Functional magnetic resonance imaging (fMRI) exploits blood-oxygen-level-dependent (BOLD) contrasts to map neural activity associated with a variety of brain functions including sensory processing, motor control, and cognitive and emotional functions. The general linear model (GLM) approach is used to reveal task-related brain areas by searching for linear correlations between the fMRI time course and a reference model. One of the limitations of the GLM approach is the assumption that the covariance across neighbouring voxels is not informative about the cognitive function under examination. Multivoxel pattern analysis (MVPA) represents a promising technique that is currently exploited to investigate the information contained in distributed patterns of neural activity to infer the functional role of brain areas and networks. MVPA is considered as a supervised classification problem where a classifier attempts to capture the relationships between spatial pattern of fMRI activity and experimental conditions. In this paper , we review MVPA and describe the mathematical basis of the classification algorithms used for decoding fMRI signals, such as support vector machines (SVMs). In addition, we describe the workflow of processing steps required for MVPA such as feature selection, dimensionality reduction, cross-validation, and classifier performance estimation based on receiver operating characteristic (ROC) curves.

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