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Pearson Correlations on Networks: Corrigendum
Published 14 Feb 2024 in cs.SI, physics.data-an, and physics.soc-ph | (2402.09489v1)
Abstract: Recently, the first author proposed a measure to calculate Pearson correlations for node values expressed in a network, by taking into account distances or metrics defined on the network. In this technical note, we show that using an arbitrary choice of distances might result in imaginary or unbounded correlation values, which is undesired. We prove that this problem is solved by restricting to a special class of distances: negative type metrics. We also discuss two natural classes of negative type metrics on graphs, for which the network correlations are properly defined.
- Geometric deep learning: going beyond Euclidean data. IEEE Signal Processing Magazine, 34(4):18–42, 2017.
- Michele Coscia. The atlas for the aspiring network scientist. arXiv preprint arXiv:2101.00863, 2021.
- Michele Coscia. Pearson correlations on complex networks. Journal of Complex Networks, 9(6):cnab036, 2021.
- Karel Devriendt. Effective resistance is more than distance: Laplacians, simplices and the Schur complement. Linear Algebra and its Applications, 639:24–49, 2022.
- Karel Devriendt. Graph geometry from effective resistances. PhD thesis, University of Oxford, 2022.
- Effective graph resistance. Linear algebra and its applications, 435(10):2491–2506, 2011.
- Miroslav Fiedler. Matrices and Graphs in Geometry. Encyclopedia of mathematics and its applications ; 139. Cambridge University Press, Cambridge, UK, 2011.
- Quantifying ideological polarization on a network using generalized Euclidean distance. Science Advances, 9(9):eabq2044, 2023.
- Matrix Analysis. Cambridge University Press, Cambridge, UK, 2nd edition, dec 2013.
- Resistance distance. Journal of mathematical chemistry, 12(1):81–95, 1993.
- Russell Lyons. Distance covariance in metric spaces. The Annals of probability, 41(5):3284–3305, 2013.
- Mark W. Meckes. Positive definite metric spaces. Positivity, 17(3):733–757, 2013.
- Deepwalk: Online learning of social representations. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 701–710, 2014.
- Clustering and embedding using commute times. IEEE transactions on pattern analysis and machine intelligence, 29(11):1873–1890, 2007.
- Isaac J. Schoenberg. Metric spaces and completely monotone functions. Annals of Mathematics, pages 811–841, 1938.
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