1 Introduction
Inferring behavior information or cognitive states from brain activation images (a.k.a. inverse inference) such as those obtained with functional Magnetic Resonance Imaging (fMRI) is a recent approach in neuroimaging cox2003 that can provide more sensitive analysis than standard statistical parametric mapping procedures kamitani2005 . Specifically, it can be used to assess the involvement of some brain regions in certain cognitive, motor or perceptual functions, by evaluating the accuracy of the prediction of a behavioral variable of interest (the target
) when the classifier is instantiated on these brain regions. Such an approach can be particularly well suited for the investigation of coding principles in the brain
dayan2001. Indeed certain neuronal populations activate specifically when a certain perceptual or cognitive parameter reaches a given value. Inferring the parameter from the neuronal activity and extracting the
spatial organization of this coding helps to decode the brain system.Brain decoding requires to define a prediction function such as a classifier that relates the image data to relevant variables. Many methods have been tested for classification or regression of activation images (Linear Discriminant Analysis, Support Vector Machines, Lasso, Elastic net regression and many others), but in this problem the major bottleneck remains the localization of predictive regions within the brain volume (see
haynes2006 for a review). Selection of relevant regions, a.k.a. feature selection, is important both to achieve accurate prediction (by alleviating the curse of dimensionality) and understand the spatial distribution of the informative features carroll2009 . In particular, when the number of features (voxels, regions) is much larger () than the numbers of samples (images) (), the prediction method overfitsthe training set, and thus does not generalize well. To date, the most widely used method for feature selection is voxelbased Anova (Analysis of Variance), that evaluates each brain voxel independently. The features that it selects can be redundant, and are not constrained by spatial information, so that they can be spread across all brain regions. Such maps are difficult to interpret, especially compared to standard brain mapping techniques such as
Statistical Parametric Maps friston1995c . Constructing spatiallyinformed predictive features gives access to meaningful maps (e.g. by constructing informative and anatomically coherent regions cordes2002 ) within the decoding framework of inverse inference.A first solution is to introduce the spatial information within a voxelbased analysis, e.g. by adding regionbased priors palatucci2007 , by using a spatiallyinformed regularization michel2010a or by keeping only the neighboring voxels for the predictive model, such as in the searchlight approach kriegeskorte2006 ; however the latter approach cannot handle longrange interactions in the information coding.
A more natural way for using the spatial information is called feature agglomeration, and consists of replacing voxelbased signals by local averages (a.k.a. parcels) flandin2002 ; mitchell2004 ; fan2006 ; thirion2006 . This is motivated by the fact that fMRI signal has a strong spatial coherence due to the spatial extension of the underlying metabolic changes and of the neural code ugurbil2003 . There is a local redundancy of the predictive information. Using these parcelbased averages of fMRI signals to fit the target naturally reduces the number of features (from voxels to parcels). These parcels can be created using only spatial information, in a purely geometrical approach kontos2004 , or using atlases mazoyer2002 ; keller2009 . In order to take into account both spatial information and functional data, clustering approaches have also been proposed, e.g.spectral clustering thirion2006
thyreau2006, Kmeans
ghebreab2008 or fuzzy clustering he2008 . The optimal number of clusters may be hard to find thyreau2006 ; filzmoser1999 , but probabilistic clustering provides a solution tucholka2008 . Moreover, as such spatial averages can lose the finegrained information, which is crucial for an accurate decoding of fMRI data cox2003 ; haynes2006 ; haynes2005 , different resolutions of information should be allowed golland2007 .In this article, we present a supervised clustering algorithm, that considers the target to be predicted during the clustering procedure and yields an adaptive segmentation into both large regions and finegrained information, and can thus be considered as multiscale. The proposed approach is a generalization of michel2010 usable with any type of prediction functions, in both classification and regression settings. Supervised clustering is presented in section 2, and is illustrated in section 3 on simulated data. In section 4, we show on real fMRI data sets in regression and classification settings, that our method can recover the discriminative pattern embedded in an image while yielding higher prediction performance than previous approaches. Moreover, supervised clustering appears to be a powerful approach for the challenging generalization across subjects (intersubject inverse inference).
