Abstract
The main challenge in analysing functional magnetic resonance imaging (fMRI) data from extended samples of subject (N > 100) is to extract as much relevant information as possible from big amounts of noisy data. When studying neurodegenerative diseases with resting-state fMRI, one of the objectives is to determine regions with abnormal background activity with respect to a healthy brain and this is often attained with comparative statistical models applied to single voxels or brain parcels within one or several functional networks. In this work, we propose a novel approach based on clustering and stochastic rank aggregation to identify parcels that exhibit a coherent behaviour in groups of subjects affected by the same disorder and apply it to default-mode network independent component maps from resting-state fMRI data sets. Brain voxels are partitioned into parcels through k-means clustering, then solutions are enhanced by means of consensus techniques. For each subject, clusters are ranked according to their median value and a stochastic rank aggregation method, TopKLists, is applied to combine the individual rankings within each class of subjects. For comparison, the same approach was tested on an anatomical parcellation. We found parcels for which the rankings were different among control subjects and subjects affected by Parkinson’s disease and amyotrophic lateral sclerosis and found evidence in literature for the relevance of top ranked regions in default-mode brain activity. The proposed framework represents a valid method for the identification of functional neuromarkers from resting-state fMRI data, and it might therefore constitute a step forward in the development of fully automated data-driven techniques to support early diagnoses of neurodegenerative diseases.
Similar content being viewed by others
Notes
The template binary mask was computed as the mean DMN map of a separate population of control subjects.
A second assumption is that pi decreases when i increases.
The original version of the Kendall tau distance simply counts the number of pairwise discordances between the two ranked lists defined on the same sets of objects; the modified version can deal also with partial lists.
References
Agosta, F., Canu, E., Valsasina, P., Riva, N., Prelle, A., Comi, G., & Filippi, M. (2013). Divergent brain network connectivity in amyotrophic lateral sclerosis. Neurobiology of Aging, 34, 419–427. https://doi.org/10.1016/j.neurobiolaging.2012.04.015.
Amboni, M., Tessitore, A., Esposito, F., Santangelo, G., Picillo, M., Vitale, C., Giordano, A., Erro, R., de Micco, R., Corbo, D., Tedeschi, G., & Barone, P. (2015). Resting-state functional connectivity associated with mild cognitive impairment in Parkinson’s disease. Journal of Neurology, 262, 425–434. https://doi.org/10.1007/s00415-014-7591-5.
Amelio, A., Pizzuti, C. (2015). Is normalized mutual information a fair measure for comparing community detection methods? In Proceedings of the 2015 IEEE/ACM international conference on advances in social networks analysis and mining 2015 - ASONAM ‘15 (pp 1584–1585). New York: ACM Press.
Beato, R., Levy, R., Pillon, B., Vidal, C., du Montcel, S. T., Deweer, B., Bonnet, A. M., Houeto, J. L., Dubois, B., & Cardoso, F. (2008). Working memory in Parkinson’s disease patients: Clinical features and response to levodopa. Arquivos de Neuro-Psiquiatria, 66, 147–151.
Bosch, O. G., Esposito, F., Dornbierer, D., Havranek, M. M., von Rotz, R., Kometer, M., Staempfli, P., Quednow, B. B., & Seifritz, E. (2018). Gamma-hydroxybutyrate increases brain resting-state functional connectivity of the salience network and dorsal nexus in humans. Neuroimage, 173, 448–459. https://doi.org/10.1016/j.neuroimage.2018.03.011.
Buckner, R. L., Andrews-Hanna, J. R., & Schacter, D. L. (2008). The Brain’s default network. Annals of the New York Academy of Sciences, 1124, 1–38. https://doi.org/10.1196/annals.1440.011.
Chiò, A., Pagani, M., Agosta, F., Calvo, A., Cistaro, A., & Filippi, M. (2014). Neuroimaging in amyotrophic lateral sclerosis: Insights into structural and functional changes. Lancet Neurology, 13, 1228–1240. https://doi.org/10.1016/S1474-4422(14)70167-X.
Convit, A., De Asis, J., De Leon, M. J., et al. (2000). Atrophy of the medial occipitotemporal, inferior, and middle temporal gyri in non-demented elderly predict decline to Alzheimer’s disease. Neurobiology of Aging, 21, 19–26. https://doi.org/10.1016/S0197-4580(99)00107-4.
