CoClust: Copula-Based Clustering Algorithm
In CoClust: Copula Based Cluster Analysis
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
Examples
Description
Cluster analysis based on copula functions
Usage
1
2
3
Arguments
m
a data matrix.
dimset
the set of dimensions for which the function tries the clustering.
noc
sample size of the set for selecting the number of clusters.
copula
a copula model.
This should be one of "normal", "t", "frank", "clayton" and "gumbel". See the Details section.
fun
combination function of the pairwise Spearman's rho used to select the k-plets. The default is median
method.ma
estimation method for margins. See the Details section.
method.c
estimation method for copula. See fitCopula.
dfree
degrees of freedom for the t copula.
writeout
writes a message on the number of allocated observations every writeout observations.
penalty
Specifies the likelihood criterion used for selecting the number of clusters.
...
further parameters for fitCopula.
Details
- Usage for Frank copula:
-
CoClust(m, nmaxmarg = 2:5, noc = 4, copula = "frank",
fun = median, method.ma=c("gaussian","empirical"), method.c = "mpl",
penalty ="BICk", ...)
CoClust is a clustering algorithm that, being based on copula functions, allows to group observations according to the multivariate dependence structure of the generating process without any assumptions on the margins.
For each k in dimset the algorithm builds a sample of noc observations (rows of the data matrix m) by using the matrix of Spearman's rho correlation coefficients which are combined by means of the function fun (median by default).
The number of clusters K is selected by means of a criterion based on the likelihood of the copula fit. The switch penalty allows to select 3 different criteria; The choice LL corresponds to using
the likelihood without penalty terms. Then, the remaining observations are allocated to the clusters as follows:
1. selects a K-plet of observations on the basis of fun applied to the pairwise Spearman's rho; 2. allocates or discards the K-plet on the basis of the likelihood of the copula fit.
The estimation approach for the copula fit is semiparametric: a range of nonparametric margins and parametric copula models can be selected by the user.
The CoClust algorithm does not require to set a priori the number of clusters nor it needs a starting classification.
Notice that the dependence structure for the Gaussian and the t copula is set to exchangeable. Non structured dependence structures will be allowed in a future version.
Value
An object of S4 class "CoClust", which is a list with the following elements:
Number.of.Clusters
the number K of identified clusters.
Index.Matrix
a n.obs by (K+1) matrix where n.obs is the number of observations put in each cluster. The matrix contains the row indexes of the observations of the data matrix m.
The last column contains the log-likelihood of the copula fit.
Data.Clusters
the matrix of the final clustering.
Dependence
a list containing:
Model the copula model used for the clustering.
Param the estimated dependence parameter between clusters.
Std.Err the standard error of Param.
P.val the p-value associated to the null hypothesis H_0: theta=0.
LogLik
the maximized log-likelihood copula fit.
Est.Method
the estimation method used for the copula fit.
Opt.Method
the optimization method used for the copula fit.
LLC
the value of the LogLikelihood Criterion for each k in dimset.
Index.dimset
a list that, for each k in dimset, contains the index matrix of the initial set of nk observations used for selecting the number of clusters, together with the associated loglikelihood.
Note
The final clustering is composed of K groups in which observations of the same group are independent whereas the observations that belong to different groups and that form a K-plet are dependent.
Author(s)
Francesca Marta Lilja Di Lascio <marta.dilascio@unibz.it>,
Simone Giannerini <simone.giannerini@unibo.it>
References
Di Lascio, F.M.L. (201x). "CoClust: An R Package for Copula-based Cluster Analysis". To be submitted.
Di Lascio, F.M.L., Durante, F. and Pappada', R. (2017). "Copula-based clustering methods", Copulas and Dependence Models with Applications, p.49-67. Eds Ubeda-Flores, M., de Amo, E., Durante, F. and Fernandez Sanchez, J., Springer International Publishing. ISBN: 978-3-319-64220-8.
Di Lascio, F.M.L. and Disegna, M. (2017). "A copula-based clustering algorithm to analyse EU country diets". Knowledge-Based Systems, 132, p.72-84. DOI: 10.1016/j.knosys.2017.06.004.
Di Lascio, F.M.L. and Giannerini, S. (2016). "Clustering dependent observations with copula functions". Statistical Papers, p.1-17. DOI 10.1007/s00362-016-0822-3.
Di Lascio, F.M.L. and Giannerini, S. (2012). "A Copula-Based Algorithm for Discovering Patterns of Dependent Observations", Journal of Classification, 29(1), p.50-75.
Di Lascio, F.M.L. (2008). "Analyzing the dependence structure of microarray data: a copula-based approach". PhD thesis, Dipartimento di Scienze Statistiche, Universita' di Bologna, Italy.
