saved (in case there are more than max.iden results with minimal error, only the first max.iden will be saved).

seed

Optional. The seed for random generation of partitions.

parGenFun

The fucntion (object) that will generate rendom partitions. The deault fuction is genRandomPar. The function has to accept the following parameters: k (number of partitions by modes, n (number of units

mingr

Minimal alowed group size

maxgr

Maximal alowed group size

addParam

A list of additional parameters for function specified above. In the usage section they are specified for the dthe default function genRandomPar:

maxTriesToFindNewPar

The maximum number of partition try when trying to find a new partition to optimize that was not yet checked before - the default value is rep*1000

...

Argumets passed to other functions, see crit.fun

Value

MThe matrix of the network analyzed
resIf return.all = TRUE - A list of results the same as best - one best for each partition optimized
bestA list of results from crit.fun.tmp with the same elements as the result of crit.fun, only without M
errIf return.err = TRUE - The vector of errors or inconsistencies of the emplirical network with the ideal network for a given blockmodel (model,approach,...) and parititions
nIterThe vector of number of iterations used - one value for each starting partition that was optimized. It can show that maxiter is to low if a lot of these values have the value of maxiter
checked.parIf selected - A list of checked parititions. If merge.save.skip.par is TRUE, this list also includs the partitions in skip.par.
callThe call used to call the function.
initial.paramIf selected - The inital parameters used.

Warning

This function can be extremly slow. The time complexity is incrising with the number od units and the number of clusters. It is advaisable to firtst time the function on a smaller network.

References

ŽIBERNA, Aleš{ZIBERNA, Ales} (2007): Generalized Blockmodeling of Valued Networks. Social Networks, Jan. 2007, vol. 29, no. 1, 105-126. http://dx.doi.org/10.1016/j.socnet.2006.04.002. ŽIBERNA, Aleš{ZIBERNA, Ales}. Direct and indirect approaches to blockmodeling of valued networks in terms of regular equivalence. J. math. sociol., 2008, vol. 32, no. 1, 57-84. http://www.informaworld.com/smpp/content?content=10.1080/00222500701790207. DOREIAN, Patrick, BATAGELJ, Vladimir, FERLIGOJ, Anuška{Anuska} (2005): Generalized blockmodeling, (Structural analysis in the social sciences, 25). Cambridge [etc.]: Cambridge University Press, 2005. XV, 384 p., ISBN 0-521-84085-6. BATAGELJ, Vladimir, MRVAR, Andrej (2006): Pajek 1.11, http://vlado.fmf.uni lj.si/pub/networks/pajek/ (accessed January 6, 2006).

Examples

Run this code

n<-8 #if larger, the number of partitions increases dramaticaly,
     #as does if we increase the number of clusters
net<-matrix(NA,ncol=n,nrow=n)
clu<-rep(1:2,times=c(3,5))
tclu<-table(clu)
net[clu==1,clu==1]<-rnorm(n=tclu[1]*tclu[1],mean=0,sd=1)
net[clu==1,clu==2]<-rnorm(n=tclu[1]*tclu[2],mean=4,sd=1)
net[clu==2,clu==1]<-rnorm(n=tclu[2]*tclu[1],mean=0,sd=1)
net[clu==2,clu==2]<-rnorm(n=tclu[2]*tclu[2],mean=0,sd=1)

#we select a random parition and then optimise it

all.par<-nkpartitions(n=n, k=length(tclu))
#forming the partitions
all.par<-lapply(apply(all.par,1,list),function(x)x[[1]])
# to make a list out of the matrix

#optimizing one partition
res<-opt.par(M=net,
   clu=all.par[[sample(1:length(all.par),size=1)]],
   approach="ss",blocks="com")
plot(res) #Hopefully we get the original partition

#optimizing 10 random chosen partitions with opt.these.par
res<-opt.these.par(M=net,
   partitions=all.par[sample(1:length(all.par),size=10)],
   approach="ss", blocks="com")
plot(res) #Hopefully we get the original partition

#optimizing 10 random chosen partitions with opt.random.par
res<-opt.random.par(M=net,k=2,rep=10,approach="ss",blocks="com")
plot(res) #Hopefully we get the original partition

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