ClustMMDD-package: 'ClustMMDD' : Clustering by Mixture Models for Discrete Data.
In ClustMMDD: Variable Selection in Clustering by Mixture Models for Discrete Data
Description
Details
Author(s)
References
See Also
Examples
Description
ClustMMDD stands for "Clustering by Mixture Models for Discrete Data". This package deals with the two-fold problem of variable selection and model-based unsupervised classification in discrete settings. Variable selection and classification are simultaneously solved via a model selection procedure using penalized criteria: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Integrated Completed Log-likelihood (ICL) or a general criterion with penalty function to be data-driven calibrated.
Details
Package: ClustMMDD
Type: Package
Version: 1.0.1
Date: 2015-05-18
License: GPL (>= 2)
In this package, K and S are respectively the number of clusters and the subset of variables that are relevant for clustering purposes. We assume that a clustering variable has different probability distributions in at least two clusters, and a non-clustering variable has the same distribution in all clusters. We consider a general situation with data described by P random variables X^l, l=1,\cdots,P, where each variable X^l is an unordered set ≤ft\{X^{l,1},\cdots,X^{l,ploidy}\right\} of ploidy categorical variables. For all l, the random variables X^{l,1},\cdots,X^{l,ploidy} take their values in the same set of levels. A typical example of such data comes from population genetics where each genotype of a diploid individual is constituted by ploidy = 2 unordered alleles.
The two-fold problem of clustering and variable selection is seen as a model selection problem. A specific collection of competing models associated to different values of (K, S) is defined, and are compared using penalized criteria. The penalized criteria are of the form
crit≤ft(K,S\right)=γ_n≤ft(K,S\right)+pen≤ft(K,S\right),
where
-
γ_n≤ft(K,S\right) is the maximum log-likelihood,
and pen≤ft(K,S\right) the penalty function.
The penalty functions used in this package are the following, where dim≤ft(K,S\right) is the dimension (number of free parameters) of the model defined by ≤ft(K,S\right) :
Akaike Information Criterion (AIC) :
pen≤ft(K,S\right) = dim≤ft(K,S\right)
Bayesian Information (BIC) :
pen≤ft(K,S\right) = 0.5*\log (n)*dim≤ft(K,S\right)
Integrated Complete Likelihood (ICL) :
pen≤ft(K,S\right) = 0.5*\log (n)*dim≤ft(K,S\right)+entropy≤ft(K,S\right),
where
entropy≤ft(K,S\right) = -∑_{i=1}^N∑_{k=1}^Kτ_{i,k}\log≤ft(τ_{i,k}\right)
and
τ_{i,k}=P≤ft(i\in\mathcal{C}_k\right)
.
More general penalty function :
pen≤ft(K,S\right) = α*λ*dim≤ft(K,S\right)
where
-
λ is a multiplicative parameter to be calibrated,
-
α a coefficient in [1.5,2] to be given by the user.
We propose a data driven procedure based the dimension jumb version of the so called "slope heuristics" (see Dominique Bontemps and Wilson Toussile (2013) and references therein).
The maximum log-likelihood is estimated via the Expectation and Maximisation algorithm. The maximum a posteriori classification is derived from the estimated parameters of the selected model.
Author(s)
Wilson Toussile
Maintainer: Wilson Toussile <wilson.toussile@gmail.com>
References
-
Dominique Bontemps and Wilson Toussile (2013) : Clustering and variable selection for categorical multivariate data. Electronic Journal of Statistics, Volume 7, 2344-2371, ISSN.
-
Wilson Toussile and Elisabeth Gassiat (2009) : Variable selection in model-based clustering using multilocus genotype data. Adv Data Anal Classif, Vol 3, number 2, 109-134.
See Also
The main functions :
em.cluster.RCompute an approximation of the maximum likelihood estimates of parameters using Expectation and Maximization algorithm, for a given value of (K,S). The maximum a posteriori classification is then derived.
backward.explorerGather the most competitive models using a backward-stepwise strategy.
dimJump.RPerform the data driven calibration of the penalty function via an estimation of λ. Two values are proposed and a graphic is proposed to help user in making a choice.
selectK.RPerform the selection of the number K of clusters for a given subset of clustering variables.
model.selection.RPerform a model selection from a collection of competing models.
Examples
1
2
3
4
5
6
7
8
9
10
data(genotype2)
head(genotype2)
data(genotype2_ExploredModels)
head(genotype2_ExploredModels)
#Calibration of the penalty function
outDimJump = dimJump.R(genotype2_ExploredModels, N = 1000, h = 5, header = TRUE)
cte1 = outDimJump[[1]][1]
outSlection = model.selection.R(genotype2_ExploredModels, cte = cte1, header = TRUE)
outSlection
Example output
Loading required package: Rcpp
ClustMMDD = Clustering by Mixture Models for Discrete Data.