2 Methods
Predictive linear model
Let us introduce the following predictive linear model for regression settings:
(1) 
where represents the behavior variable and
are the parameters to be estimated on a training set comprising
samples. A vector can be seen as an image; is the number of features (or voxels) and is called the intercept (or bias). The matrix is the design matrix. Each row is a dimensional sample, i.e., an activation map related to the observation. In the case of classification with a linear model, we have:(2) 
where and “sign
” denotes the sign function. The use of the intercept is fundamental in practice as it allows the separating hyperplane to be offseted from 0. However for the sake of simplicity in the presentation of the method, we will from now on consider
as an added coefficient in the vector . This is done by concatenating a column filled with 1 to the matrix . We note the signal in the voxel (feature) .Parcels
We define a parcel as a group of connected voxels, a parcellation being a partition of the whole set of features in a set of parcels:
(3) 
such that
(4) 
where is the number of parcels and the parcel. The parcelbased signal is the average signal of all voxels within each parcel (other representation can be considered, e.g. median values of each parcel), and the row of is noted :
(5) 
where is the number of voxels in the parcel .
Bayesian Ridge Regression
We now detail
Bayesian Ridge Regression (BRR)
which is the predictive linear model used for regression in this article, and we give implementation details on parcelbased averages . BRR is based on the following Gaussian assumption:(6) 
We assume that the noise is Gaussian with precision (inverse of the variance), i.e. . For regularization purpose, i.e. by constraining the values of the weights to be small, one can add a Gaussian prior on , i.e. , that leads to:
(7) 
where:
(8) 
In order to have a full Bayesian framework and to avoid degenerate solutions, one can add classical Gamma priors on and :
(9) 
and the parameters update reads:
(10) 
where , and
are the eigenvalues of
. In the experiments detailed in this article, we choose , i.e. weakly informative priors.BRR is solved using an iterative algorithm that maximizes the log likelihood; starting with and , we iteratively evaluate and using Eq. (8), and use these values to estimate , and , using Eq. (10). The convergence of the algorithm is monitored by the updates of , and the algorithm is stopped if , where and are the values of in two consecutive steps.
2.1 Supervised clustering
In this section, we detail an original contribution, called supervised clustering, which addresses the limitations of the unsupervised feature agglomeration approaches. The flowchart of the proposed approach is given in Fig. 1.
We first construct a hierarchical subdivision of the search domain using Ward hierarchical clustering algorithm ward1963 . The resulting nested parcel sets constructed from the functional data is isomorphic to a tree. By construction, there is a onetoone mapping between cuts of this tree and parcellations of the domain. Given a parcellation, the signal can be represented by parcelbased averages, thus providing a low dimensional representation of the data (i.e. feature agglomeration
). The method proposed in this contribution is a greedy approach that optimizes the cut in order to maximize the prediction accuracy based on the parcelbased averages. By doing so, a parcellation of the domain is estimated in a supervised learning setting, hence the name
supervised clustering. We now detail the different steps of the procedure.2.1.1 BottomUp step: hierarchical clustering
In the first step, we ignore the target information – i.e. the behavioral variable to be predicted – and use a hierarchical agglomerative clustering. We add connectivity constraints to this algorithm (only adjacent clusters can be merged together) so that only spatially connected clusters, i.e. parcels, are created. This approach creates a hierarchy of parcels represented as a tree (or dendrogram) johnson1967 . As the resulting nested parcel sets is isomorphic to the tree , we identify any tree cut with a given parcellation of the domain. The root of the tree is the unique parcel that gathers all the voxels, the leaves being the parcels with only one voxel. Any cut of the tree into subtrees corresponds to a unique parcellation , through which the data can be reduced to parcelsbased averages. Among different hierarchical agglomerative clustering, we use the varianceminimizing approach of Ward algorithm ward1963 in order to ensure that parcelbased averages provide a fair representation of the signal within each parcel. At each step, we merge together the two parcels so that the resulting parcellation minimizes the sum of squared differences within all parcels (inertia criterion).
2.1.2 TopDown step: pruning of the tree
We now detail how the tree can be pruned to create a reduced set of parcellations. Because the hierarchical subdivision of the brain volume (by successive inclusions) is naturally identified as a tree , choosing a parcellation adapted to the prediction problem means optimizing a cut of the tree. Each subtree created by the cut represents a region whose average signal is used for prediction. As no optimal solution is currently available to solve this problem, we consider two approaches to perform such a cut (see Fig. 2). In order to have parcels, these two methods start from the root of the tree (one unique parcel for the whole brain), and iteratively refine the parcellation:

The first solution consists in using the inertia criterion from Ward algorithm: the cut consists in a subdivision of the Ward’s tree into its main branches. As this does not take into account the target information , we call it unsupervised cut (UC).

