Improved methods to compare distance metrics in networks using uniform random spanning trees (DIMECOST)

We consider the network analytics problem of comparing two distance metrics on the same set of n entities. The classical solution to this problem is the Mantel test, which uses permutation testing to accept or reject the null hypothesis that there is “no relationship between the two metrics.” Its co...

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Bibliographic Details
Published inNetworks Vol. 76; no. 3; pp. 402 - 413
Main Authors Bourbour, Sara, Mehta, Dinesh P., Navidi, William C.
Format Journal Article
LanguageEnglish
Published Hoboken, USA John Wiley & Sons, Inc 01.10.2020
Wiley Subscription Services, Inc
Subjects
Complexity
correlation coefficient
Correlation coefficients
distance metrics
Graph theory
Hypotheses
Mantel test
Mathematical analysis
network analytics
Null hypothesis
Permutations
random spanning trees
Statistical methods
transportation networks
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Summary:We consider the network analytics problem of comparing two distance metrics on the same set of n entities. The classical solution to this problem is the Mantel test, which uses permutation testing to accept or reject the null hypothesis that there is “no relationship between the two metrics.” Its computational complexity is n2 times the number of permutations (based on a user supplied parameter). This work makes two contributions: (1) DIMECOSTP, a more efficient hypothesis test based on uniform random spanning trees whose complexity is n times the number of permutations. (2) DIMECOSTCC, which uses the correlation coefficient between the two sets of edge weights in a random spanning tree as an indication of the strength of the relationship between the two distance metrics. Both methods utilize sound statistical principles. Experimental results confirm the efficacy of our methods.
ISSN:0028-3045
1097-0037
DOI:10.1002/net.21949