Damoiseaux, J. S., Rombouts, S. A. R. B., Barkhof, F., Scheltens, P., Stam, C. J., Smith, S. M., & Beckmann, C. F. (2006). Consistent resting-state networks across healthy subjects. Proceedings of the National Academy of Sciences of the United States of America, 103, 13848–13853. https://doi.org/10.1073/pnas.0601417103.
De Micco, R., Tessitore, A., Paccone, A., et al. (2013). Dopaminergic modulation of the resting-state sensori-motor network in drug-naive patients with Parkinson’s disease. Movement Disorders, 28, S66–S66.
Di Rosa, E., Pischedda, D., Cherubini, P., et al. (2017). Working memory in healthy aging and in Parkinson’s disease: evidence of interference effects. Aging Neuropsychology and Cognition, 24, 281–298. https://doi.org/10.1080/13825585.2016.1202188.
Dirnberger, G., & Jahanshahi, M. (2013). Executive dysfunction in Parkinson’s disease: A review. Journal of Neuropsychology, 7, 193–224. https://doi.org/10.1111/jnp.12028.
Disbrow, E. A., Sigvardt, K. A., Franz, E. A., et al. (2013). Movement activation and inhibition in Parkinson’s disease: A functional imaging study. Journal of Parkinson's Disease, 3, 181–192. https://doi.org/10.3233/JPD-130181.
Eklund, A., Nichols, T. E., & Knutsson, H. (2016). Cluster failure: why fMRI inferences for spatial extent have inflated false-positive rates. Proceedings of the National Academy of Sciences, 113, 7900–7905. https://doi.org/10.1073/pnas.1602413113.
Esposito, F., & Goebel, R. (2011). Extracting functional networks with spatial independent component analysis: the role of dimensionality, reliability and aggregation scheme. Current Opinion in Neurology, 24, 378–385. https://doi.org/10.1097/WCO.0b013e32834897a5.
Esposito, F., Scarabino, T., Hyvarinen, A., Himberg, J., Formisano, E., Comani, S., Tedeschi, G., Goebel, R., Seifritz, E., & di Salle, F. (2005). Independent component analysis of fMRI group studies by self-organizing clustering. Neuroimage, 25, 193–205. https://doi.org/10.1016/j.neuroimage.2004.10.042.
Esposito, F., Aragri, A., Pesaresi, I., Cirillo, S., Tedeschi, G., Marciano, E., Goebel, R., & di Salle, F. (2008). Independent component model of the default-mode brain function: combining individual-level and population-level analyses in resting-state fMRI. Magnetic Resonance Imaging, 26, 905–913. https://doi.org/10.1016/J.MRI.2008.01.045.
Esposito, F., Pignataro, G., Di Renzo, G., et al. (2010). Alcohol increases spontaneous BOLD signal fluctuations in the visual network. Neuroimage, 53, 534–543. https://doi.org/10.1016/j.neuroimage.2010.06.061.
Esposito, F., Tessitore, A., Giordano, A., de Micco, R., Paccone, A., Conforti, R., Pignataro, G., Annunziato, L., & Tedeschi, G. (2013). Rhythm-specific modulation of the sensorimotor network in drug-naïve patients with Parkinson’s disease by levodopa. Brain, 136, 710–725. https://doi.org/10.1093/brain/awt007.
Galdi, P., Fratello, M., Trojsi, F., Russo, A., Tedeschi, G., Tagliaferri, R., & Esposito, F. (2017). Consensus-based feature extraction in rs-fMRI data analysis. Soft Computing, 22, 1–11. https://doi.org/10.1007/s00500-017-2596-5.
Gattellaro, G., Minati, L., Grisoli, M., Mariani, C., Carella, F., Osio, M., Ciceri, E., Albanese, A., & Bruzzone, M. G. (2009). White matter involvement in idiopathic Parkinson disease: a diffusion tensor imaging study. AJNR. American Journal of Neuroradiology, 30, 1222–1226. https://doi.org/10.3174/ajnr.A1556.
Glasser, M. F., Coalson, T. S., Robinson, E. C., Hacker, C. D., Harwell, J., Yacoub, E., Ugurbil, K., Andersson, J., Beckmann, C. F., Jenkinson, M., Smith, S. M., & van Essen, D. C. (2016). A multi-modal parcellation of human cerebral cortex. Nature, 536, 171–178. https://doi.org/10.1038/nature18933.
