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A Novel Group ICA Approach Based on Multi-scale Individual Component Clustering. Application to a Large Sample of fMRI Data

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Abstract

Functional connectivity-based analysis of functional magnetic resonance imaging data (fMRI) is an emerging technique for human brain mapping. One powerful method for the investigation of functional connectivity is independent component analysis (ICA) of concatenated data. However, this research field is evolving toward processing increasingly larger database taking into account inter-individual variability. Concatenated data analysis only handles these features using some additional procedures such as bootstrap or including a model of between-subject variability during the preprocessing step of the ICA. In order to alleviate these limitations, we propose a method based on group analysis of individual ICA components, using a multi-scale clustering (MICCA). MICCA start with two steps repeated several times: 1) single subject data ICA followed by 2) clustering of all subject independent components according to a spatial similarity criterion. A final third step consists in selecting reproducible clusters across the repetitions of the two previous steps. The core of the innovation lies in the multi-scale and unsupervised clustering algorithm built as a chain of three processes: robust proto-cluster creation, aggregation of the proto-clusters, and cluster consolidation. We applied MICCA to the analysis of 310 fMRI resting state dataset. MICCA identified 28 resting state brain networks. Overall, the cluster neuroanatomical substrate included 98% of the cerebrum gray matter. MICCA results proved to be reproducible in a random splitting of the data sample and more robust than the classical concatenation method.

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Acknowledgements

The authors are deeply indebted to Guy Perchey and Mathieu Vigneau for their help with fMRI data acquisition and analysis.

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Correspondence to Marc Joliot.

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Appendix

Appendix

Simulation of Hub in the Data: Comparison of MICCA and Concat-ICA Processing

We adapted the simulation framework developed by Daubechies et al. (2009) for the group ICA analysis using the Matlab Fast ICA toolbox (http://www.cis.hut.fi/projects/ica/fastica/). We consider two independent components, C 1 and C 2 , and two “observations” at times t 1 and t 2 . “Activation process” is simulated by a random variable with a cumulative density function (cdf) equal to:

$$ \Phi (u) = {\left[ {1 + {e^{{2\left( {2 - u} \right)}}}} \right]^{{ - 1}}} $$

whereas “background process” was associated to a random variable with a cdf equal to:

$$ \Phi (u) = {\left[ {1 + {e^{{ - 1 - u}}}} \right]^{{ - 1}}} $$

“Activations” were restricted to a sparse square of the simulated space (space: 100 × 100 pixels, C 1 (“activated”): 20x20 pixels and C 2 (“activated”): 25 × 20 pixels). Activated pixels of component C 1 were positioned at the coordinates {41,…,60} × {31,…,50}. Activated pixels of component C 2 were gradually shifted according to a parameter α, ranging from -15 to 15, and located at the coordinates {57 + α, …, 81 + α} × {46 + α,…,65 + α}. α measured the overlap between the activated regions of the two independent components from completely separated (α > 10) to highly overlapping (α < -10). α = 0 corresponds to the mathematical independence. Both components were simulated for 100 subjects (for each α value) and mixed by the same times-series: 0.5 C 1  + 0.5 C 2 at t 1 and 0.3 C 1  + 0.7 C 2 at t 2 . These observations (100 subjects x 2 time points) were then used as input for both Concat-ICA and MICCA. We used the spatial correlation to quantify the quality of the decomposition by the norm λ = || ρ(S ic ,S ic )–ρ(S ic ,E ic )|| of the difference between the autocorrelation matrix of the simulated components (S ic ), and the cross correlation matrix between the estimated components (E ic ) and the simulated components (S ic ). For accurate decomposition, λ is close to 0. Because λ depends on the particular realization of C 1 and C 2 , analyses were performed 100 times for each α value. We report the mean and standard deviation of λ. By visual inspection of “success separation”, we considered the components well separated when λ < 0.2 and not when λ > 0.3.

Figure 11 indicates the success of the separation between the two components for both Concat-ICA and MICCA. Under this sparse condition, individual ICA should not be dependent on the overlap value (Daubechies et al. 2009). In the case of independence or no overlap (α ≥ 0), both group approaches successfully estimate the components (λ < 0.2). Concat-ICA was not able to separate components when they shared a large region of “activation” (α ≤ -8). In other words, regions sharing functional connectivity with many networks (known as a “hub”) cannot be well separated using Concat-ICA; thus, networks are not successfully detected.

Fig. 11
figure 11

Rate of success of separating two components simulated for 100 subjects and delineated using Concat-ICA or MICCA. α reflects the overlap between simulated components: α < 0, large overlap; α = 0, independence; α > 0, no overlap. λ indicates the match between average simulated components and estimated components. Components are well separated when λ < 0.2 (light gray) and not well separated when λ > 0.3 (gray). The mean and standard deviation of λ for a set of 100 simulations is given

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Naveau, M., Doucet, G., Delcroix, N. et al. A Novel Group ICA Approach Based on Multi-scale Individual Component Clustering. Application to a Large Sample of fMRI Data. Neuroinform 10, 269–285 (2012). https://doi.org/10.1007/s12021-012-9145-2

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