Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis

Edge-fuzzy graphs constitute an essential modeling paradigm across a broad spectrum of domains ranging from artificial intelligence to computational neuroscience and social network analysis. Under this model, fundamental graph properties such as edge length and graph diameter become stochastic and a...
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Autor*in:	Georgios Drakopoulos [verfasserIn] Andreas Kanavos [verfasserIn] Konstantinos Tsakalidis [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	Bernoulli distribution binomial distribution Chebyshev inequality first order statistics fuzzy graphs graph analytics higher order data Jensen inequality Markov inequality Poisson distribution Random Walker principle second order statistics Walktrap algorithm

Übergeordnetes Werk:	In: Algorithms - MDPI AG, 2008, 10(2017), 2, p 40
Übergeordnetes Werk:	volume:10 ; year:2017 ; number:2, p 40

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/a10020040

Katalog-ID:	DOAJ030799937

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source	In Algorithms 10(2017), 2, p 40 volume:10 year:2017 number:2, p 40
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topic_facet	Bernoulli distribution binomial distribution Chebyshev inequality first order statistics fuzzy graphs graph analytics higher order data Jensen inequality Markov inequality Poisson distribution Random Walker principle second order statistics Walktrap algorithm Industrial engineering. Management engineering Electronic computers. Computer science
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callnumber-first	T - Technology
author	Georgios Drakopoulos
spellingShingle	Georgios Drakopoulos misc T55.4-60.8 misc QA75.5-76.95 misc Bernoulli distribution misc binomial distribution misc Chebyshev inequality misc first order statistics misc fuzzy graphs misc graph analytics misc higher order data misc Jensen inequality misc Markov inequality misc Poisson distribution misc Random Walker principle misc second order statistics misc Walktrap algorithm misc Industrial engineering. Management engineering misc Electronic computers. Computer science Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis
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topic_title	T55.4-60.8 QA75.5-76.95 Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis Bernoulli distribution binomial distribution Chebyshev inequality first order statistics fuzzy graphs graph analytics higher order data Jensen inequality Markov inequality Poisson distribution Random Walker principle second order statistics Walktrap algorithm
topic	misc T55.4-60.8 misc QA75.5-76.95 misc Bernoulli distribution misc binomial distribution misc Chebyshev inequality misc first order statistics misc fuzzy graphs misc graph analytics misc higher order data misc Jensen inequality misc Markov inequality misc Poisson distribution misc Random Walker principle misc second order statistics misc Walktrap algorithm misc Industrial engineering. Management engineering misc Electronic computers. Computer science
topic_unstemmed	misc T55.4-60.8 misc QA75.5-76.95 misc Bernoulli distribution misc binomial distribution misc Chebyshev inequality misc first order statistics misc fuzzy graphs misc graph analytics misc higher order data misc Jensen inequality misc Markov inequality misc Poisson distribution misc Random Walker principle misc second order statistics misc Walktrap algorithm misc Industrial engineering. Management engineering misc Electronic computers. Computer science
topic_browse	misc T55.4-60.8 misc QA75.5-76.95 misc Bernoulli distribution misc binomial distribution misc Chebyshev inequality misc first order statistics misc fuzzy graphs misc graph analytics misc higher order data misc Jensen inequality misc Markov inequality misc Poisson distribution misc Random Walker principle misc second order statistics misc Walktrap algorithm misc Industrial engineering. Management engineering misc Electronic computers. Computer science
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title	Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis
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title_full	Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis
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title_sort	fuzzy random walkers with second order bounds: an asymmetric analysis
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title_auth	Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis
abstract	Edge-fuzzy graphs constitute an essential modeling paradigm across a broad spectrum of domains ranging from artificial intelligence to computational neuroscience and social network analysis. Under this model, fundamental graph properties such as edge length and graph diameter become stochastic and as such they are consequently expressed in probabilistic terms. Thus, algorithms for fuzzy graph analysis must rely on non-deterministic design principles. One such principle is Random Walker, which is based on a virtual entity and selects either edges or, like in this case, vertices of a fuzzy graph to visit. This allows the estimation of global graph properties through a long sequence of local decisions, making it a viable strategy candidate for graph processing software relying on native graph databases such as Neo4j. As a concrete example, Chebyshev Walktrap, a heuristic fuzzy community discovery algorithm relying on second order statistics and on the teleportation of the Random Walker, is proposed and its performance, expressed in terms of community coherence and number of vertex visits, is compared to the previously proposed algorithms of Markov Walktrap, Fuzzy Walktrap, and Fuzzy Newman–Girvan. In order to facilitate this comparison, a metric based on the asymmetric metrics of Tversky index and Kullback–Leibler divergence is used.
abstractGer	Edge-fuzzy graphs constitute an essential modeling paradigm across a broad spectrum of domains ranging from artificial intelligence to computational neuroscience and social network analysis. Under this model, fundamental graph properties such as edge length and graph diameter become stochastic and as such they are consequently expressed in probabilistic terms. Thus, algorithms for fuzzy graph analysis must rely on non-deterministic design principles. One such principle is Random Walker, which is based on a virtual entity and selects either edges or, like in this case, vertices of a fuzzy graph to visit. This allows the estimation of global graph properties through a long sequence of local decisions, making it a viable strategy candidate for graph processing software relying on native graph databases such as Neo4j. As a concrete example, Chebyshev Walktrap, a heuristic fuzzy community discovery algorithm relying on second order statistics and on the teleportation of the Random Walker, is proposed and its performance, expressed in terms of community coherence and number of vertex visits, is compared to the previously proposed algorithms of Markov Walktrap, Fuzzy Walktrap, and Fuzzy Newman–Girvan. In order to facilitate this comparison, a metric based on the asymmetric metrics of Tversky index and Kullback–Leibler divergence is used.
abstract_unstemmed	Edge-fuzzy graphs constitute an essential modeling paradigm across a broad spectrum of domains ranging from artificial intelligence to computational neuroscience and social network analysis. Under this model, fundamental graph properties such as edge length and graph diameter become stochastic and as such they are consequently expressed in probabilistic terms. Thus, algorithms for fuzzy graph analysis must rely on non-deterministic design principles. One such principle is Random Walker, which is based on a virtual entity and selects either edges or, like in this case, vertices of a fuzzy graph to visit. This allows the estimation of global graph properties through a long sequence of local decisions, making it a viable strategy candidate for graph processing software relying on native graph databases such as Neo4j. As a concrete example, Chebyshev Walktrap, a heuristic fuzzy community discovery algorithm relying on second order statistics and on the teleportation of the Random Walker, is proposed and its performance, expressed in terms of community coherence and number of vertex visits, is compared to the previously proposed algorithms of Markov Walktrap, Fuzzy Walktrap, and Fuzzy Newman–Girvan. In order to facilitate this comparison, a metric based on the asymmetric metrics of Tversky index and Kullback–Leibler divergence is used.
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title_short	Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis
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