An R package that fits vine copula based mixture model distributions to the continuous data for a given number of components as proposed in VCMM algorithm and use its results for clustering.
It depends on VineCopula, fGarch, mclust, and univariateML.
You can install the development version from GitHub with:
# install.packages("remotes")
remotes::install_github("oezgesahin/vineclust")Below is an overview of some functions and features.
vcmm(): fits vine copula based mixture model distributions to the continuous data for a given number of components. Returns an object of classvcmm_res(). The class has the following methods:print: a brief overview of the model statistics.summary: list of fitted model components, including selected vine tree structures, bivariate copula families, univariate marginal distributions, and estimated parameters.
dvcmm(), rvcmm(): density and random generation for the vine copula based mixture model distributions.
This package works with a wide range of parametric bivariate copula families for bivariate or multivariate clustering using vine copulas. Specifically, it allows fitting elliptical (Gaussian, Student-t) and Archimedean (Clayton, Gumbel, Frank, Joe, BB1, BB6, and BB8) copulas with their possible 90, 180, 270 degrees rotations to cover a large range of dependence patterns. Their encoding is detailed on VineCopula.
This package currently includes following unimodal univariate marginal distributions.
cauchy(a,b): Cauchy distribution with location parameter a and scale parameter b,gamma(a,b): gamma distribution with shape parameter a and rate parameter b,llogis(a,b): log-logistic distribution with shape parameter a and rate parameter b,lnorm(a,b): log-normal distribution with mean parameter a and standard deviation parameter b on the logarithmic scale,logis(a,b): logistic distribution with location parameter a and scale parameter b,norm(a,b): normal distribution with mean parameter a and standard deviation parameter b,snorm(a,b,c): skew normal distribution with location parameter a, scale parameter b, and skewness parameter c.std(a,b,c): Student’s t distribution with location parameter a, scale parameter b, and shape parameter c,sstd(a,b,c,d): skew Student’s t distribution with location parameter a, scale parameter b, shape parameter c, and skewness parameter d.
This package currently implements following partition approaches to have starting values.
kmeans: performs k-means clustering (Hartigan-Wong) on given data after scaling,hcVVV: performs model-based hierarchical clustering on given data after scaling,gmm: performs model-based clustering with Gaussian mixture models on given data.
library(vineclust)
# data from UCI Machine Learning Repository
data_wisc <- read.csv("http://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data", header = FALSE) # R-vine copula based mixture model with total components 2
fit <- vcmm(data=data_wisc[,c(15,27,29,30)], total_comp=2)
# Model statistics
print(fit)
#> logLik = 2159.11 BIC = -4108.88 ICL = -4068.3 npars = 33 initial clustering = kmeans ECM iterations = 4
# Fitted vine copula distributions
summary(fit)
#> $margins
#> [,1] [,2]
#> [1,] "Lognormal" "Lognormal"
#> [2,] "Lognormal" "Gamma"
#> [3,] "Lognormal" "Skew Normal"
#> [4,] "Skew Normal" "Normal"
#>
#> $marginal_pars
#> , , 1
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 1.3257284 -1.9132582 -0.8083077 0.18916084
#> [2,] 0.5085319 0.1325288 0.3702962 0.03873749
#> [3,] NA NA NA 1.81086926
#> [4,] NA NA NA NA
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0.6513504 42.84792 0.1607200 0.07370799
#> [2,] 0.3849773 347.42118 0.1222864 0.03358325
#> [3,] NA NA 13.0380866 NA
#> [4,] NA NA NA NA
#>
#>
#> $copula
#> , , 1
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 24 1 0 0
#> [4,] 5 1 20 0
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 33 0 0 0
