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Relevant bibliographies by topics / Vertex Reinforced Random Walk

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Academic literature on the topic 'Vertex Reinforced Random Walk'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Vertex Reinforced Random Walk"

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Pemantle, Robin. "Vertex-reinforced random walk." Probability Theory and Related Fields 92, no. 1 (March 1992): 117–36. http://dx.doi.org/10.1007/bf01205239.

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Volkov, Stanislav. "Vertex-reinforced random walk on arbitrary graphs." Annals of Probability 29, no. 1 (February 2001): 66–91. http://dx.doi.org/10.1214/aop/1008956322.

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Pemantle, Robin, and Stanislav Volkov. "Vertex-Reinforced Random Walk on Z Has Finite Range." Annals of Probability 27, no. 3 (July 1999): 1368–88. http://dx.doi.org/10.1214/aop/1022677452.

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Benaïm, Michel, and Pierre Tarrès. "Dynamics of vertex-reinforced random walks." Annals of Probability 39, no. 6 (November 2011): 2178–223. http://dx.doi.org/10.1214/10-aop609.

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Sabot, Christophe, and Pierre Tarrès. "Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model." Journal of the European Mathematical Society 17, no. 9 (2015): 2353–78. http://dx.doi.org/10.4171/jems/559.

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Dai, Jack Jie. "Some results regarding vertex-reinforced random walks." Statistics & Probability Letters 66, no. 3 (February 2004): 259–66. http://dx.doi.org/10.1016/j.spl.2003.10.017.

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Dai, Jack Jie. "A note on vertex-reinforced random walks." Statistics & Probability Letters 62, no. 3 (April 2003): 275–80. http://dx.doi.org/10.1016/s0167-7152(03)00014-2.

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Tarrès, Pierre. "Vertex-reinforced random walk on ℤ eventually gets stuck on five points." Annals of Probability 32, no. 3B (July 2004): 2650–701. http://dx.doi.org/10.1214/009117907000000694.

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Chen, Jun, and Gady Kozma. "Vertex-reinforced random walk on with sub-square-root weights is recurrent." Comptes Rendus Mathematique 352, no. 6 (June 2014): 521–24. http://dx.doi.org/10.1016/j.crma.2014.03.019.

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Basdevant, Anne-Laure, Bruno Schapira, and Arvind Singh. "Localization of a vertex reinforced random walk on $$\mathbb{Z }$$ with sub-linear weight." Probability Theory and Related Fields 159, no. 1-2 (April 27, 2013): 75–115. http://dx.doi.org/10.1007/s00440-013-0502-3.

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Dissertations / Theses on the topic "Vertex Reinforced Random Walk"

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Renlund, Henrik. "Reinforced Random Walk." Thesis, Uppsala University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121389.

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Li, Dan. "Shortest paths through a reinforced random walk." Thesis, Uppsala universitet, Analys och tillämpad matematik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-153802.

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Ma, Qi. "Reinforcement in Biology : Stochastic models of group formation and network construction." Doctoral thesis, Uppsala universitet, Analys och tillämpad matematik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-186989.

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Empirical studies show that similar patterns emerge from a large number of different biological systems. For example, the group size distributions of several fish species and house sparrows all follow power law distributions with an exponential truncation. Networks built by ant colonies, slime mold and those are designed by engineers resemble each other in terms of structure and transportation efficiency. Based on the investigation of experimental data, we propose a variety of simple stochastic models to unravel the underlying mechanisms which lead to the collective phenomena in different systems. All the mechanisms employed in these models are rooted in the concept of selective reinforcement. In some systems the reinforcement can build optimal solutions for biological problem solving. This thesis consists of five papers. In the first three papers, I collaborate with biologists to look into group formation in house sparrows and the movement decisions of damsel fish. In the last two articles, I look at how shortest paths and networks are constructed by slime molds and pheromone laying ants, as well as studying speed-accuracy tradeoffs in slime molds' decision making. The general goal of the study is to better understand how macro level patterns and behaviors emerges from micro level interactions in both spatial and non-spatial biological systems. With the combination of mathematical modeling and experimentation, we are able to reproduce the macro level patterns in the studied biological systems and predict behaviors of the systems using minimum number of parameters.

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Le, Goff Line. "Formation spontanée de chemins : des fourmis aux marches aléatoires renforcées." Thesis, Paris 10, 2014. http://www.theses.fr/2014PA100180/document.

