We propose a new Inter Subject Correlation (ISC) based exploratory data analysis technique termed Functional Segmentation ISC (FuSeISC) analysis. The method provides an ISC based functional parcellation of the brain, which is based on differences in average ISCs and their subject-wise variation across different scenes of the movie stimulus. It allows simple and highly interesting interpretation of the activation/ISCs. The method is rooted on the basic ISC analysis provided by our openly available ISC toolbox and couples this with a novel clustering algorithm to allow the detection of brain areas that have similar ISC properties.
We analyzed a subset of data derived from a studyforrest data set, where participants listened to a German audio-description of the movie "Forrest Gump". 5 interesting scenes were selected for the analysis based on their publicity in social media. For each scene and each voxel, an average ISC value was computed across the subjects and its between-subject variation using the Jackknife technique. This provided 10 dimensional feature vector for each voxel. These feature vectors were then used as an input of a robust Gaussian mixture model based clustering algorithm, where the number of clusters is automatically decided based on the coarsity parameter. We decided to experiment the new method with a small number of clusters for easy interpretation of the clustering results. With the selected parameter value the clustering produced 13 clusters, 7 of which were found to be relevant. The method identified spatially coherent clusters although no information about the voxels’ spatial location were used in the clustering process.
Inter-subject correlation (ISC) analysis has been successfully used in many functional magnetic resonance imaging (fMRI) studies based on experiments involving "naturalistic" stimuli, such as movies (Hasson et al. 2004, Jääskeläinen et al. 2008, Golland et al. 2007). ISC analysis is conceptually simple, as it merely involves voxel-wise computation of a correlation coefficient between time-series of the subjects. Once the correlation coefficients have been computed across all participants exposed to an identical stimulus, subject-pairwise correlation coefficients for each voxel can be averaged and subsequently thresholded to obtain brain maps indicating which regions exhibited ISC during the stimulus (Wilson et al. 2008, Kauppi et al. 2010). A major strength of the ISC based analysis is that the method can reliably detect activated brain areas without requiring any model for a hemodynamic response function (Pajula et al. 2012).
The basic form of the ISC analysis ignores the temporal variability in activation/ISCs caused by rich, dynamic nature of naturalistic stimuli as it processes the whole time series as whole. For instance, it is plausible that during an engaging drama movie, there is spatio-temporal variation in brain activation from scene to scene for each subject. In this case, a conventional ISC analysis across a whole stimulus would easily miss interesting findings which are specific to certain scenes in a movie. Previously, temporal variation in ISCs has been captured by computing ISCs in short time windows, but investigation of several 3-dimensional ISC maps becomes easily tedious and more compact representation of ISC information would be highly preferable.
In addition, similarly to model-based brain mapping methods, ISC-based mapping represents averaged information across people, i.e., it assumes that brain mechanisms are similar for all people in different brain areas. This assumption is violated in practice, since individuals may process exactly same sensory information highly differently (Speelman and McGann, 2013). Obviously, some brain mechanisms are more similar across people than others. For instance, certain mechanisms of low-level visual information processing may be much more consistent across people than mechanisms of higher-order brain functions. Thus, a conventional approach based on averaging of the functional information across subjects easily detects high activation/ISC values in sensory areas but may completely lose findings in higher-order brain areas due to high intersubject variability. Therefore, to better understand complex functions of the brain, such as aspects of social cognition or emotions, more sensitive analysis methods are needed that can take intersubject variability better into account.
To overcome the aforementioned limitations, we propose a new ISC based exploratory data analysis technique termed FuSeISC. The method provides an ISC based functional parcellation of the brain based on differences in average ISCs and their subject-wise variation across different scenes of the movie stimulus, allowing simple and highly interesting interpretation of the activation/ISCs. Our method is rooted on the basic ISC analysis provided by our openly available ISC toolbox and couples this with a novel clustering algorithm to allow the detection of brain areas that have similar ISC properties (this algorithm’s source code is also publicly available). Many functional parcellation algorithms have been previously proposed in the literature (see e.g. Craddock et al. 2012, van den Heuvel et al. 2008). However, these approaches require two-level analysis (subject-level and group-level) and choice of ad hoc parameters such as the number of clusters or the shape and size of a spatial neighborhood of interest. FuSeISC extends this conventional approach because it works directly in group-level, naturally considers similarities and differences in brain activation between subjects and has only one easily interpretable parameter to tune. Moreover, our method does not constrain functional parcellations by any anatomic brain subdivision, allowing finding both small clusters as well as large-scale functional cluster networks simultaneously.