The second solution consists in initializing the cut at the highest level of the hierarchy and then successively finding the new subtree cut that maximizes a prediction score (e.g. explained variance, see Eq.(11) below), while using a prediction function (e.g. Support Vector Machine cortes1995 ) instantiated with the parcelsbased signal averages at the current step. As in a greedy approach, successive cuts iteratively create a finer parcellation of the search volume, yielding the set of parcellations . More specifically, one parcel is split at each step, where the choice of the split is driven by the prediction problem. After such steps of exploration, the brain is divided into parcels. This procedure, called supervised cut (SC), is detailed in algorithm 1.
2.1.3 Model Selection step: optimal subtree
In both cases, a set of nested parcellations is produced, and the optimal model among the available cuts still has to be chosen. We select the subtree that yields the optimal prediction score . The corresponding optimal parcellation is then used to create parcels on both training and test sets. A prediction function is thus trained and tested on these two set of parcels to compute the prediction accuracy of the framework.
2.2 Algorithmic considerations
The pruning of the tree and the model selection step are included in an internal crossvalidation procedure within the training set. However, this internal crossvalidation scheme rises different issues. First, it is very time consuming to include the two steps within a complete internal crossvalidation. A second, and more crucial issue, is that performing an internal crossvalidation over the two steps yields many different subtrees (one by fold). However, it is not easy to combine these different subtrees in order to obtain an average subtree that can be used for prediction on the test set oliver1995
. Moreover, the different optimal subtrees are not constructed using all the training set, and thus depend on the internal crossvalidation scheme. Consequently, we choose an empirical, and potentially biased, heuristic that consists of using sequentially two separate crossvalidation schemes
and for the pruning of the tree and the model selection step.2.3 Computational considerations
Our algorithm can be used to search informative regions in very highdimensional data, where other algorithms do not scale well. Indeed, the highest number of features considered by our approach is
, and we can use any given prediction function , even if this function is not wellsuited for high dimensional data. The computational complexity of the proposed supervised clustering algorithm depends thus on the complexity of the prediction function , and on the two crossvalidation schemes and . At the current iteration , possible features are considered in the regression model, and the regression function is fit times (in the case of a leaveoneout crossvalidation with samples). Assuming the cost of fitting the prediction function is at step , the overall cost complexity of the procedure is . In general , and the cost remains affordable as long as , which was the case in all our experiments. Higher values for might also be used, but the complexity of has to be lower.The benefits of parcellation come at a cost regarding CPU time. On a subject of the dataset on the prediction of size (with a non optimized Python implementation though), with voxels, the construction of the tree raising CPU time to seconds and the parcels definition raising CPU time (Intel(R) Xeon(R), 2.83GHz) to seconds. Nevertheless, all this remains perfectly affordable for standard neuroimaging data analyzes.
2.4 Performance evaluation
Our method is evaluated with a crossvalidation procedure that splits the available data into training and validation sets. In the following, are a learning set, a test set and refers to the predicted target, where
is estimated from the training set. For regression analysis, the performance of the different models is evaluated using
, the ratio of explained variance:(11) 
This is the amount of variability in the response that can be explained by the model. A perfect prediction yields , a constant prediction yields ). For classification analysis, the performance of the different models is evaluated using a standard classification score denoted , defined as:
(12) 
where is the number of samples in the test set, and is Kronecker’s delta.
2.5 Competing methods
In our experiments, the supervised clustering is compared to different state of the art regularization methods. For regression experiments:

Elastic net regression zou2005 , requires setting two parameters (amount of norm regularization) and (amount of norm regularization). In our analyzes, an internal crossvalidation procedure on the training set is used to optimize , where , and .

Support Vector Regression (SVR) with a linear kernel cortes1995 , which is the reference method in neuroimaging. The regularization parameter is optimized by crossvalidation in the range of to in multiplicative steps of .
For classification settings:

Sparse multinomial logistic regression
(SMLR) classification krishnapuram2007 , that requires an optimization similar to Elastic Net (two parameters and ). 
Support Vector Classification (SVC), which is optimized similarly as SVR.
All these methods are used after an Anovabased feature selection as this maximizes their performance. Indeed, irrelevant features and redundant information can decrease the accuracy of a predictor hughes1968 . This selection is performed on the training set, and the optimal number of voxels is selected in the range within a nested crossvalidation. We also check that increasing the range of voxels (i.e. adding 2000 in the range of number of selected voxels) does not increase the prediction accuracy on our real datasets. The implementation of Elastic net is based on coordinate descent friedman2009 , while SVR and SVC are based on LibSVM libsvm . Methods are used from Python via the Scikitlearn open source package scikit
. Prediction accuracies of the different methods are compared using a paired ttest.