Examples
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## ******************************************************************
## 1. builds a 3-variate copula with different margins
## (Gaussian, Gamma, Beta)
##
## 2. generates a data matrix xm with 15 rows and 21 columns and
## builds the matrix of the true cluster indexes
##
## 3. applies the CoClust to the rows of xm and recovers the
## multivariate dependence structure of the data
## ******************************************************************
## Step 1. **********************************************************
n <- 105 # total number of observations
n.col <- 21 # number of columns of the data matrix m
n.marg <- 3 # dimension of the copula
n.row <- n*n.marg/n.col # number of rows of the data matrix m
theta <- 10
copula <- frankCopula(theta, dim = n.marg)
mymvdc <- mvdc(copula, c("norm", "gamma", "beta"),list(list(mean=7, sd=2),
list(shape=3, rate=4), list(shape1=2, shape2=1)))
## Step 2. **********************************************************
set.seed(11)
x.samp <- rMvdc(n, mymvdc)
xm <- matrix(x.samp, nrow = n.row, ncol = n.col, byrow=TRUE)
index.true <- matrix(1:15,5,3)
colnames(index.true) <- c("Cluster 1","Cluster 2", "Cluster 3")
## Step 3. **********************************************************
clust <- CoClust(xm, dimset = 2:4, noc=2, copula="frank",
method.ma="empirical", method.c="ml",writeout=1)
clust
clust@"Number.of.Clusters"
clust@"Dependence"$Param
clust@"Data.Clusters"
index.clust <- clust@"Index.Matrix"
## compare with index.true
index.clust
index.true
##
Example output
Loading required package: copula
Number of clusters selected: 3
Allocated observations: 3
Allocated observations: 4
Allocated observations: 5
An object of class "CoClust"
Slot "Number.of.Clusters":
[1] 3
Slot "Index.Matrix":
Cluster 1 Cluster 2 Cluster 3 LogLik
[1,] 11 1 6 29.59298
[2,] 13 3 8 59.11185
[3,] 12 2 7 87.55890
[4,] 14 4 9 118.68674
[5,] 15 5 10 148.43749
Slot "Data.Clusters":
Cluster 1 Cluster 2 Cluster 3
[1,] 0.3821719 4.724571 0.1722283
[2,] 0.3911910 5.738707 0.1548273
[3,] 0.9923630 11.130341 1.3684076
[4,] 0.6133405 6.711067 0.5572253
[5,] 0.1489788 2.763910 0.3727072
[6,] 0.8220294 9.946755 0.7025062
[7,] 0.7748810 8.849824 0.7472348
[8,] 0.7060588 6.977426 0.6037493
[9,] 0.7420107 6.979874 1.2564989
[10,] 0.8868274 8.121758 0.8366584
[11,] 0.8408346 9.083846 0.8449545
[12,] 0.9265845 7.497380 0.5735631
[13,] 0.7366919 9.083588 0.8049378
[14,] 0.1854497 4.737831 0.1091059
[15,] 0.7962249 7.314255 0.5804155
[16,] 0.5226436 6.609135 0.4938606
[17,] 0.3812399 4.108089 0.3293736
[18,] 0.6755020 7.028995 0.5640552
[19,] 0.3773079 4.926126 0.4780587
[20,] 0.2413054 4.050170 0.2756642
[21,] 0.5509937 5.554924 0.5825189
[22,] 0.5547837 6.950117 0.5624433
[23,] 0.8341096 7.723815 1.2358954
[24,] 0.1245806 5.237230 0.2698407
[25,] 0.8439165 8.633602 1.0305195
[26,] 0.8290546 8.875230 0.7430665
[27,] 0.2653793 3.818821 0.3310576
[28,] 0.1377339 3.847222 0.1881491
[29,] 0.4238974 5.987543 0.4669754
[30,] 0.7442955 7.278040 0.6419422
[31,] 0.7690821 6.851152 0.5348509
[32,] 0.5766055 5.569177 0.5740944
[33,] 0.9077906 7.246912 1.6961565
[34,] 0.5948870 5.276076 0.3273010
[35,] 0.3188433 2.466374 0.2048978
[36,] 0.8563399 8.215923 1.0216487
[37,] 0.4859458 5.125675 0.4037320
[38,] 0.5840352 5.207848 0.4522179
[39,] 0.4421058 5.275799 0.4154543
[40,] 0.7105057 6.313148 0.5755700
[41,] 0.0623775 3.980188 0.1791108
[42,] 0.4427724 4.347047 0.1617050
[43,] 0.8102775 7.328941 0.8441203
[44,] 0.9520337 9.014100 1.0392218
[45,] 0.2989031 4.227565 0.2305394
[46,] 0.9201125 8.991290 1.3522166
[47,] 0.7760083 7.578709 0.8481472
[48,] 0.5374009 6.116144 0.5733275
[49,] 0.7421856 7.733539 0.7321689
[50,] 0.8619819 8.923534 1.2041696
[51,] 0.7675674 7.438398 1.0839021
[52,] 0.9134812 12.299546 1.2930689
[53,] 0.7558059 7.901530 0.9108837
[54,] 0.3538221 4.070995 0.3053536
[55,] 0.7324060 9.486247 0.7039008
[56,] 0.8761552 9.117614 0.7884164
[57,] 0.7343466 6.498987 0.6840582
[58,] 0.3253134 6.100498 0.5853185
[59,] 0.5710626 6.738952 0.3936210
[60,] 0.5760979 6.354835 0.6985677
[61,] 0.6924759 4.877017 0.5914819
[62,] 0.8750170 8.938650 0.6987183
[63,] 0.4963767 5.154385 0.5267843
[64,] 0.9845955 10.830024 1.6332640
[65,] 0.9130914 6.378303 0.7150011
[66,] 0.6379774 7.991038 0.5805825
[67,] 0.8735105 7.361490 0.7832649
[68,] 0.6784702 7.413119 0.7021784
[69,] 0.9622892 8.632043 1.1318317
[70,] 0.9638345 9.265671 1.4903069
[71,] 0.6172756 6.299267 0.8306458
[72,] 0.8349335 8.792616 0.9115916
[73,] 0.7755230 7.888000 0.7354790
[74,] 0.6527278 6.332678 0.5341079
[75,] 0.4630175 3.717388 0.2649272
[76,] 0.8449912 8.392278 2.3192944
[77,] 0.8263662 8.620581 1.3452385
[78,] 0.8194348 7.847350 1.1544766
[79,] 0.4565947 5.809143 0.5332319
[80,] 0.8729451 7.225545 0.5724901
[81,] 0.5329342 6.176113 0.4141617
[82,] 0.4477027 5.114751 0.4234471
[83,] 0.9191833 9.377256 1.5187152
[84,] 0.2842830 3.502181 0.4284995
[85,] 0.4114047 6.398566 0.1623977
[86,] 0.9633245 9.471324 1.3984225
[87,] 0.9856805 8.968840 1.3766028
[88,] 0.6509489 7.088675 1.1073758
[89,] 0.9299693 9.482104 1.1620751
[90,] 0.6456944 6.448404 0.5497347
[91,] 0.1856461 1.937598 0.2026946
[92,] 0.9422877 6.825404 0.7958724
[93,] 0.5364393 5.751602 0.2944656
[94,] 0.6440514 6.226674 0.6087897
[95,] 0.8683983 8.995176 0.9055552
[96,] 0.6618030 5.422601 0.4316463
[97,] 0.8657631 9.153244 0.8223764
[98,] 0.8635867 8.491585 1.0403472
[99,] 0.5914044 5.790188 0.4643897
[100,] 0.9022617 8.710650 0.9941284
[101,] 0.6248820 6.794992 0.4528421
[102,] 0.3686887 3.487050 0.2717204
[103,] 0.8063894 10.786327 1.3713073
[104,] 0.4984841 5.251239 0.2757156
[105,] 0.9103522 10.797712 1.0076279
Slot "Dependence":
$Copula
[1] "frank"
$Param
[1] 10.30767
$Std.Err
[1] 0.7387905
$P.value
[1] 0
Slot "LogLik":
[1] 148.4375
Slot "Est.Method":
[1] "maximum likelihood"
Slot "Opt.Method":
[1] "ml"
Slot "LLC":
2 3 4
-63.58120 -114.48603 -40.71821
Slot "Index.dimset":
$`2`
1 2 LogLik
[1,] 11 1 18.59320
[2,] 8 3 33.65943
$`3`
1 2 3 LogLik
[1,] 11 1 6 29.59298
[2,] 13 3 8 59.11185
$`4`
1 2 3 4 LogLik
[1,] 11 1 6 12 3.370454
[2,] 7 3 13 8 22.227938
[1] 3
[1] 10.30767
Cluster 1 Cluster 2 Cluster 3
[1,] 0.3821719 4.724571 0.1722283
[2,] 0.3911910 5.738707 0.1548273
[3,] 0.9923630 11.130341 1.3684076
[4,] 0.6133405 6.711067 0.5572253
[5,] 0.1489788 2.763910 0.3727072
[6,] 0.8220294 9.946755 0.7025062
[7,] 0.7748810 8.849824 0.7472348
[8,] 0.7060588 6.977426 0.6037493
[9,] 0.7420107 6.979874 1.2564989
[10,] 0.8868274 8.121758 0.8366584
[11,] 0.8408346 9.083846 0.8449545
[12,] 0.9265845 7.497380 0.5735631
[13,] 0.7366919 9.083588 0.8049378
[14,] 0.1854497 4.737831 0.1091059
[15,] 0.7962249 7.314255 0.5804155
[16,] 0.5226436 6.609135 0.4938606
[17,] 0.3812399 4.108089 0.3293736
[18,] 0.6755020 7.028995 0.5640552
[19,] 0.3773079 4.926126 0.4780587
[20,] 0.2413054 4.050170 0.2756642
[21,] 0.5509937 5.554924 0.5825189
[22,] 0.5547837 6.950117 0.5624433
[23,] 0.8341096 7.723815 1.2358954
[24,] 0.1245806 5.237230 0.2698407
[25,] 0.8439165 8.633602 1.0305195
[26,] 0.8290546 8.875230 0.7430665
[27,] 0.2653793 3.818821 0.3310576
[28,] 0.1377339 3.847222 0.1881491
[29,] 0.4238974 5.987543 0.4669754
[30,] 0.7442955 7.278040 0.6419422
[31,] 0.7690821 6.851152 0.5348509
[32,] 0.5766055 5.569177 0.5740944
[33,] 0.9077906 7.246912 1.6961565
[34,] 0.5948870 5.276076 0.3273010
[35,] 0.3188433 2.466374 0.2048978
[36,] 0.8563399 8.215923 1.0216487
[37,] 0.4859458 5.125675 0.4037320
[38,] 0.5840352 5.207848 0.4522179
[39,] 0.4421058 5.275799 0.4154543
[40,] 0.7105057 6.313148 0.5755700
[41,] 0.0623775 3.980188 0.1791108
[42,] 0.4427724 4.347047 0.1617050
[43,] 0.8102775 7.328941 0.8441203
[44,] 0.9520337 9.014100 1.0392218
[45,] 0.2989031 4.227565 0.2305394
[46,] 0.9201125 8.991290 1.3522166
[47,] 0.7760083 7.578709 0.8481472
[48,] 0.5374009 6.116144 0.5733275
[49,] 0.7421856 7.733539 0.7321689
[50,] 0.8619819 8.923534 1.2041696
[51,] 0.7675674 7.438398 1.0839021
[52,] 0.9134812 12.299546 1.2930689
[53,] 0.7558059 7.901530 0.9108837
[54,] 0.3538221 4.070995 0.3053536
[55,] 0.7324060 9.486247 0.7039008
[56,] 0.8761552 9.117614 0.7884164
[57,] 0.7343466 6.498987 0.6840582
[58,] 0.3253134 6.100498 0.5853185
[59,] 0.5710626 6.738952 0.3936210
[60,] 0.5760979 6.354835 0.6985677
[61,] 0.6924759 4.877017 0.5914819
[62,] 0.8750170 8.938650 0.6987183
[63,] 0.4963767 5.154385 0.5267843
[64,] 0.9845955 10.830024 1.6332640
[65,] 0.9130914 6.378303 0.7150011
[66,] 0.6379774 7.991038 0.5805825
[67,] 0.8735105 7.361490 0.7832649
[68,] 0.6784702 7.413119 0.7021784
[69,] 0.9622892 8.632043 1.1318317
[70,] 0.9638345 9.265671 1.4903069
[71,] 0.6172756 6.299267 0.8306458
[72,] 0.8349335 8.792616 0.9115916
[73,] 0.7755230 7.888000 0.7354790
[74,] 0.6527278 6.332678 0.5341079
[75,] 0.4630175 3.717388 0.2649272
[76,] 0.8449912 8.392278 2.3192944
[77,] 0.8263662 8.620581 1.3452385
[78,] 0.8194348 7.847350 1.1544766
[79,] 0.4565947 5.809143 0.5332319
[80,] 0.8729451 7.225545 0.5724901
[81,] 0.5329342 6.176113 0.4141617
[82,] 0.4477027 5.114751 0.4234471
[83,] 0.9191833 9.377256 1.5187152
[84,] 0.2842830 3.502181 0.4284995
[85,] 0.4114047 6.398566 0.1623977
[86,] 0.9633245 9.471324 1.3984225
[87,] 0.9856805 8.968840 1.3766028
[88,] 0.6509489 7.088675 1.1073758
[89,] 0.9299693 9.482104 1.1620751
[90,] 0.6456944 6.448404 0.5497347
[91,] 0.1856461 1.937598 0.2026946
[92,] 0.9422877 6.825404 0.7958724
[93,] 0.5364393 5.751602 0.2944656
[94,] 0.6440514 6.226674 0.6087897
[95,] 0.8683983 8.995176 0.9055552
[96,] 0.6618030 5.422601 0.4316463
[97,] 0.8657631 9.153244 0.8223764
[98,] 0.8635867 8.491585 1.0403472
[99,] 0.5914044 5.790188 0.4643897
[100,] 0.9022617 8.710650 0.9941284
[101,] 0.6248820 6.794992 0.4528421
[102,] 0.3686887 3.487050 0.2717204
[103,] 0.8063894 10.786327 1.3713073
[104,] 0.4984841 5.251239 0.2757156
[105,] 0.9103522 10.797712 1.0076279
Cluster 1 Cluster 2 Cluster 3 LogLik
[1,] 11 1 6 29.59298
[2,] 13 3 8 59.11185
[3,] 12 2 7 87.55890
[4,] 14 4 9 118.68674
[5,] 15 5 10 148.43749
Cluster 1 Cluster 2 Cluster 3
[1,] 1 6 11
[2,] 2 7 12
[3,] 3 8 13
[4,] 4 9 14
[5,] 5 10 15
CoClust documentation built on May 1, 2019, 8:01 p.m.
