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Version:

1.3.0

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Description:

Package providing functions for computing a collection of clustering validation or quality criteria and partition comparison indices.

Title:

Clustering Indices

Date:

2023-11-21

Suggests:

RUnit, rbenchmark

URL:

https://gitlab.com/iagogv/clusterCrit

BugReports:

https://gitlab.com/iagogv/clusterCrit/-/issues

Collate:

main.R zzz.R

NeedsCompilation:

yes

Encoding:

UTF-8

Type:

Package

Packaged:

2023-11-21 23:09:51 UTC; iago

Author:

Iago Giné-Vázquez

[cre], Bernard Desgraupes [aut]

Maintainer:

Iago Giné-Vázquez <iago.gin-vaz@protonmail.com>

Repository:

CRAN

Date/Publication:

2023-11-23 16:00:05 UTC

~ Overview: Clustering Indices ~

Description

Package:	clusterCrit
Type:	Package
Version:	1.3.0
Date:	2023-11-22
License:	GPL (>= 2)

Details

clusterCrit computes various clustering validation or quality criteria and partition comparison indices. Type

    library(help="clusterCrit")

for more info about the available functions.

Author

Bernard Desgraupes
bernard.desgraupes@u-paris10.fr
University of Paris Ouest - Nanterre
Lab Modal'X (EA 3454)

References

For more information about the algebraic background of clustering indices and their definition, see the vignette accompanying this package. To display the vignette, type the following instruction in the R console :

> vignette("clusterCrit")

Best clustering index

Description

bestCriterion returns the best index value according to a specified criterion.

Usage

  bestCriterion(x, crit)

Arguments

x

[matrix] : a numeric vector of quality index values.

crit

[character] : a string specifying the name of the criterion which was used to compute the quality indices.

Details

Given a vector of several clustering quality index values computed with a given criterion, the function bestCriterion returns the index of the "best" one in the sense of the specified criterion. Typically, a set of data has been clusterized several times (using different algorithms or specifying a different number of clusters) and a clustering index has been calculated each time : the bestCriterion function tells which value is considered the best according to the given clustering index. For instance, if one uses the Calinski_Harabasz index, the best value is the largest one.

A list of all the supported criteria can be obtained with the getCriteriaNames function. The criterion name (crit argument) is case insensitive and can be abbreviated.

Value

The index in vector x of the best value according to the criterion specified by the crit argument.

Author

Bernard Desgraupes
bernard.desgraupes@u-paris10.fr
University of Paris Ouest - Nanterre
Lab Modal'X (EA 3454)

Examples

# Create some spheric data around three distinct centers
x <- rbind(matrix(rnorm(100, mean = 0, sd = 0.5), ncol = 2),
           matrix(rnorm(100, mean = 2, sd = 0.5), ncol = 2),
           matrix(rnorm(100, mean = 4, sd = 0.5), ncol = 2))
vals <- vector()
for (k in 2:6) {
    # Perform the kmeans algorithm
    cl <- kmeans(x, k)
    # Compute the Calinski_Harabasz index
    vals <- c(vals,as.numeric(intCriteria(x,cl$cluster,"Calinski_Harabasz")))
}
idx <- bestCriterion(vals,"Calinski_Harabasz")
cat("Best index value is",vals[idx],"\n")

Compute Concordance Matrix

Description

concordance calculates the concordance matrix between two partitions of the same data.

Usage

  concordance(part1, part2)

Arguments

part1

[vector] : the first partition vector.

part2

[vector] : the second partition vector.

Details

Given two partitions, the function concordance calculates the number of pairs classified as belonging or not belonging to the same cluster with respect to partitions part1 or part2.

Value

A 2x2 matrix of the form :

      |  P1   |  P2   |
  ____________________
   P1 |  Nyy  |  Nyn  |
   P2 |  Nny  |  Nnn  |
  ____________________

where

Nyy is the number of points belonging to the same cluster both in part1 and part2
Nyn is the number of points belonging to the same cluster in part1 but not in part2
Nny is the number of points belonging to the same cluster in part2 but not in part1
Nnn is the number of points not belonging to the same cluster both in part1 and part2

Author

Bernard Desgraupes
bernard.desgraupes@u-paris10.fr
University of Paris Ouest - Nanterre
Lab Modal'X (EA 3454)

Examples

# Generate two artificial partitions
part1<-sample(1:3,150,replace=TRUE)
part2<-sample(1:5,150,replace=TRUE)

# Compute the table of concordances and discordances
concordance(part1,part2)

Compute external clustering criteria

Description

extCriteria calculates various external clustering comparison indices.

Usage

  extCriteria(part1, part2, crit)

Arguments

part1

[vector] : the first partition vector.

part2

[vector] : the second partition vector.

crit

[vector] : a vector containing the names of the indices to compute.

Details

The function extCriteria calculates external clustering indices in order to compare two partitions. The list of all the supported criteria can be obtained with the getCriteriaNames function.

