Skip to main content

Minimum Partial Correlation: An Accurate and Parameter-Free Measure of Functional Connectivity in fMRI

  • Conference paper
  • First Online:
Brain Informatics and Health (BIH 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9250))

Included in the following conference series:

Abstract

Functional connectivity, a data-driven modelling of spontaneous fluctuations in activity in spatially segregated brain regions, has emerged as a promising approach to generate hypotheses and features for prediction. The most widely used method for inferring functional connectivity is full correlation, but it cannot differentiate direct and indirect effects. This disadvantage is often avoided by fully partial correlation, but this method suffers from Berkson’s paradox. Some advanced methods, such as regularised inverse covariance and Bayes nets, have been applied. However, the connectivity inferred by these methods usually depends on crucial parameters. This paper suggests minimum partial correlation as a parameter-free measure of functional connectivity in fMRI. An algorithm, called elastic PC-algorithm, is designed to approximately calculate minimum partial correlation. Our experimental results show that the proposed method is more accurate than full correlation, fully partial correlation, regularised inverse covariance, network deconvolution algorithm and global silencing algorithm in most cases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barzel, B., Barabási, A.L.: Network link prediction by global silencing of indirect correlations. Nature Biotechnology 31(8), 720–725 (2013)

    Article  Google Scholar 

  2. Berkson, J.: Limitations of the application of fourfold table analysis to hospital data. Biometrics Bulletin, pp. 47–53 (1946)

    Google Scholar 

  3. Buckner, R.L., Krienen, F.M., Yeo, B.T.: Opportunities and limitations of intrinsic functional connectivity mri. Nature Neuroscience 16(7), 832–837 (2013)

    Article  Google Scholar 

  4. Chenga, J., Greinera, R., Kellya, J., Bellb, D., Liub, W.: Learning bayesian networks from data: an information-theory based approach. Artificial Intelligence 137, 43–90 (2002)

    Article  MathSciNet  Google Scholar 

  5. Colombo, D., Maathuis, M.H.: Order-independent constraint-based causal structure learning. Journal of Machine Learning Research 15, 3741–3782 (2014)

    MathSciNet  Google Scholar 

  6. Craddock, R.C., Jbabdi, S., Yan, C.G., Vogelstein, J.T., Castellanos, F.X., Di Martino, A., Kelly, C., Heberlein, K., Colcombe, S., Milham, M.P.: Imaging human connectomes at the macroscale. Nature Methods 10(6), 524–539 (2013)

    Article  Google Scholar 

  7. Feizi, S., Marbach, D., Médard, M., Kellis, M.: Network deconvolution as a general method to distinguish direct dependencies in networks. Nature Biotechnology 31(8), 726–733 (2013)

    Article  Google Scholar 

  8. Fisher, R.A.: The distribution of the partial correlation coefficient. Metron 3, 329–332 (1924)

    Google Scholar 

  9. Friedman, J., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9(3), 432–441 (2008)

    Article  MATH  Google Scholar 

  10. Friston, K.J.: Functional and effective connectivity: a review. Brain Connectivity 1(1), 13–36 (2011)

    Article  MathSciNet  Google Scholar 

  11. Friston, K.J., Harrison, L., Penny, W.: Dynamic causal modelling. Neuroimage 19(4), 1273–1302 (2003)

    Article  Google Scholar 

  12. Hawellek, D.J., Hipp, J.F., Lewis, C.M., Corbetta, M., Engel, A.K.: Increased functional connectivity indicates the severity of cognitive impairment in multiple sclerosis. Proceedings of the National Academy of Sciences 108(47), 19066–19071 (2011)

    Article  Google Scholar 

  13. Hermundstad, A.M., Bassett, D.S., Brown, K.S., Aminoff, E.M., Clewett, D., Freeman, S., Frithsen, A., Johnson, A., Tipper, C.M., Miller, M.B., et al.: Structural foundations of resting-state and task-based functional connectivity in the human brain. Proceedings of the National Academy of Sciences 110(15), 6169–6174 (2013)

    Article  Google Scholar 

  14. Hinne, M., Ambrogioni, L., Janssen, R.J., Heskes, T., van Gerven, M.A.: Structurally-informed bayesian functional connectivity analysis. Neuroimage 86, 294–305 (2014)

    Article  Google Scholar 

  15. Marrelec, G., Krainik, A., Duffau, H., Pélégrini-Issac, M., Lehéricy, S., Doyon, J., Benali, H.: Partial correlation for functional brain interactivity investigation in functional mri. Neuroimage 32(1), 228–237 (2006)

    Article  Google Scholar 

  16. Murphy, K.P.: Machine Learning: a Probabilistic Perspective. MIT press (2012)

    Google Scholar 

  17. Pearl, J.: Causality: Models, Reasoning and Inference. Cambridge University Press (2000)

    Google Scholar 

  18. Shirer, W., Ryali, S., Rykhlevskaia, E., Menon, V., Greicius, M.: Decoding subject-driven cognitive states with whole-brain connectivity patterns. Cerebral Cortex 22(1), 158–165 (2012)

    Article  Google Scholar 

  19. Smith, S.M., Miller, K.L., Salimi-Khorshidi, G., Webster, M., Beckmann, C.F., Nichols, T.E., Ramsey, J.D., Woolrich, M.W.: Network modelling methods for fmri. Neuroimage 54(2), 875–891 (2011)

    Article  Google Scholar 

  20. Spirtes, P., Glymour, C.N., Scheines, R.: Causation, Prediction, and Search. MIT press (2000)

    Google Scholar 

  21. Tsamardinos, I., Brown, L.E., Aliferis, C.F.: The max-min hill-climbing bayesian network structure learning algorithm. Machine Learning 65(1), 31–78 (2006)

    Article  Google Scholar 

  22. Turk-Browne, N.B.: Functional interactions as big data in the human brain. Science 342(6158), 580–584 (2013)

    Article  Google Scholar 

  23. Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., Joliot, M.: Automated anatomical labeling of activations in spm using a macroscopic anatomical parcellation of the mni mri single-subject brain. Neuroimage 15(1), 273–289 (2002)

    Article  Google Scholar 

  24. Van Essen, D.C., Smith, S.M., Barch, D.M., Behrens, T.E., Yacoub, E., Ugurbil, K., Consortium, W.M.H., et al.: The wu-minn human connectome project: an overview. Neuroimage 80, 62–79 (2013)

    Article  Google Scholar 

  25. Varoquaux, G., Gramfort, A., Poline, J.B., Thirion, B.: Brain covariance selection: better individual functional connectivity models using population prior. In: Advances in Neural Information Processing Systems, pp. 2334–2342 (2010)

    Google Scholar 

  26. Wang, Z., Chan, L.: Learning bayesian networks from markov random fields: an efficient algorithm for linear models. ACM Transactions on Knowledge Discovery from Data 6(3), 10 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yike Guo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Nie, L., Yang, X., Matthews, P.M., Xu, Z., Guo, Y. (2015). Minimum Partial Correlation: An Accurate and Parameter-Free Measure of Functional Connectivity in fMRI. In: Guo, Y., Friston, K., Aldo, F., Hill, S., Peng, H. (eds) Brain Informatics and Health. BIH 2015. Lecture Notes in Computer Science(), vol 9250. Springer, Cham. https://doi.org/10.1007/978-3-319-23344-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23344-4_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23343-7

  • Online ISBN: 978-3-319-23344-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics