Abstract
Partial correlation is a popular and principled metric for determining edges between nodes in a graph. However when the goal is to both estimate network connectivity from sample data and subsequently partition the result, methods such as spectral clustering can be applied much more efficiency and at larger scale. We derive a method that can similarly partition partial correlation networks directly from sample data. The method is closely related to spectral clustering, and can be implemented with comparable efficiency. Our results also provide new insight into the success of spectral clustering in many fields, as an approximation to clustering of partial correlation networks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brownlees, C., Gudmundsson, G.S., Lugosi, G.: Community detection in partial correlation network models. J. Bus. Econ. Stat. 1–11 (2020)
Dillon, K., Wang, Y.P.: A regularized clustering approach to brain parcellation from functional MRI data. In: Wavelets and Sparsity XVII, vol. 10394, p. 103940E. International Society for Optics and Photonics, August 2017
Dillon, K., Wang, Y.P.: Resolution-based spectral clustering for brain parcellation using functional MRI. J. Neurosci. Methods 335, 108628 (2020)
Ellett, F.S., Ericson, D.P.: Correlation, partial correlation, and causation. Synthese 67(2), 157–173 (1986)
von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)
Pourahmadi, M.: Covariance estimation: the GLM and regularization perspectives. Stat. Sci. 26(3), 369–387 (2011)
Schäfer, J., Strimmer, K.: A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat. Appl. Genet. Mol. Biol. 4(1), 32 (2005)
Van Essen, D.C., et al.: WU-Minn HCP consortium: the human connectome project: a data acquisition perspective. NeuroImage 62(4), 2222–2231 (2012)
Whittaker, J.: Graphical Models in Applied Multivariate Statistics. Wiley, New York (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
5 Appendix: Matlab Implementation of Clustering
5 Appendix: Matlab Implementation of Clustering
In this appendix we provide efficient Matlab code for performing partial correlation clustering.
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Dillon, K. (2021). Efficient Partitioning of Partial Correlation Networks. In: Torsello, A., Rossi, L., Pelillo, M., Biggio, B., Robles-Kelly, A. (eds) Structural, Syntactic, and Statistical Pattern Recognition. S+SSPR 2021. Lecture Notes in Computer Science(), vol 12644. Springer, Cham. https://doi.org/10.1007/978-3-030-73973-7_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-73973-7_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-73972-0
Online ISBN: 978-3-030-73973-7
eBook Packages: Computer ScienceComputer Science (R0)
