Abstract for: Measuring Eigenvalues’ Sensitivities via Kernel Canonical Correlation Analysis
This paper is a continuation to our previous work [Yehia, Saleh et al., System Dynamics Conf. (2014)], where we developed a many to one statistical sensitivity analysis method based on the multivariate maximal information coefficient (MMIC). The two main critiques to this method (which we previously developed), were that the complexity of the algorithm increases exponentially with the number of input variables, and that it cannot handle many (inputs) to many (outputs) relations. To overcome these two critiques, in this paper, we propose a statistical sensitivity analysis based on the Kernel Canonical Correlation method. This kernel-based method is designed to handle many to many relations, and the complexity of the algorithm depends only on the number of samples – whatever the number of input variables is. We postulate that this kernel based sensitivity analysis represents a solid foundation to study the multivariate complex nonlinear non-monotonic relationships between behavior modes – expressed by eigenvalues – and the model parameters. The experiments conducted corroborate our postulation.