The currently available indices are :

"Czekanowski_Dice"
"Folkes_Mallows"
"Hubert"
"Jaccard"
"Kulczynski"
"McNemar"
"Phi"
"Precision"
"Rand"
"Recall"
"Rogers_Tanimoto"
"Russel_Rao"
"Sokal_Sneath1"
"Sokal_Sneath2"

All the names are case insensitive and can be abbreviated. The keyword "all" can also be used as a shortcut to calculate all the external indices.

The partition vectors should not have empty subsets. No attempt is made to verify this.

Value

A list containing the computed criteria, in the same order as in the crit argument.

Author

Bernard Desgraupes
bernard.desgraupes@u-paris10.fr
University of Paris Ouest - Nanterre
Lab Modal'X (EA 3454)

References

See the bibliography at the end of the vignette.

Examples

# Generate two artificial partitions
part1<-sample(1:3,150,replace=TRUE)
part2<-sample(1:5,150,replace=TRUE)

# Compute all the external indices
extCriteria(part1,part2,"all")
# Compute some of them
extCriteria(part1,part2,c("Rand","Folkes"))
# The names are case insensitive and can be abbreviated
extCriteria(part1,part2,c("ra","fo"))

Get clustering criteria names

Description

getCriteriaNames returns the available clustering criteria names.

Usage

  getCriteriaNames(isInternal)

Arguments

isInternal

[logical] : get internal indices if TRUE, external indices otherwise.

Details

getCriteriaNames returns a list of the available internal or external clustering indices depending on the isInternal logical argument.

The internal indices can be used in the crit argument of the intCriteria function and the external indices similarly in the extCriteria function.

Value

A character vector containing the supported criteria names.

Author

Bernard Desgraupes
bernard.desgraupes@u-paris10.fr
University of Paris Ouest - Nanterre
Lab Modal'X (EA 3454)

References

See the bibliography at the end of the vignette.

Examples

getCriteriaNames(TRUE)
getCriteriaNames(FALSE)

Compute internal clustering criteria

Description

intCriteria calculates various internal clustering validation or quality criteria.

Usage

  intCriteria(traj, part, crit)

Arguments

traj

[matrix] : the matrix of observations (trajectories).

part

[vector] : the partition vector.

crit

[vector] : a vector containing the names of the indices to compute.

Details

The function intCriteria calculates internal clustering indices. The list of all the supported criteria can be obtained with the getCriteriaNames function.

The currently available indices are :

"Ball_Hall"
"Banfeld_Raftery"
"C_index"
"Calinski_Harabasz"
"Davies_Bouldin"
"Det_Ratio"
"Dunn"
"Gamma"
"G_plus"
"GDI11"
"GDI12"
"GDI13"
"GDI21"
"GDI22"
"GDI23"
"GDI31"
"GDI32"
"GDI33"
"GDI41"
"GDI42"
"GDI43"
"GDI51"
"GDI52"
"GDI53"
"Ksq_DetW"
"Log_Det_Ratio"
"Log_SS_Ratio"
"McClain_Rao"
"PBM"
"Point_Biserial"
"Ray_Turi"
"Ratkowsky_Lance"
"Scott_Symons"
"SD_Scat"
"SD_Dis"
"S_Dbw"
"Silhouette"
"Tau"
"Trace_W"
"Trace_WiB"
"Wemmert_Gancarski"
"Xie_Beni"

All the names are case insensitive and can be abbreviated. The keyword "all" can also be used as a shortcut to calculate all the internal indices.

The GDI (Generalized Dunn Indices) are designated by the following convention: GDImn, where the integers m (1<=m<=5) and n (1<=n<=3) correspond to the between-group and within-group distances respectively. See the vignette for a comprehensive definition of the various distances. GDI alone is synonym of GDI11 and is the genuine Dunn's index.

Value

A list containing the computed criteria, in the same order as in the crit argument.

Author

Bernard Desgraupes
bernard.desgraupes@u-paris10.fr
University of Paris Ouest - Nanterre
Lab Modal'X (EA 3454)

References

See the bibliography at the end of the vignette.

Examples

# Create some data
x <- rbind(matrix(rnorm(100, mean = 0, sd = 0.5), ncol = 2),
           matrix(rnorm(100, mean = 1, sd = 0.5), ncol = 2),
           matrix(rnorm(100, mean = 2, sd = 0.5), ncol = 2))
# Perform the kmeans algorithm
cl <- kmeans(x, 3)
# Compute all the internal indices
intCriteria(x,cl$cluster,"all")
# Compute some of them
intCriteria(x,cl$cluster,c("C_index","Calinski_Harabasz","Dunn"))
# The names are case insensitive and can be abbreviated
intCriteria(x,cl$cluster,c("det","cal","dav"))

~ Overview: Clustering Indices ~

Description

Details

Author

References

See Also

Best clustering index

Description

Usage

Arguments

Details

Value

Author

See Also

Examples

Compute Concordance Matrix

Description

Usage

Arguments

Details

Value

Author

See Also

Examples

Compute external clustering criteria

Description

Usage

Arguments

Details

Value

Author

References

See Also

Examples

Get clustering criteria names

Description

Usage

Arguments

Details

Value

Author

References

See Also

Examples

Compute internal clustering criteria

Description

Usage

Arguments

Details

Value

Author

References

See Also

Examples