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Cette thèse est consacrée à la modélisation de la formation spontanée de chemins préférentiels par des marcheurs déposant des traces attractives sur leurs trajectoires. Plus précisément, par une démarche pluridisciplinaire couplant modélisation et expérimentation, elle vise à dégager un ensemble de règles minimales individuelles permettant l'apparition d'un tel phénomène. Dans ce but, nous avons étudié sous différents angles les modèles minimaux que sont les marches aléatoires renforcées (MAR).Ce travail comporte deux parties principales. La première démontre de nouveaux résultats dans le domaine des probabilités et statistiques. Nous avons généralisé le travail publié par M. Benaïm et O. Raimond en 2010 afin d'étudier l'asymptotique d'une classe de MAR auxquelles les demi-tours sont interdits. Nous avons également développé une procédure statistique permettant, sous certaines conditions adéquates de régularité, d'estimer les paramètres de MAR paramétrées et d'évaluer des marges d'erreur.Dans la seconde partie, sont décrits les résultats et analyses d'une étude comportementale et expérimentale de la fourmi Linepithema humile. Une partie de notre réflexion est centrée sur le rôle et la valeur des paramètres du modèle proposé par J.-L. Deneubourg et al. en 1990. Nous nous sommes aussi demandés dans quelle mesure une MAR peut reproduire les déplacements d'une fourmi dans un réseau. Dans ces objectifs, nous avons mené des expériences confrontant des fourmis à des réseaux à une ou plusieurs bifurcations. Nous avons appliqué aux données expérimentales les outils statistiques développés dans cette thèse. Nous avons aussi effectué une étude comparative entre les simulations de plusieurs modèles et les expériences
This thesis is devoted to the modelisation of the spontaneous formation of preferential paths by walkers that deposit attractive trails on their trajectories. More precisely, through a multidisciplinary approach, which combines modelisation and experimentation, this thesis aims to bring out a set of minimal individual rules that allow the apparition of this phenomena. In this purpose, we study in several ways the minimal models, which are the Reinforced Random Walks (RRW).This work contains two main parts. The first one proves some new results in the field of probability and statistics. We have generalized the work published by M. Benaïm and O. Raimond in 2010 in order to study the asymptotics of a class of RRW, to which U-turns are forbidden. We developped also a statistical procedure that allows under some appropriate regularity hypotheses to estimate the parameters of parametized RRW and to evaluate margins of error.In the second part, we describe the results and the analyses of a experimental and behavioral study of the Linepithema humile ants. One part of our reflection is centered on the role and the value of the parameters of the model defined by J.-L. Deneubourg et al. in 1990. We investigated also the extent to which RRW could reproduce the moving of an ant in a network. To these purposes, we performed experiments that confront ants to a network of one or several forks. We applied to experimental data the statistical tools developed in this thesis and we performed a comparative study between experiments and simulations of several models

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Artemenko, Igor. "On Weak Limits and Unimodular Measures." Thèse, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/30417.

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In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation, sometimes referred to as the intrinsic mass transport principle. The so-called law of a finite graph is an example of a unimodular measure. We say that a measure is sustained by a countable graph if the set of rooted connected components of the graph has full measure. We demonstrate several new results involving sustained unimodular measures, and provide thorough arguments for known ones. In particular, we give a criterion for unimodularity on connected graphs, deduce that connected graphs sustain at most one unimodular measure, and prove that unimodular measures sustained by disconnected graphs are convex combinations. Furthermore, we discuss weak limits of laws of finite graphs, and construct counterexamples to seemingly reasonable conjectures.

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Nandanwar, Sharad. "Recommendations in Complex Networks: Unifying Structure into Random Walk." Thesis, 2019. https://etd.iisc.ac.in/handle/2005/4950.