Version 1.0.4
ClustMMDD is the R version of the stand alone c++ package named 'MixMoGenD'
that is available on www.u-psud.fr/math/~toussile.
initializing ... Loaded
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,] "109" "103" "108" "105" "107" "107" "109" "110" "107" "101" "110" "105"
[2,] "107" "106" "105" "105" "103" "104" "108" "108" "104" "105" "104" "104"
[3,] "105" "103" "101" "108" "110" "108" "106" "103" "101" "106" "107" "103"
[4,] "101" "107" "107" "107" "108" "101" "102" "105" "107" "110" "110" "101"
[5,] "106" "107" "110" "105" "103" "102" "109" "101" "103" "103" "109" "101"
[6,] "106" "109" "108" "103" "102" "106" "105" "109" "104" "107" "103" "105"
[,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20]
[1,] "101" "101" "102" "110" "109" "102" "105" "105"
[2,] "104" "105" "107" "105" "109" "107" "101" "108"
[3,] "105" "106" "108" "103" "103" "109" "105" "109"
[4,] "107" "109" "103" "110" "108" "105" "108" "105"
[5,] "110" "110" "101" "109" "102" "104" "103" "103"
[6,] "109" "101" "110" "107" "105" "104" "103" "110"
N P K S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 logLik dim entropy
1 1000 10 1 0 0 0 0 0 0 0 0 0 0 -39277.97 90 0.00000
2 1000 10 2 1 1 1 1 1 1 1 1 1 1 -38896.99 181 93.50989
3 1000 10 2 0 1 1 1 1 1 1 1 1 1 -38993.02 172 123.88414
4 1000 10 2 1 0 1 1 1 1 1 1 1 1 -38988.61 172 226.60695
5 1000 10 2 1 1 0 1 1 1 1 1 1 1 -38951.55 172 119.54232
6 1000 10 2 1 1 1 0 1 1 1 1 1 1 -38988.33 172 149.27192
N P K S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 logLik dim entropy criteria
BIC 1000 10 5 1 1 1 1 1 1 0 0 0 0 -37995.22 310 205.3947 39065.93
AIC 1000 10 5 1 1 1 1 1 1 1 1 0 0 -37843.71 382 179.5732 38225.71
ICL 1000 10 5 1 1 1 1 1 1 0 0 0 0 -37995.22 310 205.3947 39271.32
CteDim 1000 10 5 1 1 1 1 1 1 1 1 0 0 -37843.71 382 179.5732 38474.01
ClustMMDD documentation built on May 2, 2019, 2:44 p.m.
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Description Details Author(s) References See Also Examples
Description
ClustMMDD stands for "Clustering by Mixture Models for Discrete Data". This package deals with the two-fold problem of variable selection and model-based unsupervised classification in discrete settings. Variable selection and classification are simultaneously solved via a model selection procedure using penalized criteria: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Integrated Completed Log-likelihood (ICL) or a general criterion with penalty function to be data-driven calibrated.
Details
| Package: | ClustMMDD |
| Type: | Package |
| Version: | 1.0.1 |
| Date: | 2015-05-18 |
| License: | GPL (>= 2) |
In this package, K and S are respectively the number of clusters and the subset of variables that are relevant for clustering purposes. We assume that a clustering variable has different probability distributions in at least two clusters, and a non-clustering variable has the same distribution in all clusters. We consider a general situation with data described by P random variables X^l, l=1,\cdots,P, where each variable X^l is an unordered set ≤ft\{X^{l,1},\cdots,X^{l,ploidy}\right\} of ploidy categorical variables. For all l, the random variables X^{l,1},\cdots,X^{l,ploidy} take their values in the same set of levels. A typical example of such data comes from population genetics where each genotype of a diploid individual is constituted by ploidy = 2 unordered alleles.
The two-fold problem of clustering and variable selection is seen as a model selection problem. A specific collection of competing models associated to different values of (K, S) is defined, and are compared using penalized criteria. The penalized criteria are of the form
crit≤ft(K,S\right)=γ_n≤ft(K,S\right)+pen≤ft(K,S\right),
where
-
γ_n≤ft(K,S\right) is the maximum log-likelihood,
and pen≤ft(K,S\right) the penalty function.
The penalty functions used in this package are the following, where dim≤ft(K,S\right) is the dimension (number of free parameters) of the model defined by ≤ft(K,S\right) :
Akaike Information Criterion (AIC) :
pen≤ft(K,S\right) = dim≤ft(K,S\right)
Bayesian Information (BIC) :
pen≤ft(K,S\right) = 0.5*\log (n)*dim≤ft(K,S\right)
Integrated Complete Likelihood (ICL) :
pen≤ft(K,S\right) = 0.5*\log (n)*dim≤ft(K,S\right)+entropy≤ft(K,S\right),
where
entropy≤ft(K,S\right) = -∑_{i=1}^N∑_{k=1}^Kτ_{i,k}\log≤ft(τ_{i,k}\right)
and
τ_{i,k}=P≤ft(i\in\mathcal{C}_k\right)
.
