IEEE Trans Pattern Anal Mach Intell - The Sum-over-Forests Density Index: Identifying Dense Regions in a Graph.

Tópicos

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Resumo

This work introduces a novel nonparametric density index defined on graphs, the Sum-over-Forests (SoF) density index. It is based on a clear and intuitive idea: high-density regions in a graph are characterized by the fact that they contain a large amount of low-cost trees with high outdegrees while low-density regions contain few ones. Therefore, a Boltzmann probability distribution on the countable set of forests in the graph is defined so that large (high-cost) forests occur with a low probability while short (low-cost) forests occur with a high probability. Then, the SoF density index of a node is defined as the expected outdegree of this node on the set of forests, thus providing a measure of density around that node. Following the matrix-forest theorem and a statistical physics framework, it is shown that the SoF density index can be easily computed in closed form through a simple matrix inversion. Experiments on artificial and real data sets show that the proposed index performs well on finding dense regions, for graphs of various origins.

Resumo Limpo

work introduc novel nonparametr densiti index defin graph sumoverforest sof densiti index base clear intuit idea highdens region graph character fact contain larg amount lowcost tree high outdegre lowdens region contain one therefor boltzmann probabl distribut countabl set forest graph defin larg highcost forest occur low probabl short lowcost forest occur high probabl sof densiti index node defin expect outdegre node set forest thus provid measur densiti around node follow matrixforest theorem statist physic framework shown sof densiti index can easili comput close form simpl matrix invers experi artifici real data set show propos index perform well find dens region graph various origin

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