The increase in spatiotemporal resolution of neuroimaging devices is accompanied by a trend towards more powerful multivariate analysis methods. Often it is desired to interpret the outcome of these methods with respect to the cognitive processes under study. Here we discuss which methods allow for such interpretations, and provide guidelines for choosing an appropriate analysis for a given experimental goal: For a surgeon who needs to decide where to remove brain tissue it is most important to determine the origin of cognitive functions and associated neural processes. In contrast, when communicating with paralyzed or comatose patients via brain-computer interfaces, it is most important to accurately extract the neural processes specific to a certain mental state. These equally important but complementary objectives require different analysis methods. Determining the origin of neural processes in time or space from the parameters of a data-driven model requires what we call a forward model of the data; such a model explains how the measured data was generated from the neural sources. Examples are general linear models (GLMs). Methods for the extraction of neural information from data can be considered as backward models, as they attempt to reverse the data generating process. Examples are multivariate classifiers. Here we demonstrate that the parameters of forward models are neurophysiologically interpretable in the sense that significant nonzero weights are only observed at channels the activity of which is related to the brain process under study. In contrast, the interpretation of backward model parameters can lead to wrong conclusions regarding the spatial or temporal origin of the neural signals of interest, since significant nonzero weights may also be observed at channels the activity of which is statistically independent of the brain process under study. As a remedy for the linear case, we propose a procedure for transforming backward models into forward models. This procedure enables the neurophysiological interpretation of the parameters of linear backward models. We hope that this work raises awareness for an often encountered problem and provides a theoretical basis for conducting better interpretable multivariate neuroimaging analyses.

In recent years the number of active controllable joints in electrically powered hand-prostheses has increased significantly. However, the control strategies for these devices in current clinical use are inadequate as they require separate and sequential control of each degree-of-freedom (DoF). In this study we systematically compare linear and nonlinear regression techniques for an independent, simultaneous and proportional myoelectric control of wrist movements with two DoF. These techniques include linear regression, mixture of linear experts (ME), multilayer-perceptron, and kernel ridge regression (KRR). They are investigated offline with electro-myographic signals acquired from ten able-bodied subjects and one person with congenital upper limb deficiency. The control accuracy is reported as a function of the number of electrodes and the amount and diversity of training data providing guidance for the requirements in clinical practice. The results showed that KRR, a nonparametric statistical learning method, outperformed the other methods. However, simple transformations in the feature space could linearize the problem, so that linear models could achieve similar performance as KRR at much lower computational costs. Especially ME, a physiologically inspired extension of linear regression represents a promising candidate for the next generation of prosthetic devices.

Identifying temporally invariant components in complex multivariate time series is key to understanding the underlying dynamical system and predict its future behavior. In this Letter, we propose a novel technique, stationary subspace analysis (SSA), that decomposes a multivariate time series into its stationary and nonstationary part. The method is based on two assumptions: (a) the observed signals are linear superpositions of stationary and nonstationary sources; and (b) the nonstationarity is measurable in the first two moments. We characterize theoretical and practical properties of SSA and study it in simulations and cortical signals measured by electroencephalography. Here, SSA succeeds in finding stationary components that lead to a significantly improved prediction accuracy and meaningful topographic maps which contribute to a better understanding of the underlying nonstationary brain processes.

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