tclustICsol: Extracts a set of best relevant solutions obtained by `tclustIC`

Description

The function tclustICsol() takes as input an object of class tclustIC, the output of function tclustIC (that is a series of matrices which contain the values of the information criteria BIC/ICL/CLA for different values of k and c) and extracts the first best solutions. Two solutions are considered equivalent if the value of the adjusted Rand index (or the adjusted Fowlkes and Mallows index) is above a certain threshold. For each tentative solution the program checks the adjacent values of c for which the solution is stable. A matrix with adjusted Rand indexes is given for the extracted solutions.

Usage

tclustICsol(
  obj,
  whichIC = c("ALL", "MIXMIX", "MIXCLA", "CLACLA"),
  nsol = 5,
  index = c("Rand", "FM"),
  thresholdRI = 0.7,
  trace = FALSE
)

Value

The function returns an S3 object of type tclustICsol containing the following components:

call

the matched call

kk

a vector containing the values of k (number of components) which have been considered. This vector is identical to the optional argument kk (default is kk=1:5.

cc

a vector containing the values of c (values of the restriction factor) which have been considered. This vector is identical to the optional argument cc (defalt is cc=c(1, 2, 4, 8, 16, 32, 64, 128).

alpha

trimming level

whichIC

Information criteria used

MIXMIXbs

a matrix of lists of size NumberOfBestSolutions-times-5 which contains the details of the best solutions for MIXMIX (BIC). Each row refers to a solution. The information which is stored in the columns is as follows.

1st col = value of k for which solution takes place
2nd col = value of c for which solution takes place;
3rd col = a vector of length d which contains the values of c for which the solution is uniformly better.
4th col = a vector of length d + r which contains the values of c for which the solution is considered stable (i.e. for which the value of the adjusted Rand index (or the adjusted Fowlkes and Mallows index) does not go below the threshold defined in input option ThreshRandIndex).
5th col = string which contains 'true' or 'spurious'. The solution is labelled spurious if the value of the adjusted Rand index with the previous solutions is greater than ThreshRandIndex.

Remark: the field MIXMIXbs is present only if whichIC=ALL or whichIC="MIXMIX".

MIXMIXbsari

a matrix of adjusted Rand indexes (or Fowlkes and Mallows indexes) associated with the best solutions for MIXMIX. A matrix of size NumberOfBestSolutions-times-NumberOfBestSolutions whose i,j-th entry contains the adjusted Rand index between classification produced by solution i and solution j, i,j=1,2, ...,NumberOfBestSolutions.

Remark: the field MIXMIXbsari is present only if whichIC=ALL or whichIC="MIXMIX".

ARIMIX

a matrix of adjusted Rand indexes between two consecutive value of c. Matrix of size k-by-length(cc)-1. The first column contains the ARI indexes between cc[2] and cc[1] given k. The second column contains the the ARI indexes between cc[3] and cc[2] given k.

Remark: the field ARIMIX is present only if whichIC=ALL or whichIC="MIXMIX" or whichIC="MIXCLA".

MIXCLAbs

has the same structure as MIXMIXbs but referres to MIXCLA.

Remark: the field MIXCLAbs is present only if whichIC=ALL or whichIC="MIXCLA".

MIXCLAbsari

has the same structure as MIXMIXbsari but referres to MIXCLA.

Remark: the field MIXMIXbsari is present only if whichIC=ALL or whichIC="MIXCLA".

CLACLAbs

has the same structure as MIXMIXbs but referres to CLACLA.

Remark: the field CLACLAbs is present only if whichIC=ALL or whichIC="CLACLA".

CLACLAbsari

has the same structure as MIXMIXbsari but referres to CLACLA.

Remark: the field CLACLAbsari is present only if whichIC=ALL or whichIC="CLACLA".

ARICLA

Remark: the field ARICLA is present only if whichIC=ALL or whichIC="CLACLA".

x

the input data matrix of size n-times-p with which the Information Criteria were computed.