More general penalty function :
pen≤ft(K,S\right) = α*λ*dim≤ft(K,S\right)
where
-
λ is a multiplicative parameter to be calibrated,
-
α a coefficient in [1.5,2] to be given by the user.
We propose a data driven procedure based the dimension jumb version of the so called "slope heuristics" (see Dominique Bontemps and Wilson Toussile (2013) and references therein).
-
The maximum log-likelihood is estimated via the Expectation and Maximisation algorithm. The maximum a posteriori classification is derived from the estimated parameters of the selected model.
Author(s)
Wilson Toussile
Maintainer: Wilson Toussile <wilson.toussile@gmail.com>
References
-
Dominique Bontemps and Wilson Toussile (2013) : Clustering and variable selection for categorical multivariate data. Electronic Journal of Statistics, Volume 7, 2344-2371, ISSN.
-
Wilson Toussile and Elisabeth Gassiat (2009) : Variable selection in model-based clustering using multilocus genotype data. Adv Data Anal Classif, Vol 3, number 2, 109-134.
See Also
The main functions :
em.cluster.RCompute an approximation of the maximum likelihood estimates of parameters using Expectation and Maximization algorithm, for a given value of (K,S). The maximum a posteriori classification is then derived.
backward.explorerGather the most competitive models using a backward-stepwise strategy.
dimJump.RPerform the data driven calibration of the penalty function via an estimation of λ. Two values are proposed and a graphic is proposed to help user in making a choice.
selectK.RPerform the selection of the number K of clusters for a given subset of clustering variables.
model.selection.RPerform a model selection from a collection of competing models.
Examples
1 2 3 4 5 6 7 8 9 10 | data(genotype2)
head(genotype2)
data(genotype2_ExploredModels)
head(genotype2_ExploredModels)
#Calibration of the penalty function
outDimJump = dimJump.R(genotype2_ExploredModels, N = 1000, h = 5, header = TRUE)
cte1 = outDimJump[[1]][1]
outSlection = model.selection.R(genotype2_ExploredModels, cte = cte1, header = TRUE)
outSlection
|
Example output
Loading required package: Rcpp
ClustMMDD = Clustering by Mixture Models for Discrete Data.
Version 1.0.4
ClustMMDD is the R version of the stand alone c++ package named 'MixMoGenD'
that is available on www.u-psud.fr/math/~toussile.
initializing ... Loaded
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,] "109" "103" "108" "105" "107" "107" "109" "110" "107" "101" "110" "105"
[2,] "107" "106" "105" "105" "103" "104" "108" "108" "104" "105" "104" "104"
[3,] "105" "103" "101" "108" "110" "108" "106" "103" "101" "106" "107" "103"
[4,] "101" "107" "107" "107" "108" "101" "102" "105" "107" "110" "110" "101"
[5,] "106" "107" "110" "105" "103" "102" "109" "101" "103" "103" "109" "101"
[6,] "106" "109" "108" "103" "102" "106" "105" "109" "104" "107" "103" "105"
[,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20]
[1,] "101" "101" "102" "110" "109" "102" "105" "105"
[2,] "104" "105" "107" "105" "109" "107" "101" "108"
[3,] "105" "106" "108" "103" "103" "109" "105" "109"
[4,] "107" "109" "103" "110" "108" "105" "108" "105"
[5,] "110" "110" "101" "109" "102" "104" "103" "103"
[6,] "109" "101" "110" "107" "105" "104" "103" "110"
N P K S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 logLik dim entropy
1 1000 10 1 0 0 0 0 0 0 0 0 0 0 -39277.97 90 0.00000
2 1000 10 2 1 1 1 1 1 1 1 1 1 1 -38896.99 181 93.50989
3 1000 10 2 0 1 1 1 1 1 1 1 1 1 -38993.02 172 123.88414
4 1000 10 2 1 0 1 1 1 1 1 1 1 1 -38988.61 172 226.60695
5 1000 10 2 1 1 0 1 1 1 1 1 1 1 -38951.55 172 119.54232
6 1000 10 2 1 1 1 0 1 1 1 1 1 1 -38988.33 172 149.27192
N P K S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 logLik dim entropy criteria
BIC 1000 10 5 1 1 1 1 1 1 0 0 0 0 -37995.22 310 205.3947 39065.93
AIC 1000 10 5 1 1 1 1 1 1 1 1 0 0 -37843.71 382 179.5732 38225.71
ICL 1000 10 5 1 1 1 1 1 1 0 0 0 0 -37995.22 310 205.3947 39271.32
CteDim 1000 10 5 1 1 1 1 1 1 1 1 0 0 -37843.71 382 179.5732 38474.01
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