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Making recommendations or predicting links which are likely to exist in the future is one of the central problems in network science and graph mining. In spite of modern state-of- the-art approaches for link prediction, the traditional approaches like Resource Allocation Index, Adamic Adar still fi nd heavy use, because of their simplistic nature yet competitive performance. Our preliminary investigation reveals that a major fraction of missing links which are observed in the near future, are the links which are between one-hop distant nodes. Current \friend of friend is a friend" based approaches, provide a mechanism for aggregating the effect of triangles getting closed by inclusion of an edge. In this work we look beyond these triangles, and hunt for higher order structures in common neighborhood. However, with an idealistic choice of cliques as higher order structures, the problem easily gets out of hand, even for common ego-networks involving 50-100 nodes. In wake of this, we de ne a dense structure k-support, as an approximation to the clique. Further, for a given k value, we propose a goodness measure to capture the contribution of the common neighborhood w.r.t. k-support, towards the link strength. The proposed goodness measure with different k values is then exploited in learning a supervised model. We next take a multi-class classifi cation view to the recommendation problem. This is suited for the cases where cardinality of the set of target objects is reasonably small. Classi fication of entities based on the underlying network structure is an important problem and has been studied extensively in literature. Networks encountered in practice are sparse and have many missing and noisy links. Statistical learning techniques have been used in intra-network classi fication; however, they typically exploit only the local neighborhood, so may not perform well. We propose a novel structural neighborhood-based classi fier learning using a random walk, where we label a node based on how nodes in the respective kth-level neighborhood are labeled. We observe that random walks of short length are helpful in classi fication, while emphasizing role of longer random walks may cause the underlying Markov chain to converge to a stationary distribution. Considering this, we take a lazy random walk based approach with variable termination probability for each node, based on the node's structural properties including its degree. Further, we observe that conventional loss functions penalize a node based on a function of its predicted label and target label. Such loss functions under-perform while learning on a network having overlapping classes. In relational setting, even though the ground truth is not known for the unlabeled nodes, some evidence is present in the form of labeling acquired by the nodes in their neighborhood. Considering this, we propose a structural loss function for learning in networks based on the hypothesis that loss is induced when a node fails to acquire a label that is consistent with the labels of the majority of the nodes in its neighborhood. We further combine this with a novel semantic regularizer, which we call homophily regularizer, to capture the smooth transition of discriminatory power and behavior of semantically similar nodes. Hybrid recommender systems have shown the power of exploiting relationships amongst objects which directly or indirectly effect the recommendation task. However, the effect of all relations is not equal, and choosing their right balance for a recommendation problem at hand is non-trivial. We model these interactions using a Heterogeneous Information Network, and propose a systematic framework for learning their inluence weights for a given recommendation task. We address the issue of redundant results, which is very much prevalent in recommender systems. To alleviate redundancy in recommendations we use Vertex Reinforced Random Walk (a non-Markovian random walk) over a heterogeneous graph. It works by boosting the transitions to the influential nodes, while simultaneously shrinking the weights of others. This helps in discouraging recommendation of multiple influential nodes which lie in close proximity of each other, thus ensuring diversity.

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Book chapters on the topic "Vertex Reinforced Random Walk"

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Xiao, Wenyi, Huan Zhao, Vincent W. Zheng, and Yangqiu Song. "Vertex-reinforced Random Walk for Network Embedding." In Proceedings of the 2020 SIAM International Conference on Data Mining, 595–603. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2020. http://dx.doi.org/10.1137/1.9781611976236.67.

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Holmes, Mark, and Daniel Kious. "A Monotonicity Property for Once Reinforced Biased Random Walk on $$\mathbb {Z}^d$$." In Springer Proceedings in Mathematics & Statistics, 255–73. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0302-3_10.

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Dai, Qionghai, and Yue Gao. "Typical Hypergraph Computation Tasks." In Artificial Intelligence: Foundations, Theory, and Algorithms, 73–99. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0185-2_5.

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AbstractAfter hypergraph structure generation for the data, the next step is how to conduct data analysis on the hypergraph. In this chapter, we introduce four typical hypergraph computation tasks, including label propagation, data clustering, imbalance learning, and link prediction. The first typical task is label propagation, which is to predict the labels for the vertices, i.e., assigning a label to each unlabeled vertex in the hypergraph, based on the labeled information. In general cases, label propagation is to propagate the label information from labeled vertices to unlabeled vertices through structural information of the hyperedges. In this part, we discuss the hypergraph cut on hypergraphs and random walk interpretation of label propagation on hypergraphs. The second typical task is data clustering, which is formulated as dividing the vertices into several parts in a hypergraph. In this part, we introduce a hypergraph Laplacian smoothing filter and an embedded model for hypergraph clustering tasks. The third typical task is cost-sensitive learning, which targets on learning with different mis-classification costs. The fourth typical task is link prediction, which aims to discover missing relations or predict new coming hyperedges based on the observed hypergraph.

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Zhou, Yifei, and Conor Hayes. "Graph-Based Diffusion Method for Top-N Recommendation." In Communications in Computer and Information Science, 292–304. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-26438-2_23.

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AbstractData that may be used for personalised recommendation purposes can intuitively be modelled as a graph. Users can be linked to item data; item data may be linked to item data. With such a model, the task of recommending new items to users or making new connections between items can be undertaken by algorithms designed to establish the relatedness between vertices in a graph. One such class of algorithm is based on the random walk, whereby a sequence of connected vertices are visited based on an underlying probability distribution and a determination of vertex relatedness established. A diffusion kernel encodes such a process. This paper demonstrates several diffusion kernel approaches on a graph composed of user-item and item-item relationships. The approach presented in this paper, RecWalk*, consists of a user-item bipartite combined with an item-item graph on which several diffusion kernels are applied and evaluated in terms of top-n recommendation. We conduct experiments on several datasets of the RecWalk* model using combinations of different item-item graph models and personalised diffusion kernels. We compare accuracy with some non-item recommender methods. We show that diffusion kernel approaches match or outperform state-of-the-art recommender approaches.