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Description Usage Arguments Details Value Note Author(s) References Examples
Description
Cluster analysis based on copula functions
Usage
1 2 3 |
Arguments
m |
a data matrix. |
dimset |
the set of dimensions for which the function tries the clustering. |
noc |
sample size of the set for selecting the number of clusters. |
copula |
a copula model. This should be one of "normal", "t", "frank", "clayton" and "gumbel". See the Details section. |
fun |
combination function of the pairwise Spearman's rho used to select the k-plets. The default is |
method.ma |
estimation method for margins. See the Details section. |
method.c |
estimation method for copula. See |
dfree |
degrees of freedom for the t copula. |
writeout |
writes a message on the number of allocated observations every writeout observations. |
penalty |
Specifies the likelihood criterion used for selecting the number of clusters. |
... |
further parameters for |
Details
- Usage for Frank copula:
-
CoClust(m, nmaxmarg = 2:5, noc = 4, copula = "frank", fun = median, method.ma=c("gaussian","empirical"), method.c = "mpl", penalty ="BICk", ...)
CoClust is a clustering algorithm that, being based on copula functions, allows to group observations according to the multivariate dependence structure of the generating process without any assumptions on the margins.
For each k in dimset the algorithm builds a sample of noc observations (rows of the data matrix m) by using the matrix of Spearman's rho correlation coefficients which are combined by means of the function fun (median by default).
The number of clusters K is selected by means of a criterion based on the likelihood of the copula fit. The switch penalty allows to select 3 different criteria; The choice LL corresponds to using
the likelihood without penalty terms. Then, the remaining observations are allocated to the clusters as follows:
1. selects a K-plet of observations on the basis of fun applied to the pairwise Spearman's rho; 2. allocates or discards the K-plet on the basis of the likelihood of the copula fit.
The estimation approach for the copula fit is semiparametric: a range of nonparametric margins and parametric copula models can be selected by the user. The CoClust algorithm does not require to set a priori the number of clusters nor it needs a starting classification.
Notice that the dependence structure for the Gaussian and the t copula is set to exchangeable. Non structured dependence structures will be allowed in a future version.
Value
An object of S4 class "CoClust", which is a list with the following elements:
Number.of.Clusters |
the number K of identified clusters. | |||||||||
Index.Matrix |
a n.obs by (K+1) matrix where n.obs is the number of observations put in each cluster. The matrix contains the row indexes of the observations of the data matrix | |||||||||
Data.Clusters |
the matrix of the final clustering. | |||||||||
Dependence |
a list containing:
| |||||||||
LogLik |
the maximized log-likelihood copula fit. | |||||||||
Est.Method |
the estimation method used for the copula fit. | |||||||||
Opt.Method |
the optimization method used for the copula fit. | |||||||||
LLC |
the value of the LogLikelihood Criterion for each k in | |||||||||
Index.dimset |
a list that, for each k in |
Note
The final clustering is composed of K groups in which observations of the same group are independent whereas the observations that belong to different groups and that form a K-plet are dependent.
Author(s)
Francesca Marta Lilja Di Lascio <marta.dilascio@unibz.it>,
Simone Giannerini <simone.giannerini@unibo.it>
References
Di Lascio, F.M.L. (201x). "CoClust: An R Package for Copula-based Cluster Analysis". To be submitted.
Di Lascio, F.M.L., Durante, F. and Pappada', R. (2017). "Copula-based clustering methods", Copulas and Dependence Models with Applications, p.49-67. Eds Ubeda-Flores, M., de Amo, E., Durante, F. and Fernandez Sanchez, J., Springer International Publishing. ISBN: 978-3-319-64220-8.
Di Lascio, F.M.L. and Disegna, M. (2017). "A copula-based clustering algorithm to analyse EU country diets". Knowledge-Based Systems, 132, p.72-84. DOI: 10.1016/j.knosys.2017.06.004.
Di Lascio, F.M.L. and Giannerini, S. (2016). "Clustering dependent observations with copula functions". Statistical Papers, p.1-17. DOI 10.1007/s00362-016-0822-3.
Di Lascio, F.M.L. and Giannerini, S. (2012). "A Copula-Based Algorithm for Discovering Patterns of Dependent Observations", Journal of Classification, 29(1), p.50-75.
