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The analysis of time series obtained by functional magnetic resonance imaging (FMRI) may be approached by fitting predictive parametric models, such as nearest-neighbor autoregressive models with exogeneous input (NNARX). As a part of the modeling procedure, it is possible to apply instantaneous linear transformations to the data. Spatial smoothing, a common preprocessing step, may be interpreted as such a transformation. The autoregressive parameters may be constrained, such that they provide a response behavior that corresponds to the canonical haemodynamic response function (HRF). We present an algorithm for estimating the parameters of the linear transformations and of the HRF within a rigorous maximum-likelihood framework. Using this approach, an optimal amount of both the spatial smoothing and the HRF can be estimated simultaneously for a given FMRI data set. An example from a motor-task experiment is discussed. It is found that, for this data set, weak, but non-zero, spatial smoothing is optimal. Furthermore, it is demonstrated that activated regions can be estimated within the maximum-likelihood framework.

The huge number of voxels in fMRI over time poses a major challenge to for effective analysis. Fast, accurate, and reliable classifiers are required for estimating the decoding accuracy of brain activities. Although machine-learning classifiers seem promising, individual classifiers have their own limitations. To address this limitation, the present paper proposes a method based on the ensemble of neural networks to analyze fMRI data for cognitive state classification for application across multiple subjects. Similarly, the fuzzy integral (FI) approach has been employed as an efficient tool for combining different classifiers. The FI approach led to the development of a classifiers ensemble technique that performs better than any of the single classifier by reducing the misclassification, the bias, and the variance. The proposed method successfully classified the different cognitive states for multiple subjects with high accuracy of classification. Comparison of the performance improvement, while applying ensemble neural networks method, vs. that of the individual neural network strongly points toward the usefulness of the proposed method.