Dissociating functional brain networks by decoding the between-subject variability

In this study we illustrate how the functional networks involved in a single task (e.g. the sensory, cognitive and motor components) can be segregated without cognitive subtractions at the second-level. The method used is based on meaningful variability in the patterns of activation between subjects with the assumption that regions belonging to the same network will have comparable variations from subject to subject. fMRI data were collected from thirty nine healthy volunteers who were asked to indicate with a button press if visually presented words were semantically related or not. Voxels were classified according to the similarity in their patterns of between-subject variance using a second-level unsupervised fuzzy clustering algorithm. The results were compared to those identified by cognitive subtractions of multiple conditions tested in the same set of subjects. This illustrated that the second-level clustering approach (on activation for a single task) was able to identify the functional networks observed using cognitive subtractions (e.g. those associated with vision, semantic associations or motor processing). In addition the fuzzy clustering approach revealed other networks that were not dissociated by the cognitive subtraction approach (e.g. those associated with high- and low-level visual processing and oculomotor movements). We discuss the potential applications of our method which include the identification of “hidden” or unpredicted networks as well as the identification of systems level signatures for different subgroupings of clinical and healthy populations.

clustering by focusing mainly on meaningful voxels (i.e. avoiding artifactual or outlier voxels). In our analysis, we limited the volume of interest for the unsupervised fuzzy clustering to all voxels with F-value > 5 (p uncorrected < 0.032, d.f. = [1,36]) in a one sample t-test of on the effect of semantic categorisation relative to fixation.
This identified voxels that are affected by these conditions irrespective of the direction of the effect. It resulted in a total of approximately n = 77000 voxels for the FCM. Figure S1 illustrates the distribution of the selected n voxels.

2-Fuzzy c-mean (FCM) algorithm:
In this work, we used the popular fuzzy c-mean (FCM) algorithm (Bezdek, 1981;Bezdek et al., 1997). In practice, we select n voxels that we want to assign to c clusters. Each voxel i has a vector X i of p values that correspond to the number of properties (e.g. here, number of subjects). Each cluster j is characterised by a centroid V j , which is its characteristic profile. The resemblance between each voxel i and each centroid V j is assessed by the distance D ij between X i and V j . The degree of membership U ij is calculated for each voxel i by comparing D ij for each cluster j to all other clusters.
Practically, the algorithm is based on minimising the following function J m : where "m" is the degree of fuzziness.
Degree of membership U and centroids V are thus defined as: For appropriate clustering, the choice of distance (similarity) measure D, the degree of fuzziness m and the number of expected clusters are critical. In our context, we used the hyperbolic correlation distance proposed previously by Golay et al. (1998) in the context of first-level data-driven fMRI analysis. Accordingly, D is defined as (Fadili et al., 2000;Golay et al., 1998): Where ij CC is the Pearson correlation coefficient between X i and V j .

3-Outlier subjects:
Before running the FCM algorithm on all subjects, we first checked that all subjects have normal activation levels in order to avoid some clusters being dominated by outlier subjects. For this aim, we used a modified fuzzy clustering approach that allows the detection of outlier subjects (for more details about this procedure, see (Seghier et al., 2007)). Practically, this procedure used fuzzy clustering to identify voxels that are dominated by only one subject (i.e. a given subject is an outlier at a given voxel). Then, a global measure, noted G, is estimated by computing a whole brain score that indicates how each subject is dominating in a relative sense the group activation pattern. Using a tuning factor equal to 3 (α = 3 in equation (1) Figure S2A illustrates the global measure G for our 39 subjects. Two subjects (number 16 and 39 in Figure S2A) had high G values. When these two subjects were included in the clustering of all voxels, the centroids of some clusters were clearly dominated by these subjects (see Figure S2B for an illustration). These centroids are not meaningful in the context of our second-level clustering because they represent the particular case of the activated pattern that is dominated by one subject. On this basis, we excluded these two outlier subjects which left 37 subjects for second-level clustering.

4-Optimal number of clusters:
Critically, the "true" number of clusters (i.e. optimal number of classes) is usually unknown in FCM. In this perspective, several cluster-validity indices have previously been proposed in the literature to appreciate, in an unsupervised manner, the optimal number of clusters (for a review see (Wang and Zhang, 2007)). These indices combined different measures of compactness and separation of the clustering in order to ensure that identified clusters are compact and well-separated. In our context, we used a modified version of the Rezaee-Lelieveldt-Reider (RLR) cluster-validity index (Rezaee et al., 1998) as suggested previously by Sun et al. (Sun et al., 2004).
The Rezaee-Lelieveldt-Reider index (RLR) was defined as: The constant α is a weighting constant and X σ is the variance of the whole data set.
V j , U ij and D ij are respectively the centroid of the j-th cluster, the degree of membership of the i-th voxel to the j-th cluster, and the distance between the i-th voxel and the j-th cluster. The best c-partition is obtained by minimising RLR with respect to the number of clusters c. In the original definition of RLR, the constant α was set to 1; however, here we set α equal to the value of SS V V d d ⋅ min max when c reached the maximum number of clusters as suggested previously (for more details, see (Sun et al., 2004)).
Practically, FCM was repeated several times with the number of clusters varying from 2 to 39, and the number of clusters that minimise the RLR index were considered as the optimal number of clusters for our dataset. Here, we found that the RLR clustervalidity index showed an optimal (minimum) value when the number of clusters was Figure S3. The optimal number of clusters (c=10, marked with stars) that minimised the RLR index.