Di Lascio, F.M.L. (2008). "Analyzing the dependence structure of microarray data: a copula-based approach". PhD thesis, Dipartimento di Scienze Statistiche, Universita' di Bologna, Italy.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | ## ******************************************************************
## 1. builds a 3-variate copula with different margins
## (Gaussian, Gamma, Beta)
##
## 2. generates a data matrix xm with 15 rows and 21 columns and
## builds the matrix of the true cluster indexes
##
## 3. applies the CoClust to the rows of xm and recovers the
## multivariate dependence structure of the data
## ******************************************************************
## Step 1. **********************************************************
n <- 105 # total number of observations
n.col <- 21 # number of columns of the data matrix m
n.marg <- 3 # dimension of the copula
n.row <- n*n.marg/n.col # number of rows of the data matrix m
theta <- 10
copula <- frankCopula(theta, dim = n.marg)
mymvdc <- mvdc(copula, c("norm", "gamma", "beta"),list(list(mean=7, sd=2),
list(shape=3, rate=4), list(shape1=2, shape2=1)))
## Step 2. **********************************************************
set.seed(11)
x.samp <- rMvdc(n, mymvdc)
xm <- matrix(x.samp, nrow = n.row, ncol = n.col, byrow=TRUE)
index.true <- matrix(1:15,5,3)
colnames(index.true) <- c("Cluster 1","Cluster 2", "Cluster 3")
## Step 3. **********************************************************
clust <- CoClust(xm, dimset = 2:4, noc=2, copula="frank",
method.ma="empirical", method.c="ml",writeout=1)
clust
clust@"Number.of.Clusters"
clust@"Dependence"$Param
clust@"Data.Clusters"
index.clust <- clust@"Index.Matrix"
## compare with index.true
index.clust
index.true
##
|
Example output
Loading required package: copula
Number of clusters selected: 3
Allocated observations: 3
Allocated observations: 4
Allocated observations: 5
An object of class "CoClust"
Slot "Number.of.Clusters":
[1] 3
Slot "Index.Matrix":
Cluster 1 Cluster 2 Cluster 3 LogLik
[1,] 11 1 6 29.59298
[2,] 13 3 8 59.11185
[3,] 12 2 7 87.55890
[4,] 14 4 9 118.68674
[5,] 15 5 10 148.43749
Slot "Data.Clusters":
Cluster 1 Cluster 2 Cluster 3
[1,] 0.3821719 4.724571 0.1722283
[2,] 0.3911910 5.738707 0.1548273
[3,] 0.9923630 11.130341 1.3684076
[4,] 0.6133405 6.711067 0.5572253
[5,] 0.1489788 2.763910 0.3727072
[6,] 0.8220294 9.946755 0.7025062
[7,] 0.7748810 8.849824 0.7472348
[8,] 0.7060588 6.977426 0.6037493
[9,] 0.7420107 6.979874 1.2564989
[10,] 0.8868274 8.121758 0.8366584
[11,] 0.8408346 9.083846 0.8449545
[12,] 0.9265845 7.497380 0.5735631
[13,] 0.7366919 9.083588 0.8049378
[14,] 0.1854497 4.737831 0.1091059
[15,] 0.7962249 7.314255 0.5804155
[16,] 0.5226436 6.609135 0.4938606
[17,] 0.3812399 4.108089 0.3293736
[18,] 0.6755020 7.028995 0.5640552
[19,] 0.3773079 4.926126 0.4780587
[20,] 0.2413054 4.050170 0.2756642
[21,] 0.5509937 5.554924 0.5825189
[22,] 0.5547837 6.950117 0.5624433
[23,] 0.8341096 7.723815 1.2358954
[24,] 0.1245806 5.237230 0.2698407
[25,] 0.8439165 8.633602 1.0305195
[26,] 0.8290546 8.875230 0.7430665
[27,] 0.2653793 3.818821 0.3310576
[28,] 0.1377339 3.847222 0.1881491
[29,] 0.4238974 5.987543 0.4669754
[30,] 0.7442955 7.278040 0.6419422
[31,] 0.7690821 6.851152 0.5348509
[32,] 0.5766055 5.569177 0.5740944
[33,] 0.9077906 7.246912 1.6961565
[34,] 0.5948870 5.276076 0.3273010
[35,] 0.3188433 2.466374 0.2048978
[36,] 0.8563399 8.215923 1.0216487
