An algorithm for independent component analysis using a general class of copula-based dependence criteria

The efficiency of Independent Component Analysis ($\rm ICA$) algorithms relies heavily on the choice of objective function and optimization algorithms. The design of objective functions for $\rm ICA$ algorithms necessitate a foundation built upon specific dependence criteria. This paper will investigate a general class of dependency criteria based on the copula density function. One of the aims of this study is to characterize the independence between two random variables and investigate their properties. Additionally, this paper introduces a novel algorithm for $\rm ICA$ based on estimators derived from the proposed criteria. To compare the performance of the proposed algorithm against existing methods, a Monte Carlo simulation-based approach was employed. The results of this simulation revealed significant improvements in the algorithm's outputs. Finally, the algorithm was tested on a batch of time series data related to the international tourism receipts index. It served as a pre-processing procedure within a hybrid clustering algorithm alongside ${\tt PAM}$. The obtained results demonstrated that the utilization of this algorithm led to improved performance in clustering countries based on their international tourism receipts index.