3 Simulated data
3.1 Simulated onedimensional data
We illustrate the supervised clustering on a simple simulated data set, where the informative features have a block structure:
(13) 
with and is defined as for , for , and elsewhere, where
is the uniform distribution between
and . We have features and images. The supervised cut is used with , Bayesian Ridge Regression (BRR) as prediction function , and procedures and are set to 4fold crossvalidation.3.2 Simulated neuroimaging data
The simulated data set consists in images (size voxels) with a set of four cubic Regions of Interest (ROIs) (size ). We call the support of the ROIs (i.e. the resulting voxels of interest). Each of the four ROIs has a fixed weight in . We call the weight of the voxel. To simulate the spatial variability between images (intersubject variability, movement artifacts in intrasubject variability), we define a new support of the ROIs, called such as, for each image, half (randomly chosen) of the weights are set to zero. Thus, we have . We simulate the signal in the voxel of the image as:
(14) 
The resulting images are smoothed with a Gaussian kernel with a standard deviation of
voxels, to mimic the correlation structure observed in real fMRI data. The target for the image is simulated as:(15) 
and is a Gaussian noise with standard deviation We choose in order to have a signaltonoise (SNR) ratio of dB. The SNR is defined here as times the log of the ratio between the norm of the signal and the norm of the added noise. We create a training set of images, and then we validate on other images simulated according to Eq. 1415. We compare the supervised clustering approach with the unsupervised clustering and the two reference algorithms, Elastic net and SVR. The two reference methods are optimized by 4fold crossvalidation within the training set in the range described below. We also compare the methods to a searchlight approach kriegeskorte2006 (radius of and voxels, combined with a SVR approach ()), which has emerged as a reference approach for decoding local finegrained information within the brain.
Both supervised cut and unsupervised cut algorithms are used with , Bayesian Ridge Regression (BRR) as prediction function , and optimized with an internal 4fold crossvalidation.
3.3 Results on onedimensional simulated data
The results of the supervised clustering algorithm are given in Fig. 4. On the top, we give the tree , where the parcels found by the supervised clustering are represented by red squares, and the bottom row are the input features. The features of interest are represented by green dots. We note that the algorithm focuses the parcellation on two subregions, while leaving other parts of the tree unsegmented. The weights found by the prediction function based on the optimal parcellation (bottom) clearly outlines the two simulated informative regions. The predicted weights are normalized by the number of voxels in each parcel.
3.4 Results on simulated neuroimaging data
We compare different methods on the simulated data, see Fig. 4. The predicted weights of the two parcelbased approaches are normalized by the number of voxels in each parcel. Only the supervised clustering (e) extracts the simulated discriminative regions. The unsupervised clustering (f) does not retrieve the whole support of the weights, as the created parcels are constructed based only on the signal and spatial information, and thus do not consider the target to be predicted. Elastic net (h) only retrieves part of the support of the weights, and yields an overly sparse solution which is not easy to interpret. SVR (g) approach yields weights in the primal space that depend on the smoothness of the images. The searchlight approach (c,d), which is a commonly used brain mapping techniques, shows here its limits: it does not cope with the long range multivariate structure of the weights, and yields very blurred informative maps, because this method naturally degrades data resolution.
4 Experiments and results on real data
4.1 Details on real data
We apply the different methods to analyze ten subjects from an fMRI dataset related to the study of the visual representation of objects in the brain (see eger2007 for details). During the experiment, ten healthy volunteers viewed objects of two categories (each one of the two categories is used in half of the subjects) with four different exemplars in each category. Each exemplar was presented at three different sizes (yielding different experimental conditions per subject). Each stimulus was presented four times in each of the six sessions. We averaged data from the four repetitions, resulting in a total of images by subject (one image of each stimulus by session). Functional images were acquired on a 3T MR system with eightchannel head coil (Siemens Trio, Erlangen, Germany) as T2*weighted echoplanar image (EPI) volumes. Twenty transverse slices were obtained with a repetition time of 2s (echo time, 30ms; flip angle, ; mm voxels; mm gap). Realignment, normalization to MNI space, and General Linear Model (GLM) fit were performed with the SPM5 software^{1}^{1}1http:// www.fil.ion.ucl.ac.uk/spm/software/spm5. In the GLM, the time course of each of the stimuli convolved with a standard hemodynamic response function was modeled separately, while accounting for serial autocorrelation with an AR(1) model and removing lowfrequency drift terms with a highpass filter with a cutoff of 128 s. In the present work we used the resulting sessionwise parameter estimate images. All the analysis are performed on the whole brain volume.
