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Bistochastic vs. Disparity Filters for Multiscale Network Reduction: A U. S. Intercounty Migration Case Study | | Paul B. Slater
; | | Date: |
14 Jul 2009 | | Abstract: | One possible approach to controlling for multiscale effects in networks is to
transform the matrix of (in general) weighted, directed internodal flows to
bistochastic (doubly-stochastic) form, using the iterative proportional fitting
procedure. The dominant entries in the bistochasticized table can then be
employed for network reduction, using strong component hierarchical clustering.
We illustrate various facets of this well-established two-stage algorithm with
the 3, 107 x 3, 107 (asymmetric) 1995-2000 intercounty migration table for the
United States. Additionally, we compare its results with those obtained using
the disparity filter recently put forth by Serrano, Boguna and Vespignani
(Proc. Natl. Acad. Sci. 106 [2009], 6483), for the extraction of the multiscale
backbone of complex weighted networks. The performance of the bistochastic
filter appears to be superior in, at least, two respects: (1) it requires far
fewer links to complete a stongly-connected backbone; and (2) it "belittles"
small flows and nodes less, in the sense that the correlations of the nonzero
raw flows are considerably weaker with the corresponding bistochastized links
than with the significance levels yielded by the disparity filter. | | Source: | arXiv, 0907.2393 | | Services: | Forum | Review | PDF | Favorites | |
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