Comparison of orthogonal search and canonical variate analysis for the identification of neurobiological systems

In this paper, we investigate two general methods of modeling and prediction which have been applied to neurobiological systems, the orthogonal search (OS) method and the canonical variate analysis (CVA) approach. In these methods, nonlinear autoregressive moving average with observed inputs (ARX) and state affine models are developed as one step predictors by minimizing the mean-squared-error. An unknown nonlinear time-invariant system is assumed to have the Markov property of finite order so that the one step predictors are finite dimensional. No special assumptions are made about model terms, model order or state dimensions. Three examples are presented. The first is a numerical example which demonstrates the differences between the two methods, while the last two examples are computer simulations for a bilinear system and the Lorenz attractor which can serve as a model for the EEG. These two methods produce comparable results in terms of minimizing the mean-square-error; however, the OS method produces an ARX model with fewer terms, while the CVA method produces a state model with fewer state dimensions.