We analyzed preprocessed fMRI data sets of 19 subjects provided by the organization committee of the studyforrest project and data challenge (Hanke et al. 2014). The details of the experiment, data collection and preprocessing are also provided in (Hanke et al. 2014). In brief, the participants listened to a German audio-description (Koop, Michalski, Beckmann, Meinhardt & Benecke, produced by Bayrischer Rundfunk, 2009) of the movie "Forrest Gump" (R. Zemeckis, Paramount Pictures, 1994) as broadcast as an additional audio track for visually impaired listeners on Swiss public television. The audio content is largely identical to the dubbed German soundtrack of the movie except for interspersed narrations by a male speaker who describes the visual content of a scene. The entire data set consisted of 8 runs (lasting approximately 15 minutes each) for each subject from which we selected five highly attractive clips for our analysis. We ranked the attractiveness of the clips based on an internet survey on online video services such as Youtube and movie discussion forums.
The data set for the analysis was defined from the original preprocessed linear anatomical alignment set of studyforrest data. The exact time points used to create the five clips are listed in the following table 1:
|Clip||Run||Start timepoint||Stop timepoint||Total length||Description|
|Clip0||1||1||50||50||Feather flies and actors are described|
|Clip1||2||1||50||50||Scene with 'Run, Forrest, Run' cry|
|Clip2||2, 3||432 (run 2), 1 (run 3)||441 (run 2), 45 (run 3)||54||Scene where Bubba and Forrest discuss about shrimps and how to cook them|
|Clip3||6||158||404||246||Forrest runs accross the USA from coast to coast|
|Clip4||7||46||107||51||Forrest explains to Jenny about his adventures next to the Jenny’s bed and at the end of the scene Jenny dies|
ISC based feature extraction
We extracted ISC based features from the data sets describing the extent and between subject variability of the ISC within each clip. First, we computed average ISC maps separately for each clip across the whole brain using the ISC toolbox (Kauppi et al. 2014). In these maps, each voxel represents mean of the correlation coefficients computed across all 171 subject pairs. We call these five values per voxel as voxel’s mean ISC features. In addition to the mean ISC features, we computed the variability features of the ISC within each voxel using a leave-one-subject-out Jackknife procedure. More specifically, we computed 19 mean ISC maps so that each subject was left out from the original sample one at a time. The Jackknife standard deviation estimate was then produced based on these 19 mean ISC maps for each voxel; A similar procedure has been applied by Pajula and Tohka (2014), where a more technical description of the procedure can be found. These 5 values per voxel are called variability features. Because the scale of the mean ISCs and variability features is different, we balanced the importance of the features by scaling variance features by a factor 10 before subsequent analysis. Because we computed mean and variability features separately for each five clips across the whole brain, we obtained 10 features in total from 457 528 voxels for further analysis.
Clustering of ISC features
Next, we clustered the ISC based features extracted from each voxel across the whole brain to produce FuSeISC functional segmentation of the brain. The idea is that the voxels showing similar mean ISC and inter-subject variability across different stimuli should belong to the same cluster/functional segment.
We used a Gaussian mixture model (GMM) for clustering (Duda et al. 2012), accompanied with a robust cluster initialization scheme based on automated shared nearest neighbor (SNN) graph selection procedure (Kauppi et al. 2011b, Kauppi 2011c). The proposed clustering method has several advantages when analyzing large and highly complex fMRI data sets. For instance, 1) our method can detect clusters of varying densities, shapes and sizes, 2) it can estimate the number of clusters automatically, 3) it requires only single easily interpretable parameter as an input, 4) it is robust against outliers, and 5) it is capable of processing a high number of brain voxels with low memory cost and in feasible time. The steps of our clustering algorithm are as follows:
- Compute k-nearest neighbor (k-NN) list of the data. We used the Euclidean distance between ISC features to construct the k-NN list. The selection of k is discussed in a separate section below.
- Compute a weighted SNN graph of the data. In a weighted SNN graph, two data points are connected only if they belong to each other’s k-NN lists (Jarvis and Patrick, 1973). The connections are further weighted by the number of shared data points the connected points share in their k-NN lists.