Regression experiments: The four different exemplars in each of the two categories were pooled, leading to images labeled according to the 3 possible sizes of the object. By doing so, we are interested in finding discriminative information to predict the size of the presented object. This reduces to a regression problem, in which our goal is to predict a simple scalar factor (size or scale of the presented object).
We perform an intersubject regression analysis on the sizes. This analysis relies on subjectspecific fixedeffects activations, i.e. for each condition, the six activation maps corresponding to the six sessions are averaged together. This yields a total of twelve images per subject, one for each experimental condition. The dimensions of the real data set are and (divided into three different sizes). We evaluate the performance of the method by crossvalidation (leaveonesubjectout). The parameters of the reference methods are optimized with a nested leaveonesubjectout crossvalidation within the training set, in the ranges given before. The supervised clustering and unsupervised clustering are used with Bayesian Ridge Regression (BRR) (as described in section 3.3 in bishop2007 ) as prediction function . Internally, a leaveonesubjectout crossvalidation is used and we set the maximal number of parcels to . The optimal number of parcels is thus selected between and by a nested crossvalidation loop.
A major asset of BRR is that it adapts the regularization to the data at hand, and thus can cope with the different dimensions of the problem: in the first steps of the supervised clustering
algorithm, we have more samples than features, and for the last steps, we have more features than samples. The two hyperparameters that governed the gamma distribution of the regularization term of BRR are both set to
(the prior is weakly informative). We do not optimize these hyperparameters, due to computational considerations, but we check that with more informative priors we obtain similar results in the regression experiment ( and with respectively and ).Classification experiments: We evaluate the performance on a second type of discrimination which is object classification. In that case, we averaged the images for the three sizes and we are interested in discriminating between individual object shapes. For each of the two categories, this can be handled as a classification problem, where we aim at predicting the shape of an object corresponding to a new fMRI scan. We perform two analyses corresponding to the two categories used, each one including five subjects.
In this experiment, the supervised clustering and unsupervised clustering are used with SVC () as prediction function . Such value of yields a good regularization of the weights in the proposed approach, and the results are not too sensitive to this parameter ( for )
4.2 Results for the prediction of size
The results of the intersubjects analysis are given in Tab.2. Both parcelbased methods perform better than voxelbased reference methods. Parcels can be seen as an accurate method for compressing information without loss of prediction performance. Fig. 5 gives the weights found for the supervised cut, the two reference methods and the searchlight ( with and a radius of voxels), using the whole data set. As one can see, the proposed algorithm yields clustered loadings map, compared to the maps yielded by the voxelbased methods, which are very sparse and difficult to represent. Compared to the searchlight, the supervised clustering creates more clusters that are also easier to interpret as they are well separated. Moreover, the proposed approach yields a prediction accuracy for the whole brain analysis, a contrario to the searchlight that only gives a local measure of information.
The majority of informative parcel are located in the posterior part of the occipital cortex, most likely corresponding to primary visual cortex, with few additional slightly more anterior parcels in posterior lateral occipital cortex. This is consistent with the previous findings eger2007 where a gradient of sensitivity to size was observed across object selective lateral occipital ROIs, while the most accurate discrimination of sizes is obtained in primary visual cortex.
Methods  mean  std  max  min  pval to UC 

SVR  
Elastic net  
UC  BRR    
SC  BRR 
Methods  mean  std  max  min  pval to SC 

SVC  **  
SMLR  **  
UC  SVC  
SC  SVC   
Methods  mean (std)  mean (std)  Mean nb. feat. 

cat. 1  cat.2  (voxels/parcels)  
SVC  
SMLR  
UC  SVC  
SC  SVC 
4.3 Results for the prediction of shape
The results of the intersubjects analysis are given in Tab.2. The supervised cut method outperforms the other approaches. In particular, the classification score is higher than with voxelbased SVC and higher than with voxelbased SMLR. Both parcelbased approaches are significantly more accurate and more stable than the voxelbased approaches. The number of features used show the good compression of information performed by the parcels. With ten times less features than voxelbased approaches, the prediction accuracies of parcelbased approaches are higher. The lower performances of SVC and SMLR can be explained by the fact that voxelbased approaches can not deal with intersubject variability, especially in such cases where information can be encoded in pattern of voxels that can vary spatially across subjects.