#> [3,] 33 23 0 0
#> [4,] 10 3 14 0
#>
#>
#> $copula_first_par
#> , , 1
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0.0000000 0.0000000 0.000 0
#> [2,] -0.3781992 0.0000000 0.000 0
#> [3,] -1.0644572 -0.2277139 0.000 0
#> [4,] 2.1769280 0.3734696 5.682 0
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0.00000000 0.00000000 0.00000 0
#> [2,] -0.09652639 0.00000000 0.00000 0
#> [3,] -0.19082564 -0.07882284 0.00000 0
#> [4,] 1.30499379 0.41096477 2.66261 0
#>
#>
#> $copula_second_par
#> , , 1
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0.0000000 0
#> [2,] 0 0 0.0000000 0
#> [3,] 0 0 0.0000000 0
#> [4,] 0 0 0.6308382 0
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0.0000000 0 0 0
#> [2,] 0.0000000 0 0 0
#> [3,] 0.0000000 0 0 0
#> [4,] 0.9357103 0 0 0
#>
#>
#> $vine_structure
#> , , 1
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 2 0 0 0
#> [2,] 1 1 0 0
#> [3,] 4 3 3 0
#> [4,] 3 4 4 4
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 1 0 0 0
#> [2,] 3 2 0 0
#> [3,] 2 3 3 0
#> [4,] 4 4 4 4
#>
#>
#> $mixture_probs
#> [1] 0.3524161 0.6475839
# Evaluate the density of the fitted model at (2.747, 0.1467, 0.13, 0.05334)
RVMs_fitted <- list()
RVMs_fitted[[1]] <- VineCopula::RVineMatrix(Matrix=fit$output$vine_structure[,,1],
family=fit$output$bicop_familyset[,,1],
par=fit$output$bicop_param[,,1],
par2=fit$output$bicop_param2[,,1])
RVMs_fitted[[2]] <- VineCopula::RVineMatrix(Matrix=fit$output$vine_structure[,,2],
family=fit$output$bicop_familyset[,,2],
par=fit$output$bicop_param[,,2],
par2=fit$output$bicop_param2[,,2])
dvcmm(c(2.747, 0.1467, 0.13, 0.05334), fit$output$margin, fit$output$marginal_param, RVMs_fitted, fit$output$mixture_prob)
#> [1] 26.70683# C-vine copula based mixture model
fit_cvine <- vcmm(data=data_wisc[,c(15,27,29,30)], total_comp=2, is_cvine=1)
# Confusion matrix w.r.t. true classification
table(fit_cvine$cluster, data_wisc$V2)
#>
#> B M
#> 1 325 21
#> 2 32 191# Fit only bivariate Clayton copula for pairs of variables in both components
fit_clayton <- vcmm(data=data_wisc[,c(15,27,29,30)], total_comp=2, bicop=c(3)) # Fix vine tree structures of both components
fit_fix_vinestr <- vcmm(data=data_wisc[,c(15,27,29,30)], total_comp=2,
vinestr=matrix(c(1,2,3,4,0,2,4,3,0,0,4,3,0,0,0,3),4,4)) # Run ECM iterations shorter with a smaller threshold than the default threshold
fit_sthr <- vcmm(data=data_wisc[,c(15,27,29,30)], total_comp=2, threshold=0.001) # Use a different initial partition approach from k-means
fit_best_init <- vcmm(data=data_wisc[,c(15,27,29,30)], total_comp=2, methods=c("gmm")) # Simulation setup given in Section 5.2 of the paper at https://arxiv.org/pdf/2102.03257.pdf
dims <- 3
obs <- c(500,500)
RVMs <- list()
RVMs[[1]] <- VineCopula::RVineMatrix(Matrix=matrix(c(1,3,2,0,3,2,0,0,2),dims,dims),
family=matrix(c(0,3,4,0,0,14,0,0,0),dims,dims),
par=matrix(c(0,0.8571429,2.5,0,0,5,0,0,0),dims,dims),
par2=matrix(sample(0, dims*dims, replace=TRUE),dims,dims))
RVMs[[2]] <- VineCopula::RVineMatrix(Matrix=matrix(c(1,3,2,0,3,2,0,0,2), dims,dims),
family=matrix(c(0,6,5,0,0,13,0,0,0), dims,dims),
par=matrix(c(0,1.443813,11.43621,0,0,2,0,0,0),dims,dims),
par2=matrix(sample(0, dims*dims, replace=TRUE),dims,dims))
margin <- matrix(c('Normal', 'Gamma', 'Lognormal', 'Lognormal', 'Normal', 'Gamma'), 3, 2)
margin_pars <- array(0, dim=c(2, 3, 2))
margin_pars[,1,1] <- c(1, 2)
margin_pars[,1,2] <- c(1.5, 0.4)
margin_pars[,2,1] <- c(1, 0.2)
margin_pars[,2,2] <- c(18, 5)
margin_pars[,3,1] <- c(0.8, 0.8)
margin_pars[,3,2] <- c(1, 0.2)
x_data <- rvcmm(dims, obs, margin, margin_pars, RVMs)Please contact O.Sahin@tudelft.nl if you have any questions.
Sahin, {"O}., & Czado, C. (2022). Vine copula mixture models and clustering for non-Gaussian data. Econometrics and Statistics. doi:10.1016/j.ecosta.2021.08.011. preprint, article