Section: New Results
Brain decoding techniques
Participants : Bertrand Thirion, Vincent Michel, Gaël Varoquaux.
Traditional inference in neuroimaging consists in describing the fluctuations of brain activity related to the modification of a stimulation parameter (a functional contrast). There might exist a relationship that relates functional contrasts and brain states. Inferring functional contrasts from a certain dataset is known as inverse inference . The quality of this inference is easily characterized by a correct classification rate if the target variable belongs to some finite set. Such estimation of is usually carried out using classifiers.
Classification and decoding
We have used classification techniques to study various brain systems:
First we compared brain activation in two different tasks: eye saccades and mental computation. Throughout the history of mathematics, concepts of number and space have been tightly intertwined. We tested the hypothesis that cortical circuits for spatial attention contribute to mental arithmetic in humans. We trained a multivariate classifier algorithm to infer the direction of an eye movement, left or right, from the brain activation measured in the posterior parietal cortex. Without further training, the classifier then generalized to an arithmetic task. Its left versus right classification could be used to sort out subtraction versus addition trials, whether performed with symbols or with sets of dots. These findings are consistent with the suggestion that mental arithmetic co-opts parietal circuitry associated with spatial coding. 
We also applied these techniques to study the mental representation of quantities, assessing e.g. the number of points that were perceived and mentally processed by some subjects. We could find that some brain regions are particularly important to encode the quantity information when presented either as a set of dots or as a symbolic number  .
We were less successful in applying these techniques to a pleasantness experiment  . We observed that in that case, traditional data analyses were more sensitive than classification-based analysis.
Regularized regression approach
In some cases, the information y that has to be predicted is a continuous variable (such as a reaction time or a number); then it can be predicted through regression techniques. We have presented a novel method for regularized regression and apply it to the prediction of a behavioural variable from brain activation images  . In the context of neuroimaging, regression or classification techniques are often plagued by the curse of dimensionality, due to the extremely high number of voxels and the limited number of activation maps. A commonly used solution is regularization of the weights used in the parametric prediction function. To solve the difficult issue of choosing the correct amount of regularization in the model, we have proposed a Bayesian framework, with efficient model specification and evaluation techniques to balance adaptiveness and sparsity.
We have thus introduced an adaptive mixture regularization that generalizes previous approaches. Based on a Variational Bayes estimation framework, our algorithm is robust to over-fitting and more adaptive than other regularization methods. Results on both simulated and real data show the accuracy of the method in the context of brain activation images  .
Extracting resting-state networks with Independent Component Analysis
Spatial Independent Component Analysis (ICA) is an increasingly used data-driven method to analyze functional Magnetic Resonance Imaging (fMRI) data. To date, it has been used to extract meaningful patterns without prior information. However, ICA is not robust to mild data variation and remains a parameter-sensitive algorithm. The validity of the extracted patterns is hard to establish, as well as the significance of differences between patterns extracted from different groups of subjects.
Parietal has introduced an innovative approach for ICA data analysis,  ,  : This approach builds on a generative model of the fMRI group data to introduce a probabilistic ICA pattern-extraction algorithm, called CanICA (Canonical ICA). This approach includes an explicit noise model and identifies noise and signal of interest subspace automatically, with an automatic calibration of the parameters. The group level model is built through canonical correlation analysis, and identifies the group-reproducible data subspace before performing ICA. We have compared our method to state-of-the-art multi-subject fMRI ICA methods and shown that the features extracted are more reproducible  .
The correlation between the activity of distant regions may be an important marker of the disruption of certain cognitive networks in patient populations. This measure can provide important information for characterizing the impact of various diseases on brain function, especially when only some sub-networks show a differential effect across populations.
Technically, this analysis requires unbiased measure of functional connectivity (correlation between distant regions) based on the time courses observed in fMRI datasets, and adequate statistical procedures to detect significant differences across individuals.
Parietal is actively collaborating with psychiatrists to release adapted modelling and statistical analysis tools, and help them to reach meaningful conclusions from their data. This is illustrated in fig. 6 , with an ongoing study that addresses the differences between schizophrenic and normal subjects in a task that implies memory processing.
Pushing the resolution of neuroimaging data is an important issue and it is a major incentive to turn to high-field neuroimaging.
In 2009, Parietal researchers have performed the first acquisition of functional images on a 7T scanner in France. The result is qualitatively satisfactory (see fig. 7 ). This image reveals the functional organisation of visual regions at a 1.5mm resolution. This will be useful to decode the content of these images.