5 Discussion
In this paper, we have presented a new method for enhancing the prediction of experimental variables from fMRI brain images. The proposed approach constructs parcels (groups of connected voxels) by feature agglomeration within the whole brain, and allows to take into account both the spatial structure and the multivariate information within the whole brain.
Given that an fMRI brain image has typically to voxels, it is perfectly reasonable to use intermediate structures such as parcels for reducing the dimensionality of the data. We also confirmed by different experiments that parcels are a good way to tackle the spatial variability problem in intersubjects studies. Thus feature agglomeration is an accurate approach for the challenging intersubject generalization of brainreading haxby2006 ; haynes2006 . This can be explained by the fact that considering parcels allows to localize functional activity across subjects and thus find a common support of neural codes of interest (see Fig. 6). On the contrary, voxelbased methods suffer from the intersubject spatial variability and their performances are relatively lower.
Our approach entails the technical difficulty of optimizing the parcellation with respect to the spatial organization of the information within the image. To break the combinatorial complexity of the problem, we have defined a recursive parcellation of the volume using Ward algorithm, which is furthermore constrained to yield spatially connected clusters. Note that it is important to define the parcellation on the training database to avoid data overfit. The sets of possible volume parcellations is then reduced to a tree, and the problem reduces to finding the optimal cut of the tree. We propose a supervised cut approach that attempts to optimize the cut with respect to the prediction task. Although finding an optimal solution is infeasible, we adopt a greedy strategy that recursively finds the splits that most improve the prediction score. However, there is still no guarantee that the optimal cut might be reached with this strategy. Model selection is then performed a posteriori by considering the best generalizing parcellation among the available models. Additionally, our method is tractable on real data and runs in a very reasonable of time (a few minutes without specific optimization).
In terms of prediction accuracy, the proposed methods yield better results for the intersubjects study on the different experiments, compared to state of the art approaches (SVR, Elastic net, SVC and SMLR). The supervised cut yields similar or higher prediction accuracy than the unsupervised cut
. In the size prediction analysis, the information is probably coarser than in the object prediction analysis, and thus the simple heuristic of
unsupervised cut yields a good prediction accuracy. Indeed, the unsupervised clustering still optimizes a cost function by selecting the number of parcels that maximizes the prediction accuracy. Thus, in simple prediction task such as the regression problem detailed in this article, this approach allows to extract almost all the relevant information. However, in the prediction of more finegrained information, such as in the classification task, the UC procedure does not provide a sufficient exploration of the different parcellations, and does not extract all the relevant information. Contrariwise, the SC approach explores relevant parcellations using supervised information, and thus performs better than UC.In terms of interpretability, we have shown on simulations and real data that this approach has the particular capability to highlight regions of interest, while leaving uninformative regions unsegmented, and it can be viewed as a multiscale segmentation scheme michel2010 . The proposed scheme is further useful to locate contiguous predictive regions and to create interpretable maps, and thus can be viewed as an intermediate approach between brain mapping and inverse inference. Moreover, compared to a state of the art approach for finegrained decoding, namely the searchlight, the proposed method yields similar maps, but additionally, takes into account nonlocal information and yields only one prediction score corresponding to whole brain analysis. From a neuroscientific point of view, the proposed approach retrieves wellknown results, i.e. that differences between sizes (or between stimuli with different spatial envelope in general) are most accurately represented in the signals of early visual regions that have small and retinotopically laidout receptive fields.
More generally, this approach is not restricted to a given prediction function and can be used with many different classification/regression methods. Indeed, by restricting the search of the best subset of voxels to a tree pruning problem, our algorithm allows us to guide the construction of the prediction function in a lowdimensional representation of a highdimensional dataset. Moreover, this method is not restricted to brain images, and might be used in any dataset where multiscale structure is considered as important (e.g. medical or satellite images).
In conclusion, this paper proposes a method for extracting information from brain images, that builds relevant features by feature agglomeration rather than simple selection. A particularly important property of this approach is its ability to focus on relatively small but informative regions while leaving vast but uninformative areas unsegmented. Experimental results demonstrate that this algorithm performs well for intersubjects analysis where the accuracy of the prediction is tested on new subjects. Indeed, the spatial averaging of the signal induced by the parcellation appears as a powerful way to deal with intersubject variability.
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