Gorges, M., Müller, H.-P., Lulé, D., Ludolph, A. C., Pinkhardt, E. H., & Kassubek, J. (2013). Functional connectivity within the default mode network is associated with saccadic accuracy in Parkinson’s disease: a resting-state FMRI and videooculographic study. Brain Connectivity, 3, 265–272. https://doi.org/10.1089/brain.2013.0146.
Goutte, C. (1999). On clustering fMRI time series.
Goutte, C., Hansen, L. K., Liptrot, M. G., & Rostrup, E. (2001). Feature-space clustering for fMRI meta-analysis. Human Brain Mapping, 13, 165–183. https://doi.org/10.1002/hbm.1031.
Greicius, M. D., Krasnow, B., Reiss, A. L., & Menon, V. (2003). Functional connectivity in the resting brain: a network analysis of the default mode hypothesis. PNAS, 100, 253–258. https://doi.org/10.1073/pnas.0135058100.
Greicius, M. D., Srivastava, G., Reiss, A. L., & Menon, V. (2004). Default-mode network activity distinguishes Alzheimer’s disease from healthy aging: evidence from functional MRI. Proceedings of the National Academy of Sciences of the United States of America, 101, 4637–4642. https://doi.org/10.1073/pnas.0308627101.
Greicius, M. D., Flores, B. H., Menon, V., Glover, G. H., Solvason, H. B., Kenna, H., Reiss, A. L., & Schatzberg, A. F. (2007). Resting-state functional connectivity in major depression: abnormally increased contributions from Subgenual cingulate cortex and thalamus. Biological Psychiatry, 62, 429–437. https://doi.org/10.1016/j.biopsych.2006.09.020.
Hall, P., & Schimek, M. G. (2012). Moderate-deviation-based inference for random degeneration in paired rank lists. Journal of the American Statistical Association, 107, 661–672. https://doi.org/10.1080/01621459.2012.682539.
Hanakawa, T., Fukuyama, H., Katsumi, Y., Honda, M., & Shibasaki, H. (1999). Enhanced lateral premotor activity during paradoxical gait in parkinson’s disease. Annals of Neurology, 45, 329–336. https://doi.org/10.1002/1531-8249(199903)45:3<329::AID-ANA8>3.0.CO;2-S.
Hänggi, J., Streffer, J., Jäncke, L., & Hock, C. (2011). Volumes of lateral temporal and parietal structures distinguish between healthy aging, mild cognitive impairment, and Alzheimer’s disease. Journal of Alzheimer's Disease, 26, 719–734. https://doi.org/10.3233/JAD-2011-101260.
Harrison, B. J., Pujol, J., Lopez-Sola, M., Hernandez-Ribas, R., Deus, J., Ortiz, H., Soriano-Mas, C., Yucel, M., Pantelis, C., & Cardoner, N. (2008). Consistency and functional specialization in the default mode brain network. Proceedings of the National Academy of Sciences, 105, 9781–9786. https://doi.org/10.1073/pnas.0711791105.
Hepp, D. H., Foncke, E. M. J., Olde Dubbelink, K. T. E., van de Berg, W. D. J., Berendse, H. W., & Schoonheim, M. M. (2017). Loss of functional connectivity in patients with Parkinson disease and visual hallucinations. Radiology, 285, 896–903. https://doi.org/10.1148/radiol.2017170438.
Herrington, T. M., Briscoe, J., & Eskandar, E. (2017). Structural and functional network dysfunction in Parkinson disease. Radiology, 285, 725–727. https://doi.org/10.1148/radiol.247172401.
Huettel, S. A., Singerman, J. D., & McCarthy, G. (2001). The effects of aging upon the hemodynamic response measured by functional MRI. Neuroimage, 13, 161–175. https://doi.org/10.1006/nimg.2000.0675.
Hyvarinen, A. (1999). Fast and robust fixed-point algorithm for independent component analysis. IEEE Transactions on Neural Networks, 10, 626–634.
Hyvärinen, A., & Oja, E. (2000). Independent component analysis: algorithms and applications. Neural Networks, 13, 411–430.