- Compute SNN density of each data point. SNN "density" is simply a sum of the connection weights associated with each data point in the weighted SNN graph (note that despite of its name, SNN density is not a real measure of density). The highly interesting property of the SNN density is that it obtains a high value when a data point is relatively close to its neighbors (in the Euclidean sense) with respect to surrounding data points, allowing reliable detection of clusters with varying densities (Ertöz et al. 2002, Tan et al. 2013).
- Create all possible sparsifications of the weighted SNN graph based on SNN density values. Sparsification means removal of those graph connections whose weights do not exceed a certain threshold. In our procedure, all possible sparsified graphs are created to avoid manual selection of a threshold value.
- Compute centroids of the connected components for each sparsified SNN graph. We used the means of the data points belonging to each component as centroids. Note that the number of connected components (and thus the number of centroids) can vary notably between the sparsified graphs.
- Use a minimum error criterion to find centroids (belonging to one sparsified SNN graph) which best describe the underlying data. We used the mean-squared-error (MSE) as the criterion between centroids and data points. Interestingly, we have observed in various simulations generated from very complex GMMs including a high number of outliers that the proposed model selection procedure tends to provide highly meaningful solutions where all clusters in data are robustly represented by at least one centroid. Such initial solution is highly desirable for subsequent clustering algorithms, such as the K-means and the expectation maximization (EM) algorithm, because the sensitivity of these methods to converge towards local extrema is efficiently reduced.
- Run K-means clustering using the found centroids to estimate the initial mean and covariance matrices of the GMM. Obviously, K refers to the number of centroids provided in the previous step.
- Estimate the GMM using the EM algorithm and extract final clusters using maximum a posteriori -rule. Due to high complexity of our data, we estimated unrestricted and unique covariance matrices for each Gaussian component.
- As a post-processing, for each cluster, find their spatially distinct "subclusters" and remove those subclusters whose sizes are smaller than k as noise.
- For each retained subcluster, find their densest data point for better anatomical localization of the clusters. For each data point, we used the minimum distance to kth nearest neighbor as a ranking criterion for density.
Selection of neighborhood size k
Our method contains only a single parameter, neighborhood size k, to adjust. The selection of this parameter is meaningful because it naturally defines the resolution of the analysis: To detect all meaningful clusters, k should roughly equal to the number of data points in the smallest cluster of interest. This choice guarantees high SNN density values within all clusters (despite of cluster size and irrespective of the total number of clusters) whose modes are captured by our algorithm. In practice, the choice of k depends on the goal of the analysis, because the difference between "noise" (non-interesting structure) and "cluster" (meaningful structure) in complex fMRI data is subtle. For instance, it may not be meaningful to use very small k to avoid capturing non-interesting structures related to noise or effects of spatial smoothing. In this study, we wanted to analyze a relatively low number of clusters to simplify interpretations and validate our method. For this reason, we run clustering several times using increasing values for k and returned the first solution providing less than 15 clusters (we started from k = 100 and used increments of 25; the desired solution was achieved with k = 275). 15 clusters provides obviously very crude parcellation for human brain, but should nevertheless be enough to identify some main functions during the natural stimulus. Moreover, with a high number of clusters, reasonability of the results might be more difficult to check. The clustering algorithm in itself has been validated in (Kauppi et al. 2011b).
Standard ISC analysis
The average ISC maps across subject pairs for the 5 movie clips are displayed below (the maps were FDR corrected across the whole brain using q = 0.001). As expected, the highest ISCs were observed in the auditory cortices for all the clips. Most clips showed also significant ISCs in the frontal cortex, particularly at anterior cingulum. Some clips (1 and 2) showed significant ISCs in the occipital cortex particularly in the calcarine and in the lingual gyrus. With the exception of auditory cortex which was detected with all the movies clips, there was marked variation in the ISC patterns between the movie clips.
The FuseISC clustering with k = 275 produced 13 clusters. Seven of these 13 clusters were selected for further inspection by visual judgement. However, it would not be difficult to implement an algorithm to perform the same task automatically using a set of heuristics, because the remaining 6 clusters were clearly noise (many small disconnected components) and/or consisted mainly of white matter/cerebro-spinal fluid voxels. We provide volumes of all the clusters (also the spurious ones) as nifti-file to let others to make their own judgements about the relevance of the clusters. However, we limit our discussion below to the seven clusters we selected as relevant.
