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Approximately Factorizable Networks

  • Steve Horvath
Chapter

Abstract

In factorizable networks, the adjacency (connection strength) between two nodes can be factored into node-specific contributions, named node “conformity”. Often the ith node conformity, CF i is approximately equal to the scaled connectivity k i  ∕ sum(k) of the ith node. We describe (a) an algorithm for computing the conformity CF and for measuring the “factorizability” of a general network, and (b) a module- and CF-based decomposition of a general adjacency matrix, which can be used to arrive at a parsimonious description of a network. Approximately factorizable networks have important practical and theoretical applications, e.g., we use them to derive relationships between network concepts. Collaborative work with Jun Dong has shown that network modules (i.e., subnetworks comprised of module nodes) tend to be approximately factorizable (Dong and Horvath BMC Syst Biol 1(1):24, 2007).

Keywords

Adjacency Matrix Factorizability Function Module Assignment Conformity Vector Factorizable Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Deeds EJ, Ashenberg O, Shakhnovich EI (2006) A simple physical model for scaling in protein–protein interaction networks. Proc Natl Acad Sci USA 103(2):311–316PubMedCrossRefGoogle Scholar
  2. Dong J, Horvath S (2007) Understanding network concepts in modules. BMC Syst Biol 1(1):24PubMedCrossRefGoogle Scholar
  3. Gifi A (1990) Nonlinear multivariate analysis. Wiley, Chichester, EnglandGoogle Scholar
  4. Horn RA, Johnson CR (1991) Topics in matrix analysis. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  5. Lange K (2004) Optimization. Springer, New YorkGoogle Scholar
  6. de Leeuw J, Michailidis G (2000) Block relaxation algorithms in statistics. J Comput Graph Stat 9:26–31Google Scholar
  7. Ranola JMO, Ahn S, Sehl ME, Smith DJ, Lange K (2010) A Poisson model for random multigraphs. Bioinformatics 26(16):2004–2011PubMedCrossRefGoogle Scholar
  8. Ranola JMO, Langfelder P, Song L, Horvath S, Lange K (2011) An MM algorithm for module and propensity based decomposition of a network. UCLA Technical ReportGoogle Scholar
  9. Servedio VDP, Caldarelli G, Butta P (2004) Vertex intrinsic fitness: How to produce arbitrary scale-free networks. Phys Rev E – Stat Nonlin Soft Matter Phys 70(5):056126Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of California, Los AngelesLos AngelesUSA

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