Iyer, P. M., Egan, C., Pinto-Grau, M., Burke, T., Elamin, M., Nasseroleslami, B., Pender, N., Lalor, E. C., & Hardiman, O. (2015). Functional connectivity changes in resting-state EEG as potential biomarker for amyotrophic lateral sclerosis. PLoS One, 10. https://doi.org/10.1371/journal.pone.0128682.
Jahanshahi, M., Obeso, I., Baunez, C., Alegre, M., & Krack, P. (2015). Parkinson’s disease, the subthalamic nucleus, inhibition, and Impulsivity. Movement Disorders, 30, 128–140. https://doi.org/10.1002/mds.26049.
Kiernan, M. C., Vucic, S., Cheah, B. C., Turner, M. R., Eisen, A., Hardiman, O., Burrell, J. R., & Zoing, M. C. (2011). Amyotrophic lateral sclerosis. Lancet, 377, 942–955. https://doi.org/10.1016/S0140-6736(10)61156-7.
Lin, S. (2010). Rank aggregation methods. Wiley Interdisciplinary Reviews: Computational Statistics, 2, 555–570. https://doi.org/10.1002/wics.111.
Lin, S., Ding, J. (2009). Integration of Ranked Lists via Cross Entropy Monte Carlo with Applications to mRNA and microRNA Studies on JSTOR. In: Biometrics. http://www.jstor.org/stable/25502239?seq=1#page_scan_tab_contents. Accessed 7 Jan 2016.
Lomen-Hoerth, C., Murphy, J., Langmore, S., Kramer, J. H., Olney, R. K., & Miller, B. (2003). Are amyotrophic lateral sclerosis patients cognitively normal? Neurology, 60, 1094–1097. https://doi.org/10.1212/01.WNL.0000055861.95202.8D.
Luo, C., Chen, Q., Huang, R., Chen, X. P., Chen, K., Huang, X. Q., Tang, H. H., Gong, Q. Y., & Shang, H. F. (2012). Patterns of spontaneous brain activity in amyotrophic lateral sclerosis: A resting-state fMRI study. PLoS One, 7, e45470. https://doi.org/10.1371/journal.pone.0045470.
Luo, C., Guo, X., Song, W., Chen, Q., Yang, J., Gong, Q. Y., & Shang, H. F. (2015). The trajectory of disturbed resting-state cerebral function in Parkinson’s disease at different Hoehn and Yahr stages. Human Brain Mapping, 36, 3104–3116. https://doi.org/10.1002/hbm.22831.
McKinlay, A., Grace, R. C., Dalrymple-Alford, J. C., & Roger, D. (2010). Characteristics of executive function impairment in Parkinsons disease patients without dementia. Journal of the International Neuropsychological Society, 16, 268–277. https://doi.org/10.1017/S1355617709991299.
Meilă, M. (2007). Comparing clusterings—An information based distance. Journal of Multivariate Analysis, 98, 873–895. https://doi.org/10.1016/J.JMVA.2006.11.013.
Menke, R. A. L., Agosta, F., Grosskreutz, J., Filippi, M., & Turner, M. R. (2017). Neuroimaging endpoints in amyotrophic lateral sclerosis. Neurotherapeutics, 14, 11–23. https://doi.org/10.1007/s13311-016-0484-9.
Mohammadi, B., Kollewe, K., Samii, A., Krampfl, K., Dengler, R., & Münte, T. F. (2009). Changes of resting state brain networks in amyotrophic lateral sclerosis. Experimental Neurology, 217, 147–153. https://doi.org/10.1016/j.expneurol.2009.01.025.
Monchi, O., Petrides, M., Mejia-Constain, B., & Strafella, A. P. (2007). Cortical activity in Parkinson’s disease during executive processing depends on striatal involvement. Brain, 130, 233–244. https://doi.org/10.1093/brain/awl326.
Olde Dubbelink, K. T. E. E., Hillebrand, A., Stoffers, D., et al. (2014). Disrupted brain network topology in Parkinson’s disease: A longitudinal magnetoencephalography study. Brain, 137, 197–207. https://doi.org/10.1093/brain/awt316.
Pereira, J. B., Junqué, C., Martí, M. J., et al. (2009). Neuroanatomical substrate of visuospatial and visuoperceptual impairment in Parkinson’s disease. Movement Disorders, 24, 1193–1199. https://doi.org/10.1002/mds.22560.