Interestingly, the seven relevant clusters were spatially coherent although no information about voxels’ spatial locations were used in the clustering algorithm and the amount of spatial smoothing was kept minimal following suggestions of Pajula and Tohka (2014). Also, the clusters seemed to be functionally relevant although we refrain making specific inferences on the functional roles of each cluster, since that would be impossible to confirm in the naturalistic stimulation experiments. The clusters are shown in the images below and briefly described next.
Of the seven interesting FuSeISC clusters, Cluster 1 contained voxels only in the auditory cortices and was characterized by high values for all 10 features. The identification of the main sensory area for the audio stimulus as a clearly separable cluster is a promising result. Cluster 13 was concentrated on the occipital cortex containing voxels from Calcarine, Cuneus, and Lingual Gyrus and thus could be speculated to be related to the visual imagery. The cluster was characterized by much higher feature values for the first three clips than for the remaining two clips.
Clusters 2,10, and 11 could be characterized as network clusters as the voxels in them were distributed across the brain. Cluster 2 contained voxels from several ares including medial frontal cortex, anterior and posterior cingulate, angular gyrus and surrounding temporal and occipital areas as well as from cuneus and precuneus. Cluster 10 included voxels from the caudal part of anterior cingulum as well as from inferior frontal cortex and middle temporal cortex - many of these areas have been found to be related to the language processing. Cluster 11 contained voxels from posterior cingulus, precuneus, cuneus, insula, middle and superior temporal cortices and middle frontal gyrus. Clusters 10 and 11 could be clearly distinguished from cluster 2 also based on their ISC features: the feature values of clusters 10 and 11 were high for Clip 1 whereas the values for cluster 2 were (relatively) high for the two final clips.
Cluster 8 and 9 encompassed mainly frontal areas, cluster 8 occupied the region near brain surface and was characterised by very low mean ISC feature values, typical to noise clusters. However, the feature values were stable across different clips and also the variability features had higher values than for the noise clusters. Cluster 9 contained voxels from different parts of the frontal cortex and was characterised by smaller feature values for later clips.
The coordinates of densiest points of selected clusters are listed in table 2. The table shows in volume spatial coordinates and corresponding MNI coordinates.
|Cluster||Centroid#||X||Y||Z||MNI X||MNI Y||MNI Z|
We propose a new ISC based exploratory data analysis technique termed FuSeISC. The method provides an ISC based functional parcellation of the brain based on differences in average ISCs and their subject-wise variation across different scenes of the movie stimulus, allowing simple and highly interesting interpretation of the activation/ISCs. We experimented the method with the studyforrest dataset and identified a coarse functional brain parcellation into seven functionally similar regions. Less coarse parcellations are possible by simply decreasing the value of the parameter k controlling the coarseness of the clustering.
Traditionally in functional neuroimaging, high intersubject variability is regarded merely as noise (Speelman and McGann 2013). However, recent studies suggest that intersubject variability in functional connectivity is heterogeneous across the cortex and that this variability contains meaningful information which should be carefully investigated (Zilles and Amunts 2013, Mueller 2013). FuSeISC takes such heterogeneity naturally into account, making the method a highly attractive tool for analysis of human brain functions.
All resulting statistics and clusters are provided in following list.
- Sum binary mask for ISC analysis. Mask contains voxels which are common to functional data of all subjects
- Masked MNI-152 template. Original MNI-152 template from *studyforrest*t data repository masked with ISC binary mask.
- Full ISC map for Clip 0
- Full ISC map for Clip 1
- Full ISC map for Clip 2
- Full ISC map for Clip 3
- Full ISC map for Clip 4
- Jackknife std estimate map for Clip 0
- Jackknife std estimate map for Clip 1
- Jackknife std estimate map for Clip 2
- Jackknife std estimate map for Clip 3
- Jackknife std estimate map for Clip 4
- Functional segmentation map with neighborhood size k=275
Implementation, codes, and other details needed to reproduce the analysis
All scripts and software needed for this analysis are available in table 4 after the step descriptions.
The data is separated from the studyforrest GIT-annex repository. Before this step, the git-annex meta-data repository for studyforrest must be cloned and set ready to use. See more instructions from http://studyforrest.org/pages/access.html.
In this step the time points corresponding to the selected movie clips are separated from the original data. The data is also spatially smoothed with 3mm FWHM Gaussian kernel using fslmath. This procedure also generates a brain mask for ISC analysis. The brain mask is used to exclude those voxels which were not present in every functional data of subjects and it is smaller than the one originally provided by studyforrest data.
