scholarly journals Random Walks in Hypergraph

Author(s):  
Abdelghani Bellaachia ◽  
Mohammed Al-Dhelaan

Random walks on graphs have been extensively used for a variety of graph-based problems such as ranking vertices, predicting links, recommendations, and clustering. However, many complex problems mandate a high-order graph representation to accurately capture the relationship structure inherent in them. Hypergraphs are particularly useful for such models due to the density of information stored in their structure. In this paper, we propose a novel extension to defining random walks on hypergraphs. Our proposed approach combines the weights of destination vertices and hyperedges in a probabilistic manner to accurately capture transition probabilities. We study and analyze our generalized form of random walks suitable for the structure of hypergraphs. We show the effectiveness of our model by conducting a text ranking experiment on a real world data set with a 9% to 33% improvement in precision and a range of 7% to 50% improvement in Bpref over other random walk approaches.

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yi-Chun Chang ◽  
Kuan-Ting Lai ◽  
Seng-Cho T. Chou ◽  
Wei-Chuan Chiang ◽  
Yuan-Chen Lin

PurposeTelecommunication (telecom) fraud is one of the most common crimes and causes the greatest financial losses. To effectively eradicate fraud groups, the key fraudsters must be identified and captured. One strategy is to analyze the fraud interaction network using social network analysis. However, the underlying structures of fraud networks are different from those of common social networks, which makes traditional indicators such as centrality not directly applicable. Recently, a new line of research called deep random walk has emerged. These methods utilize random walks to explore local information and then apply deep learning algorithms to learn the representative feature vectors. Although effective for many types of networks, random walk is used for discovering local structural equivalence and does not consider the global properties of nodes.Design/methodology/approachThe authors proposed a new method to combine the merits of deep random walk and social network analysis, which is called centrality-guided deep random walk. By using the centrality of nodes as edge weights, the authors’ biased random walks implicitly consider the global importance of nodes and can thus find key fraudster roles more accurately. To evaluate the authors’ algorithm, a real telecom fraud data set with around 562 fraudsters was built, which is the largest telecom fraud network to date.FindingsThe authors’ proposed method achieved better results than traditional centrality indices and various deep random walk algorithms and successfully identified key roles in a fraud network.Research limitations/implicationsThe study used co-offending and flight record to construct a criminal network, more interpersonal relationships of fraudsters, such as friendships and relatives, can be included in the future.Originality/valueThis paper proposed a novel algorithm, centrality-guided deep random walk, and applied it to a new telecom fraud data set. Experimental results show that the authors’ method can successfully identify the key roles in a fraud group and outperform other baseline methods. To the best of the authors’ knowledge, it is the largest analysis of telecom fraud network to date.


1990 ◽  
Vol 4 (4) ◽  
pp. 489-492 ◽  
Author(s):  
José Luis Palacios

Aleliunas et al. [3] proved that for a random walk on a connected raph G = (V, E) on N vertices, the expected minimum number of steps to visit all vertices is bounded by 2|E|(N - 1), regardless of the initial state. We give here a simple proof of that result through an equality involving hitting times of vertices that can be extended to an inequality for hitting times of edges, thus obtaining a bound for the expected minimum number of steps to visit all edges exactly once in each direction.


2001 ◽  
Vol 38 (4) ◽  
pp. 1018-1032 ◽  
Author(s):  
T. Komorowski ◽  
G. Krupa

We prove the law of large numbers for random walks in random environments on the d-dimensional integer lattice Zd. The environment is described in terms of a stationary random field of transition probabilities on the lattice, possessing a certain drift property, modeled on the Kalikov condition. In contrast to the previously considered models, we admit possible correlation of transition probabilities at different sites, assuming however that they become independent at finite distances. The possible dependence of sites makes impossible a direct application of the renewal times technique of Sznitman and Zerner.


Author(s):  
MOKHTAR H. KONSOWA

We study the relationship between the type of the random walk on some random trees and the structure of those trees in terms of fractal and resistance dimensions. This paper generalizes some results of Refs. 8–10.


1994 ◽  
Vol 7 (3) ◽  
pp. 411-422
Author(s):  
D. J. Daley ◽  
L. D. Servi

Identities between first-passage or last-exit probabilities and unrestricted transition probabilities that hold for left- or right-continuous lattice-valued random walks form the basis of an intuitively based approximation that is demonstrated by computation to hold for certain random walks without either the left- or right-continuity properties. The argument centers on the use of ladder variables; the identities are known to hold asymptotically from work of Iglehart leading to Brownian meanders.


2021 ◽  
Author(s):  
Annabel Louisa Davies ◽  
Theodoros Papakonstantinou ◽  
Adriani Nikolakopoulou ◽  
Gerta Rucker ◽  
Tobias Galla

Network meta-analysis (NMA) is a central tool for evidence synthesis in clinical research. The results of an NMA depend critically on the quality of evidence being pooled. In assessing the validity of an NMA, it is therefore important to know the proportion contributions of each direct treatment comparison to each network treatment effect. The construction of proportion contributions is based on the observation that each row of the hat matrix represents a so-called 'evidence flow network' for each treatment comparison. However, the existing algorithm used to calculate these values is associated with ambiguity according to the selection of paths. In this work we present a novel analogy between NMA and random walks. We use this analogy to derive closed-form expressions for the proportion contributions. A random walk on a graph is a stochastic process that describes a succession of random 'hops' between vertices which are connected by an edge. The weight of an edge relates to the probability that the walker moves along that edge. We use the graph representation of NMA to construct the transition matrix for a random walk on the network of evidence. We show that the net number of times a walker crosses each edge of the network is related to the evidence flow network. By then defining a random walk on the directed evidence flow network, we derive analytically the matrix of proportion contributions. The random-walk approach, in addition to being computationally more efficient, has none of the associated ambiguity of the existing algorithm.


2018 ◽  
Vol 55 (3) ◽  
pp. 862-886 ◽  
Author(s):  
F. Alberto Grünbaum ◽  
Manuel D. de la Iglesia

Abstract We consider upper‒lower (UL) (and lower‒upper (LU)) factorizations of the one-step transition probability matrix of a random walk with the state space of nonnegative integers, with the condition that both upper and lower triangular matrices in the factorization are also stochastic matrices. We provide conditions on the free parameter of the UL factorization in terms of certain continued fractions such that this stochastic factorization is possible. By inverting the order of the factors (also known as a Darboux transformation) we obtain a new family of random walks where it is possible to state the spectral measures in terms of a Geronimus transformation. We repeat this for the LU factorization but without a free parameter. Finally, we apply our results in two examples; the random walk with constant transition probabilities, and the random walk generated by the Jacobi orthogonal polynomials. In both situations we obtain urn models associated with all the random walks in question.


1998 ◽  
Vol 11 (1) ◽  
pp. 9-28 ◽  
Author(s):  
Jacek Banasiak ◽  
Janusz R. Mika

In the paper we analyze singularly perturbed telegraph systems applying the newly developed compressed asymptotic method and show that the diffusion equation is an asymptotic limit of singularly perturbed telegraph system of equations. The results are applied to the random walk theory for which the relationship between correlated and uncorrelated random walks is explained in asymptotic terms.


2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Serguei Yu. Popov

International audience We review some recent results for a system of simple random walks on graphs, known as \emphfrog model. Also, we discuss several modifications of this model, and present a few open problems. A simple version of the frog model can be described as follows: There are active and sleeping particles living on some graph. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1-p. When an active particle hits a sleeping particle, the latter becomes active.


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