Poldrack, R. A., Mumford, J. A., Schonberg, T., Kalar, D., Barman, B., & Yarkoni, T. (2012). Discovering relations between mind, brain, and mental disorders using topic mapping. PLoS Computational Biology, 8, e1002707. https://doi.org/10.1371/journal.pcbi.1002707.
Possin, K. L., Filoteo, J. V., Song, D. D., & Salmon, D. P. (2008). Spatial and object working memory deficits in Parkinson’s disease are due to impairment in different underlying processes. Neuropsychology, 22, 585–595. https://doi.org/10.1037/a0012613.
Raichle, M. E. (2015). The Brain’s default mode network. Annual Review of Neuroscience, 38, 433–447. https://doi.org/10.1146/annurev-neuro-071013-014030.
Samuel, M., Ceballos-Baumann, A. O., Blin, J., et al. (1997). Evidence for lateral premotor and parietal overactivity in Parkinson’s disease during sequential and bimanual movements. A PET study. Brain, 120, 963–976. https://doi.org/10.1093/brain/120.6.963.
Schimek, M. G., Myšičková, A., & Budinská, E. (2012). An inference and integration approach for the consolidation of ranked lists. Communications in Statistics: Simulation and Computation, 41, 1152–1166. https://doi.org/10.1080/03610918.2012.625843.
Schimek, M. G., Budinská, E., Kugler, K. G., Švendová, V., Ding, J., & Lin, S. (2015). TopKLists: A comprehensive R package for statistical inference, stochastic aggregation, and visualization of multiple omics ranked lists. Statistical Applications in Genetics and Molecular Biology, 14, 311–316. https://doi.org/10.1515/sagmb-2014-0093.
Smith, S. M., Fox, P. T., Miller, K. L., Glahn, D. C., Fox, P. M., Mackay, C. E., Filippini, N., Watkins, K. E., Toro, R., Laird, A. R., & Beckmann, C. F. (2009). Correspondence of the brain’s functional architecture during activation and rest. Proceedings of the National Academy of Sciences, 106, 13040–13045. https://doi.org/10.1073/pnas.0905267106.
Suo, X., Lei, D., Li, N., Cheng, L., Chen, F., Wang, M., Kemp, G. J., Peng, R., & Gong, Q. (2017). Functional brain connectome and its relation to Hoehn and Yahr stage in Parkinson disease. Radiology, 285, 904–913. https://doi.org/10.1148/radiol.2017162929.
Tedeschi, G., & Esposito, F. (2009). Neuronal networks observed with resting state functional magnetic resonance imaging in clinical populations. Neuroimaging – Cognitive and Clinical Neuroscience. https://doi.org/10.5772/23290.
Tedeschi, G., Trojsi, F., Tessitore, A., Corbo, D., Sagnelli, A., Paccone, A., D'Ambrosio, A., Piccirillo, G., Cirillo, M., Cirillo, S., Monsurrò, M. R., & Esposito, F. (2012). Interaction between aging and neurodegeneration in amyotrophic lateral sclerosis. Neurobiology of Aging, 33, 886–898. https://doi.org/10.1016/j.neurobiolaging.2010.07.011.
Terada, T., Obi, T., Miyata, J., Kubota, M., Yoshizumi, M., Murai, T., Yamazaki, K., & Mizoguchi, K. (2016). Correlation of frontal atrophy with behavioral changes in amyotrophic lateral sclerosis. Neurol Clin Neurosci, 4, 85–92. https://doi.org/10.1111/ncn3.12046.
Tessitore, A., Amboni, M., Esposito, F., Russo, A., Picillo, M., Marcuccio, L., Pellecchia, M. T., Vitale, C., Cirillo, M., Tedeschi, G., & Barone, P. (2012a). Resting-state brain connectivity in patients with Parkinson’s disease and freezing of gait. Parkinsonism & Related Disorders, 18, 781–787. https://doi.org/10.1016/j.parkreldis.2012.03.018.
Tessitore, A., Esposito, F., Vitale, C., Santangelo, G., Amboni, M., Russo, A., Corbo, D., Cirillo, G., Barone, P., & Tedeschi, G. (2012b). Default-mode network connectivity in cognitively unimpaired patients with Parkinson disease. Neurology, 79, 2226–2232. https://doi.org/10.1212/WNL.0b013e31827689d6.