This whole step can be done in Linux environment using ForrestDataGenerator.m script in Matlab (2014a or newer). The script requires that FSL is installed in the same environment because Matlab performs the Gaussian smoothing with fslmath program through unix command. This phase is quite time-consuming and requires approximately 20 Gb of HDD space.
Average ISC maps for each five clip are computed separately using the ISC toolbox. The parameters must be set-up using the ISCtoolbox start-up GUI (in Matlab: "ISCanalysis"). The parameters for the toolbox are the same for each clip:
- a single Session where the full directory paths of mat files are listed for every subject of the current clip (same order of subjects must be the same for each clip). The mat-files were generated in Step 1 for each clip.
- basic ISC analysis
- removal of memory mapped data after analysis
- de-selected template and use the separately defined binary map (generated in Step 1)
- ISC map settings:
- calculate average ISC maps
- calculate median quartile std and t-score ISC maps
- Save ISC matrices
- Resampling based statistical maps:
- 100 000 realizations
- 100 batches
- total of 10 000 000 realizations
- If supported cluster environment is available it can be used by de-selecting "Always force local computing" and defining the grid parameters according the available grid. Toolbox supports currently Slurm and SGE grid engines.
ISC analysis for each clip can take hours depending on the used computer and environment. Each ISC result will require approximately 900 MB of HDD space due to large correlation matrices required in the next phase of this analysis. During the analysis, each ISC run requires approximately 20 GB of HDD space for temporary files.
After all ISC analyses are finished, the variability features of the ISC must be computed within each voxel using a leave-one-subject-out Jackknife procedure. This is done in Matlab using StdEstimate.m script. The script needs the ISCJackKnife -function to compute estimates for the jackknifed ISC statistics. The ISCJackKnife -function is included in ISCtoolbox svn repository and will be used in future releases of ISC toolbox. The function is under same MIT license as ISCtoolbox.
After defining the variability features for each clip the StdEstimate script vectorizes the data (removes spatial information) and gathers it in a single feature matrix X. Data is first combined with the corresponding voxel vice mean ISC values as [2 x 449612] matrices for each clip and then these five matrices are combined to a complete [10 x 449612] matrix. This matrix defines the 10 dimensional features for each brain voxel inside the brain mask generated in Step 1.
The feature matrix X is given to a clustering algorithm to compute the clusters in 10 dimensional feature space. This procedure can be executed with script runFuSeISCclustering.m in Matlab (2014a or newer). The script requires FuSeISC components from ISCtoolbox svn repository which are under MIT license. At the beginning of the script a result path must be defined. The process saves there temporary clustering results for the later use. If needed the clustering sources must be compiled for current environment (the FuSeISC package contains mex sources but also most common binaries). When binaries are functional the clustering is performed. After this the resulting clusters are cleaned from too small instances and finally most densiest points of the clusters are computed using the temporary files of clustering algorithm.
As a final phase for the analysis the local Centroids are computed for every selected clusters. Script ClusterCentroidsAndNifti.m computes these values as well as MNI coordinates for the detected centroids. The script prints them on Matlab command line. The clip also generates NifTi file from all detected clusters and another from the selected clusters.
The results can be visualized for example with fslview by using the reduced MNI-152 template as a background image. In the clustering results each voxel has a single label value corresponding to the cluster number. The results are in the same space as the linear alignment data of studyforrest dataset.
|Data generation script for the analysis||ForrestDataGenerator.m|
|FSL software, required for ForrestDataGenerator.m script||FSL Homepage|
|ISCtoolbox for Matlab||ISCtoolbox Homepage|
|StdEstimate Matlab script for ISC results||StdEstimate.m|
|ISCJackknife function for StdEstimate scripti||ISCJackKnife.m from isc-toolbox SVN|
|FuSeISC components for the clustering procedure||fuseISCclustering.zip from isc-toolbox SVN|
|ClusterCentroidsAndNifti.m script for matlab to compute the centroids and create nifti files for visual inspection||ClusterCentroidsAndNifti.m|
About this work
This article was a submission to the real-life cognition contest by Juha Pajula (Department of Signal Processing, Tampere University of Technology), Jussi Tohka (Department of Signal Processing, Tampere University of Technology), and Jukka-Pekka Kauppi (Department of Computer Science, University of Helsinki).
