Neurocomputing 52–54 (2003) 683–690 www.elsevier.com/locate/neucom Extraction of nonlinear features in MEG and fMRI data of human brain Liya Wang a , Boris Baryshnikov b , Hamid Eghbalnia c , Amir H. Assadi d ; ∗ a Department of Biomedical Engineering, University of Wisconsin, Madison, WI 53706, USA b Department of Medical Physics, University of Wisconsin, Madison, WI 53706, USA c Department of Biochemistry, University of Wisconsin, Madison, WI 53706, USA d Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA Abstract We have determined a new method for quantifying the nonlinearities of brain imaging data sets to allow comparison of measures of nonlinearity across comparable experiments. We have an ecient algorithm for nding nonlinear features of high dimensional data from variations in two- dimensional projections and slices. By computing the second-order statistics of these fea- tures, we are able to construct an analogue of the Riemann Curvature Tensor, thereby describing the nonlinearity of the data set. We demonstrate the usefulness of this technique on real MEG and fMRI data. c  2002 Elsevier Science B.V. All rights reserved. Keywords: Principal components analysis; Multi-channel; Data analysis; Biomagnetism; Auditory perception 1. Introduction Working with massive “real world” data is inherently dicult because we often do not know important factors that are signicant in any pattern recognition and feature extraction tasks. These factors range from the signal-to-noise ratio in the data, lack of a statistical distribution for the uncontaminated data, to situations such as not having a robust statistical model for the noise. A simplifying assumption is often helpful, but we must be certain to assess the impact of the assumptions that are made along the way on the nal outcome of the analysis. Bayesian methods have the advantage that * Corresponding author. Fax: +1-608-263-8891. E-mail address: ahassadi@facsta.wisc.edu (A.H. Assadi). 0925-2312/03/$-see front matter c  2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-2312(02)00731-2