Arguments

obj

An S3 object of class tclustIC (output of tclustIC) containing the values of the information criteria BIC (MIXMIX), ICL (MIXCLA) or CLA (CLACLA), for different values of k (number of groups) and different values of c (restriction factor), for a prespecified level of trimming.

whichIC

A character value which Specifies the information criterion to use to extract best solutions. Possible values for whichIC are:

"MIXMIX": a mixture model is fitted and for computing the information criterion the mixture likelihood is used. This option corresponds to the use of the Bayesian Information criterion (BIC). In output just the matrix MIXMIX is given.
"MIXCLA": a mixture model is fitted but to compute the information criterion the classification likelihood is used. This option corresponds to the use of the Integrated Complete Likelihood (ICL). In the output just the matrix MIXCLA is given.
"CLACLA": everything is based on the classification likelihood. This information criterion will be called CLA. In the output just the matrix CLACLA is given.
"ALL": both classification and mixture likelihood are used. In this case all three information criteria CLA, ICL and BIC are computed. In the output all three matrices MIXMIX, MIXCLA and CLACLA are given.

nsol

Number of best solutions to extract from BIC/ICL matrix. The default value of NumberOfBestSolutions is 5

index

Index to use to compare partitions. If index=Rand (default) the adjusted Rand index is used, else, index="FM", the adjusted Fowlkes and Mallows index is used

thresholdRI

Threshold to identify spurious solutions - the threshold of the adjusted Rand index to use to consider two solutions as equivalent. The default value of ThreshRandIndex is 0.7

trace

Whether to print intermediate results. Default is trace=FALSE.

References

Cerioli, A., Garcia-Escudero, L.A., Mayo-Iscar, A. and Riani M. (2017). Finding the Number of Groups in Model-Based Clustering via Constrained Likelihoods, Journal of Computational and Graphical Statistics, pp. 404--416, https://doi.org/10.1080/10618600.2017.1390469.

Hubert L. and Arabie P. (1985), Comparing Partitions, Journal of Classification, Vol. 2, pp. 193--218.

Examples

Run this code


 #--- EXAMPLE 1 ------------------------------------------
 # \donttest{
 data(geyser2)
 (out <- tclustIC(geyser2, whichIC="MIXMIX", alpha=0.1))

 ##  Show the first two best solutions using as Information criterion MIXMIX
 cat("\nBest solutions using MIXMIX\n")
 outsol <- tclust::tclustICsol(out, whichIC="MIXMIX", nsol=2)
 print(outsol$MIXMIXbs)
 # }

 #--- EXAMPLE 2 ------------------------------------------
 # \donttest{
 data(flea)
 Y <- as.matrix(flea[, 1:(ncol(flea)-1)])    # select only the numeric variables
 rownames(Y) <- 1:nrow(Y)
 head(Y)

 (out <- tclustIC(Y, whichIC="CLACLA", alpha=0.1))
 ## Find the smallest value inside the table and write the corresponding
 ## values of k (number of groups) and c (restriction factor)
 inds <- which(out$CLACLA == min(out$CLACLA), arr.ind=TRUE)
 vals <- out$CLACLA[inds]
 cat("\nThe Smallest value of the IC is ", vals, 
     " and takes place for k=", out$kk[inds[1]], " and c=",   
     out$cc[inds[2]], "\n")

 ##  Show the first two best solutions using as Information criterion CLACLA
 cat("\nBest solutions using CLACLA\n")
 outsol <- tclust::tclustICsol(out, whichIC="CLACLA", nsol=2)
 print(outsol$CLACLAbs)
 
 # }

 #--- EXAMPLE 3 ------------------------------------------
 # \donttest{
 data(swissbank)
 (out <- tclustIC(swissbank, whichIC="ALL"))
 
 outsol <- tclust::tclustICsol(out, whichIC="ALL", nsol=2)
 print(outsol$CLACLAbs)
 
 # }