Tessitore, A., Giordano, A., De Micco, R., et al. (2014). Sensorimotor connectivity in Parkinson’s disease: The role of functional neuroimaging. Frontiers in Neurology, 5, 180. https://doi.org/10.3389/fneur.2014.00180.
Thirion, B., Flandin, G., Pinel, P., Roche, A., Ciuciu, P., & Poline, J. B. (2006). Dealing with the shortcomings of spatial normalization: Multi-subject parcellation of fMRI datasets. Human Brain Mapping, 27, 678–693. https://doi.org/10.1002/hbm.20210.
Thirion, B., Varoquaux, G., Dohmatob, E., & Poline, J.-B. (2014). Which fMRI clustering gives good brain parcellations? Frontiers in Neuroscience, 8, 167. https://doi.org/10.3389/fnins.2014.00167.
Trojsi, F., Esposito, F., de Stefano, M., Buonanno, D., Conforti, F. L., Corbo, D., Piccirillo, G., Cirillo, M., Monsurrò, M. R., Montella, P., & Tedeschi, G. (2015). Functional overlap and divergence between ALS and bvFTD. Neurobiology of Aging, 36, 413–423. https://doi.org/10.1016/j.neurobiolaging.2014.06.025.
Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D. et al (2002). Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain.
van den Heuvel, M., Mandl, R., & Pol, H. H. (2008). Normalized cut group clustering of resting-state fMRI data. PLoS One, 3, e2001. https://doi.org/10.1371/JOURNAL.PONE.0002001.
Van Eimeren, T., Monchi, O., Ballanger, B., & Strafella, A. P. (2009). Dysfunction of the default mode network in Parkinson disease: a functional magnetic resonance imaging study. Archives of Neurology, 66, 877–883. https://doi.org/10.1001/archneurol.2009.97.
Verstraete, E., & Foerster, B. R. (2015). Neuroimaging as a new diagnostic modality in amyotrophic lateral sclerosis. Neurotherapeutics, 12, 403–416. https://doi.org/10.1007/s13311-015-0347-9.
Verstraete, E., Veldink, J. H., van den Berg, L. H., & van den Heuvel, M. P. (2014). Structural brain network imaging shows expanding disconnection of the motor system in amyotrophic lateral sclerosis. Human Brain Mapping, 35, 1351–1361. https://doi.org/10.1002/hbm.22258.
Vinh, N.X., Epps, J. (2009). A novel approach for automatic number of clusters detection in microarray data based on consensus clustering. In 2009 Ninth IEEE International Conference on Bioinformatics and BioEngineering. (pp 84–91). IEEE.
Vinh N.X., Epps, J., Bailey, J. (2009). Information theoretic measures for clusterings comparison. In Proceedings of the 26th Annual International Conference on Machine Learning - ICML ‘09. (pp 1–8).
von Luxburg, U. (2010). Clustering stability: an overview. Foundations and Trends in Machine Learning, 2, 235–274. https://doi.org/10.1561/2200000008.
Whitfield-Gabrieli, S., & Ford, J. M. (2012). Default mode network activity and connectivity in psychopathology. Annual Review of Clinical Psychology, 8, 49–76. https://doi.org/10.1146/annurev-clinpsy-032511-143049.
Wicks, P., Turner, M. R., Abrahams, S., Hammers, A., Brooks, D. J., Leigh, P. N., & Goldstein, L. H. (2008). Neuronal loss associated with cognitive performance in amyotrophic lateral sclerosis: An ( 11 C)-flumazenil PET study. Amyotrophic Lateral Sclerosis, 9, 43–49. https://doi.org/10.1080/17482960701737716.
Yarkoni, T., Poldrack, R. A., Nichols, T. E., van Essen, D. C., & Wager, T. D. (2011). Large-scale automated synthesis of human functional neuroimaging data. Nature Methods, 8, 665–670. https://doi.org/10.1038/nmeth.1635.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no conflict of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Galdi, P., Fratello, M., Trojsi, F. et al. Stochastic Rank Aggregation for the Identification of Functional Neuromarkers. Neuroinform 17, 479–496 (2019). https://doi.org/10.1007/s12021-018-9412-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12021-018-9412-y