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Algorithms 2017, 10(2), 40; doi:10.3390/a10020040

Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis

1
Computer Engineering and Informatics Department, University of Patras, 26504 Patras, Greece
2
Cheriton School of Computer Science, University of Waterloo, Waterloo, ON N2L3G1, Canada
*
Author to whom correspondence should be addressed.
Academic Editors: Katia Lida Kermanidis, Christos Makris, Phivos Mylonas and Spyros Sioutas
Received: 22 December 2016 / Revised: 22 March 2017 / Accepted: 27 March 2017 / Published: 30 March 2017
(This article belongs to the Special Issue Humanistic Data Processing)
View Full-Text   |   Download PDF [315 KB, uploaded 30 March 2017]   |  

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. View Full-Text
Keywords: 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 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
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Drakopoulos, G.; Kanavos, A.; Tsakalidis, K. Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis. Algorithms 2017, 10, 40.

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