[37,] 0.4859458 5.125675 0.4037320
[38,] 0.5840352 5.207848 0.4522179
[39,] 0.4421058 5.275799 0.4154543
[40,] 0.7105057 6.313148 0.5755700
[41,] 0.0623775 3.980188 0.1791108
[42,] 0.4427724 4.347047 0.1617050
[43,] 0.8102775 7.328941 0.8441203
[44,] 0.9520337 9.014100 1.0392218
[45,] 0.2989031 4.227565 0.2305394
[46,] 0.9201125 8.991290 1.3522166
[47,] 0.7760083 7.578709 0.8481472
[48,] 0.5374009 6.116144 0.5733275
[49,] 0.7421856 7.733539 0.7321689
[50,] 0.8619819 8.923534 1.2041696
[51,] 0.7675674 7.438398 1.0839021
[52,] 0.9134812 12.299546 1.2930689
[53,] 0.7558059 7.901530 0.9108837
[54,] 0.3538221 4.070995 0.3053536
[55,] 0.7324060 9.486247 0.7039008
[56,] 0.8761552 9.117614 0.7884164
[57,] 0.7343466 6.498987 0.6840582
[58,] 0.3253134 6.100498 0.5853185
[59,] 0.5710626 6.738952 0.3936210
[60,] 0.5760979 6.354835 0.6985677
[61,] 0.6924759 4.877017 0.5914819
[62,] 0.8750170 8.938650 0.6987183
[63,] 0.4963767 5.154385 0.5267843
[64,] 0.9845955 10.830024 1.6332640
[65,] 0.9130914 6.378303 0.7150011
[66,] 0.6379774 7.991038 0.5805825
[67,] 0.8735105 7.361490 0.7832649
[68,] 0.6784702 7.413119 0.7021784
[69,] 0.9622892 8.632043 1.1318317
[70,] 0.9638345 9.265671 1.4903069
[71,] 0.6172756 6.299267 0.8306458
[72,] 0.8349335 8.792616 0.9115916
[73,] 0.7755230 7.888000 0.7354790
[74,] 0.6527278 6.332678 0.5341079
[75,] 0.4630175 3.717388 0.2649272
[76,] 0.8449912 8.392278 2.3192944
[77,] 0.8263662 8.620581 1.3452385
[78,] 0.8194348 7.847350 1.1544766
[79,] 0.4565947 5.809143 0.5332319
[80,] 0.8729451 7.225545 0.5724901
[81,] 0.5329342 6.176113 0.4141617
[82,] 0.4477027 5.114751 0.4234471
[83,] 0.9191833 9.377256 1.5187152
[84,] 0.2842830 3.502181 0.4284995
[85,] 0.4114047 6.398566 0.1623977
[86,] 0.9633245 9.471324 1.3984225
[87,] 0.9856805 8.968840 1.3766028
[88,] 0.6509489 7.088675 1.1073758
[89,] 0.9299693 9.482104 1.1620751
[90,] 0.6456944 6.448404 0.5497347
[91,] 0.1856461 1.937598 0.2026946
[92,] 0.9422877 6.825404 0.7958724
[93,] 0.5364393 5.751602 0.2944656
[94,] 0.6440514 6.226674 0.6087897
[95,] 0.8683983 8.995176 0.9055552
[96,] 0.6618030 5.422601 0.4316463
[97,] 0.8657631 9.153244 0.8223764
[98,] 0.8635867 8.491585 1.0403472
[99,] 0.5914044 5.790188 0.4643897
[100,] 0.9022617 8.710650 0.9941284
[101,] 0.6248820 6.794992 0.4528421
[102,] 0.3686887 3.487050 0.2717204
[103,] 0.8063894 10.786327 1.3713073
[104,] 0.4984841 5.251239 0.2757156
[105,] 0.9103522 10.797712 1.0076279
Slot "Dependence":
$Copula
[1] "frank"
$Param
[1] 10.30767
$Std.Err
[1] 0.7387905
$P.value
[1] 0
Slot "LogLik":
[1] 148.4375
Slot "Est.Method":
[1] "maximum likelihood"
Slot "Opt.Method":
[1] "ml"
Slot "LLC":
2 3 4
-63.58120 -114.48603 -40.71821
Slot "Index.dimset":
$`2`
1 2 LogLik
[1,] 11 1 18.59320
[2,] 8 3 33.65943
$`3`
1 2 3 LogLik
[1,] 11 1 6 29.59298
[2,] 13 3 8 59.11185
$`4`
1 2 3 4 LogLik
[1,] 11 1 6 12 3.370454
[2,] 7 3 13 8 22.227938
[1] 3
[1] 10.30767
Cluster 1 Cluster 2 Cluster 3
[1,] 0.3821719 4.724571 0.1722283
[2,] 0.3911910 5.738707 0.1548273
[3,] 0.9923630 11.130341 1.3684076
[4,] 0.6133405 6.711067 0.5572253
[5,] 0.1489788 2.763910 0.3727072
[6,] 0.8220294 9.946755 0.7025062
[7,] 0.7748810 8.849824 0.7472348
[8,] 0.7060588 6.977426 0.6037493
[9,] 0.7420107 6.979874 1.2564989
[10,] 0.8868274 8.121758 0.8366584
[11,] 0.8408346 9.083846 0.8449545
[12,] 0.9265845 7.497380 0.5735631
[13,] 0.7366919 9.083588 0.8049378
[14,] 0.1854497 4.737831 0.1091059
[15,] 0.7962249 7.314255 0.5804155
