Struggling with copula clustering I read many articles about clustering using copula. I know that copula is a multivariate function that is used to describe the relationship between variables. However, in clustering we try to group our data into groups. So, my question here, how does copula clustering work? For example, if I have a data with two variables, then by using copula model we can describe the relationship between these two variables, but how we can fit the clustering? Any help with example, please?
 A: For clustering using copula you need to follow some steps:
Update: all listed functions and packages are R-program packages

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*Clusters your data (divide your data into groups). For this step, you can use kmeans: kmeans(your-data, 2) ## two here means to divide your data into two clusters.

You can repeat this step using a different number of clusters and then select the most appropriate one for your data. Or you can simply use mclustBIC() function from mclust package to find the best number of clusters for your data.


*Say you have two clusters, then, for each cluster's data, you need to
fit a copula (or vine copula) model to receive starting values for your model. For example, if you are working with a bivariate case, then just fit the BiCopSelect function from the VineCopula package to each cluster of your data. It will then select the best bivariate copula and estimate the corresponding parameter(s) (for each cluster).


*Then you just simply fit an EM-algorithm with your initial values. Copula then captures the dependency in your data.
The copula clustering method is similar to any traditional clustering method, however, it is able to deal with complex dependencies exhibited in the data. Kindly note that the VineCopula package is free of margins. That is, it does not take into account the marginal distribution, as they use the semiparametric method to estimate the margins. That is, the margins are estimated non-parametrically. The vinecopulib package considers the margins (if you are interested in estimating the margins parametrically).