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Dorogovtsev, Sergey N., and José F. F. Mendes. "Temporal Networks." In The Nature of Complex Networks, 345–55. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780199695119.003.0011.

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Abstract When a process takes place on an evolving network or this network serves as an evolving substrate of a dynamical system, two time scales naturally emerge: (i) the shortest time of structural changes in a local neighbourhood of each vertex, and (ii) the shortest time (time step) of a process. The notion of a temporal network assumes that local structural changes in an evolving network occur faster than the time step of a process or that these two time scales are comparable. The simplest example of such structural changes is sufficiently frequent emergence and disappearance of edges in a network. A standard example of a process on a network is a random walk, whose shortest time scale is the minimal time a walker stays on a vertex between two moves. Loosely speaking, a temporal network changes locally faster than a process on it or with equal speed. Still, this state of a network can be steady.

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Conference papers on the topic "Vertex Reinforced Random Walk"

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Wu, Jun, Jingrui He, and Yongming Liu. "ImVerde: Vertex-Diminished Random Walk for Learning Imbalanced Network Representation." In 2018 IEEE International Conference on Big Data (Big Data). IEEE, 2018. http://dx.doi.org/10.1109/bigdata.2018.8622603.

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Ma, Zongjie, Yi Fan, Kaile Su, Chengqian Li, and Abdul Sattar. "Random Walk in Large Real-World Graphs for Finding Smaller Vertex Cover." In 2016 IEEE 28th International Conference on Tools with Artificial Intelligence (ICTAI). IEEE, 2016. http://dx.doi.org/10.1109/ictai.2016.0109.

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Chen, Yun-Nung, and Florian Metze. "Two-layer mutually reinforced random walk for improved multi-party meeting summarization." In 2012 IEEE Spoken Language Technology Workshop (SLT 2012). IEEE, 2012. http://dx.doi.org/10.1109/slt.2012.6424268.

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Andrade, Matheus Guedes de, Franklin De Lima Marquezino, and Daniel Ratton Figueiredo. "Characterizing the Relationship Between Unitary Quantum Walks and Non-Homogeneous Random Walks." In Concurso de Teses e Dissertações da SBC. Sociedade Brasileira de Computação, 2021. http://dx.doi.org/10.5753/ctd.2021.15756.

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Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the relationship between quantum and random walks has been recently discussed in specific scenarios, this work establishes a formal equivalence between the two processes on arbitrary finite graphs and general conditions for shift and coin operators. It requires empowering random walks with time heterogeneity, where the transition probability of the walker is non-uniform and time dependent. The equivalence is obtained by equating the probability of measuring the quantum walk on a given node of the graph and the probability that the random walk is at that same node, for all nodes and time steps. The first result establishes procedure for a stochastic matrix sequence to induce a random walk that yields the exact same vertex probability distribution sequence of any given quantum walk, including the scenario with multiple interfering walkers. The second result establishes a similar procedure in the opposite direction. Given any random walk, a time-dependent quantum walk with the exact same vertex probability distribution is constructed. Interestingly, the matrices constructed by the first procedure allows for a different simulation approach for quantum walks where node samples respect neighbor locality and convergence is guaranteed by the law of large numbers, enabling efficient (polynomial-time) sampling of quantum graph trajectories. Furthermore, the complexity of constructing this sequence of matrices is discussed in the general case.

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Fan, Yi, Nan Li, Chengqian Li, Zongjie Ma, Longin Jan Latecki, and Kaile Su. "Restart and Random Walk in Local Search for Maximum Vertex Weight Cliques with Evaluations in Clustering Aggregation." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/87.

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The Maximum Vertex Weight Clique (MVWC) problem is NP-hard and also important in real-world applications. In this paper we propose to use the restart and the random walk strategies to improve local search for MVWC. If a solution is revisited in some particular situation, the search will restart. In addition, when the local search has no other options except dropping vertices, it will use random walk. Experimental results show that our solver outperforms state-of-the-art solvers in DIMACS and finds a new best-known solution. Also it is the unique solver which is comparable with state-of-the-art methods on both BHOSLIB and large crafted graphs. Furthermore we evaluated our solver in clustering aggregation. Experimental results on a number of real data sets demonstrate that our solver outperforms the state-of-the-art for solving the derived MVWC problem and helps improve the final clustering results.

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Chen, Yun-Nung, and Florian Metze. "Multi-layer mutually reinforced random walk with hidden parameters for improved multi-party meeting summarization." In Interspeech 2013. ISCA: ISCA, 2013. http://dx.doi.org/10.21437/interspeech.2013-140.

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