[16,] 0.5226436 6.609135 0.4938606
[17,] 0.3812399 4.108089 0.3293736
[18,] 0.6755020 7.028995 0.5640552
[19,] 0.3773079 4.926126 0.4780587
[20,] 0.2413054 4.050170 0.2756642
[21,] 0.5509937 5.554924 0.5825189
[22,] 0.5547837 6.950117 0.5624433
[23,] 0.8341096 7.723815 1.2358954
[24,] 0.1245806 5.237230 0.2698407
[25,] 0.8439165 8.633602 1.0305195
[26,] 0.8290546 8.875230 0.7430665
[27,] 0.2653793 3.818821 0.3310576
[28,] 0.1377339 3.847222 0.1881491
[29,] 0.4238974 5.987543 0.4669754
[30,] 0.7442955 7.278040 0.6419422
[31,] 0.7690821 6.851152 0.5348509
[32,] 0.5766055 5.569177 0.5740944
[33,] 0.9077906 7.246912 1.6961565
[34,] 0.5948870 5.276076 0.3273010
[35,] 0.3188433 2.466374 0.2048978
[36,] 0.8563399 8.215923 1.0216487
[37,] 0.4859458 5.125675 0.4037320
[38,] 0.5840352 5.207848 0.4522179
[39,] 0.4421058 5.275799 0.4154543
[40,] 0.7105057 6.313148 0.5755700
[41,] 0.0623775 3.980188 0.1791108
[42,] 0.4427724 4.347047 0.1617050
[43,] 0.8102775 7.328941 0.8441203
[44,] 0.9520337 9.014100 1.0392218
[45,] 0.2989031 4.227565 0.2305394
[46,] 0.9201125 8.991290 1.3522166
[47,] 0.7760083 7.578709 0.8481472
[48,] 0.5374009 6.116144 0.5733275
[49,] 0.7421856 7.733539 0.7321689
[50,] 0.8619819 8.923534 1.2041696
[51,] 0.7675674 7.438398 1.0839021
[52,] 0.9134812 12.299546 1.2930689
[53,] 0.7558059 7.901530 0.9108837
[54,] 0.3538221 4.070995 0.3053536
[55,] 0.7324060 9.486247 0.7039008
[56,] 0.8761552 9.117614 0.7884164
[57,] 0.7343466 6.498987 0.6840582
[58,] 0.3253134 6.100498 0.5853185
[59,] 0.5710626 6.738952 0.3936210
[60,] 0.5760979 6.354835 0.6985677
[61,] 0.6924759 4.877017 0.5914819
[62,] 0.8750170 8.938650 0.6987183
[63,] 0.4963767 5.154385 0.5267843
[64,] 0.9845955 10.830024 1.6332640
[65,] 0.9130914 6.378303 0.7150011
[66,] 0.6379774 7.991038 0.5805825
[67,] 0.8735105 7.361490 0.7832649
[68,] 0.6784702 7.413119 0.7021784
[69,] 0.9622892 8.632043 1.1318317
[70,] 0.9638345 9.265671 1.4903069
[71,] 0.6172756 6.299267 0.8306458
[72,] 0.8349335 8.792616 0.9115916
[73,] 0.7755230 7.888000 0.7354790
[74,] 0.6527278 6.332678 0.5341079
[75,] 0.4630175 3.717388 0.2649272
[76,] 0.8449912 8.392278 2.3192944
[77,] 0.8263662 8.620581 1.3452385
[78,] 0.8194348 7.847350 1.1544766
[79,] 0.4565947 5.809143 0.5332319
[80,] 0.8729451 7.225545 0.5724901
[81,] 0.5329342 6.176113 0.4141617
[82,] 0.4477027 5.114751 0.4234471
[83,] 0.9191833 9.377256 1.5187152
[84,] 0.2842830 3.502181 0.4284995
[85,] 0.4114047 6.398566 0.1623977
[86,] 0.9633245 9.471324 1.3984225
[87,] 0.9856805 8.968840 1.3766028
[88,] 0.6509489 7.088675 1.1073758
[89,] 0.9299693 9.482104 1.1620751
[90,] 0.6456944 6.448404 0.5497347
[91,] 0.1856461 1.937598 0.2026946
[92,] 0.9422877 6.825404 0.7958724
[93,] 0.5364393 5.751602 0.2944656
[94,] 0.6440514 6.226674 0.6087897
[95,] 0.8683983 8.995176 0.9055552
[96,] 0.6618030 5.422601 0.4316463
[97,] 0.8657631 9.153244 0.8223764
[98,] 0.8635867 8.491585 1.0403472
[99,] 0.5914044 5.790188 0.4643897
[100,] 0.9022617 8.710650 0.9941284
[101,] 0.6248820 6.794992 0.4528421
[102,] 0.3686887 3.487050 0.2717204
[103,] 0.8063894 10.786327 1.3713073
[104,] 0.4984841 5.251239 0.2757156
[105,] 0.9103522 10.797712 1.0076279
Cluster 1 Cluster 2 Cluster 3 LogLik
[1,] 11 1 6 29.59298
[2,] 13 3 8 59.11185
[3,] 12 2 7 87.55890
[4,] 14 4 9 118.68674
[5,] 15 5 10 148.43749
Cluster 1 Cluster 2 Cluster 3
[1,] 1 6 11
[2,] 2 7 12
[3,] 3 8 13
[4,] 4 9 14
[5,] 5 10 15
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