Comput Visual Sci (2007) 10:99–105 DOI 10.1007/s00791-006-0037-6 REGULAR ARTICLE Feature evaluation in fMRI data using random matrix theory Marotesa Voultsidou · Silke Dodel · J. Michael Herrmann Received: 27 March 2006 / Accepted: 19 July 2006 / Published online: 1 December 2006 © Springer-Verlag 2006 Abstract Quantitative descriptors of intrinsic prop- erties of fMRI data can be obtained from the theory of random matrices. We study data reduction based on the comparison of empirical correlation matrices with a suitably chosen ensemble of random positive matrices. Accordingly, data dimensions can be discarded if the quality of fit of the data spectrum deviates locally from the theoretical result, which is derived here analytically. Further, more complex quantities such as the number variance are discussed and shown to be potentially use- ful in an analogous manner. 1 Introduction 1.1 fMRI data In recent years a number of interesting algorithms have been proposed for the analysis of data from fMRI exper- iments, which allow us to locate the regions in the brain Communicated by G.Wittum. M. Voultsidou Department of Physics, University of Crete, P.O. Box 2208 Heraklion, Crete, Greece e-mail: marotesa@physics.uoc.gr S. Dodel Center for Complex Systems and Brain Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA e-mail: dodel@ccs.fau.edu J. M. Herrmann (B ) Institut für Nichtlineare Dynamik, Universität Göttingen, Bunsenstr. 10, 37073 Göttingen, Germany e-mail: michael@chaos.gwdg.de that are coherently activated by a certain type of sensation or activity, e.g. the movement of a subject’s fingers. Often the extraction of more delicate features becomes computationally complex and cannot be per- formed online [9]. Moreover, the robustness of some algorithms suffers from the large number of dimensions. Finally, a dimensional reduction is a precondition for the visualization of fMRI data. Thus, data reduction seems to be useful, provided that it does not reduce the rele- vant information available to the later processing stages. The main contribution to high dimensionality is from noisy components. fMRI recordings are usually cor- rupted by several influences such as head movement, cardiac and respiratory activity and noise form the scan- ning equipment. Besides structural noise, random noise is also present in the data, thus its suppression is required for the registration of functionally relevant brain regions. Noise can be partially eliminated by dimensionality reduction of the high-dimensional fMRI data with the additional benefit that by decreasing the redundancy the computational requirements for subsequent analy- sis are reduced. The universal behavior of the statistics of the spectrum of random matrices can serve as a base- line, the deviations from which indicate significant data features. The data components which have similar sta- tistical properties as random matrices are identified as noisy while those who differ from the random case are characterized as informative and should be subject to further analysis. The data set which are analyzed here has been obtained from the brain of human subjects who are per- forming a simple motor task. The time course of the task can be shown to be correlated to local excitations of the measured activity. The main part of the variance of the time course is, however, caused mainly by noise or by