All source code and materials related to this submission are copyright (c) 2014 by the authors listed above and are made available under the terms of the MIT license.
- Craddock, RC., James, GA., Holtzheimer, PE., Hu, XP. and Mayberg, HS. A whole brain fMRI atlas generated via spatially constrained spectral clustering. Human brain mapping, 33(8), 1914-1928, 2012.
- Duda, RO., Hart, PE., and Stork, DG. Pattern Classification. Wiley, 2nd Edition, 2012.
- Ertöz, L., Steinbach, M., and Kumar, V. A new shared nearest neighbor clustering algorithm and its applications. In Workshop on Clustering High Dimensional Data and its Applications at 2nd SIAM International Conference on Data Mining, 105-115, 2002.
- Golland, Y., Bentin, S., Gelbard, H., Benjamini, Y., Heller, R., Nir, Y., et al. Extrinsic and intrinsic systems in the posterior cortex of the human brain revealed during natural sensory stimulation. Cerebral Cortex, 17(4), 766–777, 2007.
- Hanke, M, Baumgartner, FJ., Ibe, P., Kaule, FR., Pollmann, S., Speck, O., Zinke, W. and Stadler, J. A high-resolution 7-Tesla fMRI dataset from complex natural stimulation with an audio movie. Scientific Data 1, Article number: 140003, 2014. doi:10.1038/sdata.2014.3
- Hasson U, Nir Y, Levy I, Fuhrmann G, Malach R Intersubject synchronization of cortical activity during natural vision. Science 303: 1634–1640, 2004. doi: 10.1126/science.1089506
- Jarvis, RA., and Patrick, EA. Clustering using a similarity measure based on shared near neighbors. IEEE Transactions on Computers, 100(11), 1025-1034, 1973.
- Jääskeläinen, IP., Koskentalo, K., Balk, MH. et al. Inter-subject synchronization of prefrontal cortex hemodynamic activity during natural viewing, The Open Neuroimaging Journal 2(14), 2008.
- Kauppi, J-P., Pajula, J., and Tohka, J. A versatile software package for inter-subject correlation based analyses of fMRI. Frontiers in neuroinformatics 8, 2014.
- Kauppi, J-P., Jääskeläinen, IP., Sams, M., and Tohka, J. Inter-subject correlation of brain hemodynamic responses during watching a movie: localization in space and frequency, Frontiers in Neuroinformatics 4:5, 2010.
- Kauppi, J-P., Nykter, M., and Niemi, J. Clustering method for data having outliers and clusters with varying sizes and densities. Report, Department of Signal Processing, Tampere University of Technology, 2011:3, 2011b.
- Kauppi, J-P., Pattern classification method to analyze dynamic complex systems: applications with fMRI, gene expression and radar data, PhD thesis, Tampere University of Technology, Finland, 2011c.
- Mueller, S., Wang, D., Fox, MD., Yeo, BT., Sepulcre, J., Sabuncu, MR., …, and Liu, H. Individual variability in functional connectivity architecture of the human brain. Neuron, 77(3), 586-595, 2013.
- Pajula J, Kauppi J-P, Tohka J. Inter-Subject Correlation in fMRI: Method Validation against Stimulus-Model Based Analysis. PLoS ONE 7(8): e41196, 2012. doi:10.1371/journal.pone.0041196
- Pajula, J. and Tohka, J. Effects of spatial smoothing on inter-subject correlation based analysis of FMRI, Magnetic Resonance Imaging, 32(9), 1114-1124, 2014. http://dx.doi.org/10.1016/j.mri.2014.06.001
- Speelman CP., and McGann M. How mean is the mean? Frontiers in Psychology 4:451, 2013. doi: 10.3389/fpsyg.2013.00451
- Tan, PN., Steinbach, M, and Kumar, V. Introduction to Data Mining. Addison-Wesley, 2nd Edition, 2013.
- van den Heuvel, M., Mandl, R., Hulshoff Pol, H. Normalized cut group clustering of resting-state fMRI data. PLoS ONE 3(4): e2001, 2008. doi:10.1371/journal.pone.0002001
- Wilson, SM., Molnar-Szakacs, I., and Iacoboni, M. Beyond superior temporal cortex: intersubject correlations in narrative speech comprehension, Cerebral Cortex 18(1), 230-242, 2008.
- Zilles, K., and Amunts, K. Individual variability is not noise. Trends in cognitive sciences, 17(4), 153-155, 2013.