A Unifying Tool for Comparing Stochastic Realization Algorithms and Model Reduction Techniques

The RV-coefficient recently introduced in the multivariate statistics literature as a measure of similarity between two sets of random variables is considered in this paper as a unifying tool for comparing stochastic realization algorithms and model reduction techniques. It is shown that previous algorithms either based on canonical correlation analysis or some variants of principal component analysis are specific cases of this generalized framework of analysis. Also considered in this analysis is the direct extension of Moore's deterministic balancing conditions to the stochastic case. Furthermore the model reduction dilemma raised by Arun and Rung is viewed from the point of view of the RV-coefficient method and the link between canonical correlation analysis and principal components of instrumental variables (also Karhunen-Loeve expansion) is given by a redundancy index which has a strong connection to an antibalancing transformation.