Section: New Results

Total variation regularization for fMRI-based prediction of behaviour

While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task related or spontaneous neuronal activity, are classically analyzed in a mass-univariate procedure yielding statistical parametric maps. This analysis framework disregards some important principles of brain organization: population coding, distributed and overlapping representations. Multivariate pattern analysis, i.e., the prediction of behavioural variables from brain activation patterns better captures this structure. To cope with the high dimensionality of the data, the learning method has to be regularized. However, the spatial structure of the image is not taken into account in standard regularization methods, so that the extracted features are often hard to interpret. More informative and interpretable results can be obtained with the ${\ell }_1$ norm of the image gradient, a.k.a. its Total Variation (TV), as regularization. We apply for the first time this method to fMRI data, and show that TV regularization is well suited to the purpose of brain mapping while being a powerful tool for brain decoding. Moreover, this article presents the first use of TV regularization for classification. See also [15] and Fig. 3 .

Figure 3. Regression - Sizes prediction experiment - Inter-subject analysis. Maps of weights found by TV regression for various values of the regularization parameter $\lambda$. When $\lambda$ decreases, the TV regression algorithm creates different clusters of weights with constant values. These clusters are easily interpretable, compared to voxel-based map (see below). The TV regression algorithm is very stable for different values of $\lambda$.