Constructing Networks from Matrices

  • Steve Horvath


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.


Adjacency Matrix Symmetric Matrix Positive Definite Matrix Dissimilarity Measure Dissimilarity Matrix 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of California, Los AngelesLos AngelesUSA

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