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Constructing Networks from Matrices

  • Steve Horvath
Chapter

Abstract

Methods for defining an adjacency matrix are also known as network construction-, inference-, or deconvolution methods. The network adjacency matrix can be defined by transforming a similarity or dissimilarity matrix, a symmetric matrix, or even a general square matrix. Multiple similarity matrices can be combined into a single “consensus” network, which allows one to define consensus modules. A signed correlation network turns out to be rank-equivalent to a Euclidean-distance-based network between scaled vectors. Sample networks, which are often defined as distance-based networks, are useful for identifying outlying samples or observations. A distance-based adjacency function yields an adjacency matrix A for which \(dissA = 1 - A\) satisfies the triangle inequality and other distance properties. Distance-based adjacency functions are useful for generalizing the ARACNE algorithm to general networks. We describe how the Kullback–Leibler pre-dissimilarity can be used (a) for measuring the difference between matrices and (b) for network construction.

Keywords

Adjacency Matrix Symmetric Matrix Positive Definite Matrix Dissimilarity Measure Dissimilarity Matrix 
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. Kaufman L, Rousseeuw PJ (1990) Finding groups in data: An introduction to cluster analysis. Wiley, New YorkCrossRefGoogle Scholar
  2. Langfelder P, Horvath S (2007) Eigengene networks for studying the relationships between co-expression modules. BMC Syst Biol 1(1):54PubMedCrossRefGoogle Scholar
  3. Oldham MC, Langfelder P, Horvath S (2011) Sample networks for enhancing cluster analysis of genomic data: Application to huntington’s disease. Technical ReportGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of California, Los AngelesLos AngelesUSA

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