Independent Component Analysis (ICA) is a method of decomposing a multivariate signal into statistically independent components. In contrast to its simplistic counterpart, principle component analysis, ICA is particularly useful when the signal components have non-Gaussian probability distributions. ICA is based on two major assumptions of non-Gaussian distribution and statistical independence of the components, and it involves minimizing mutual information or maximizing non-Gaussianity of the components .
In recent years, ICA has found applications in process monitoring and control. In multivariate process monitoring, ICA can be used to analyze sensor measurements to find statistically-independent source components that have generated the sensor data. These components can be processed further for use in monitoring and diagnosis  and in process control systems . These applications have motivated the development of a variety of ICA methods [4, 5, 6]. In most ICA methods, probability distributions are assumed to be describable by a few leading moments of the distributions. As in practice variables can have any probability distribution, the use of a few leading moments to capture dependence structures can lead to poor predictions .
In this work, we propose an alternative ICA method that is based on capturing the dependence structure of variables using a semi-parametric approach. This approach combines parametric copulas with non-parametrically-estimated marginal distributions. The approach allows for modeling non-elliptical and highly nonlinear dependence structures and offers a flexible framework to represent non-Gaussian marginal distributions. The proposed ICA method offers an alternative way to efficiently calculate rotation matrices for complicated interactions that cannot be described by a few leading moments. The application and performance of the method will be shown using examples.
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