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PageRank Optimization in Polynomial Time by Stochastic Shortest Path Reformulation [chapter]

Balázs Csanád Csáji, Raphaël M. Jungers, Vincent D. Blondel
2010 Lecture Notes in Computer Science  
By applying results from Markov decision theory, we show that an optimal solution to this problem can be found in polynomial time.  ...  The importance of a node in a directed graph can be measured by its PageRank.  ...  Stochastic Shortest Path Problems In this section we give an overview on stochastic shortest path problems, since our solutions to PageRank optimization are built upon their theory.  ... 
doi:10.1007/978-3-642-16108-7_11 fatcat:ylugdked6fb63b2ckl3jr4q2zq

PageRank optimization by edge selection

Balázs Csanád Csáji, Raphaël M. Jungers, Vincent D. Blondel
2014 Discrete Applied Mathematics  
By applying results from Markov decision theory, we show that an optimal solution to this problem can be found in polynomial time.  ...  The importance of a node in a directed graph can be measured by its PageRank.  ...  Stochastic Shortest Path Problems In this section we give an overview on stochastic shortest path problems, since our solutions to PageRank optimization are built upon their theory.  ... 
doi:10.1016/j.dam.2014.01.007 fatcat:atamsrcpsna5ljo7uap7elflze

PageRank Beyond the Web

David F. Gleich
2015 SIAM Review  
The mathematics of PageRank, however, are entirely general and apply to any graph or network in any domain.  ...  Thus, PageRank is now regularly used in bibliometrics, social and information network analysis, and for link prediction and recommendation.  ...  For instance, a node is important in the network if many shortest paths require that node.  ... 
doi:10.1137/140976649 fatcat:odab3aoaqbfddidyh653kn4oem

Editors' Introduction [chapter]

Sanjay Jain, Rémi Munos, Frank Stephan, Thomas Zeugmann
2013 Lecture Notes in Computer Science  
using a polynomial amount of data and processing time, provided that the distributions of the samples are restricted to be generated by one of a large family of related probabilistic deterministic finite  ...  In particular, he studied the unsupervised learning of natural languages; his findings are also relevant to first language acquisition in humans.  ...  Balázs Csáji, Raphaël Jungers and Vincent Blondel dedicate their paper PageRank Optimization in Polynomial Time by Stochastic Shortest Path Reformulation to the question on how a member-node of a network  ... 
doi:10.1007/978-3-642-40935-6_1 fatcat:pchrsvhjezfbvh6dfplqhxhgcy

Semi-supervised learning for graph to signal mapping: A graph signal wiener filter interpretation

Benjamin Girault, Paulo Goncalves, Eric Fleury, Arashpreet Singh Mor
2014 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
In this contribution, we investigate a graph to signal mapping with the objective of analysing intricate structural properties of graphs with tools borrowed from signal processing.  ...  We successfully use a graph-based semi-supervised learning approach to map nodes of a graph to signal amplitudes such that the resulting time series is smooth and the procedure efficient and scalable.  ...  Actually, this choice is relatively free, and therefore we adopt the most obvious one that amounts to identify two most distant nodes in the graph (w.r.t. the shortest path) and to label those as the centroids  ... 
doi:10.1109/icassp.2014.6853770 dblp:conf/icassp/GiraultGFM14 fatcat:m4ra7uh6k5dm5hpaz7e3xcvnyi

Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks [article]

Zhiqian Chen, Fanglan Chen, Lei Zhang, Taoran Ji, Kaiqun Fu, Liang Zhao, Feng Chen, Lingfei Wu, Charu Aggarwal, Chang-Tien Lu
2021 arXiv   pre-print
We show the framework's generalization power by reformulating existing GNNs models. This conclusion is based on various historical and technologically current works covered in this survey.  ...  This is equivalent to Polynomial Aggregation (A-2). GPR [32] generalize PageRank and found the equivalence of GPR and Polynomial Approximation (B-2).  ... 
arXiv:2107.10234v3 fatcat:5pu74kvwf5hnzmsch6hewiydzm

Network Representation [chapter]

Zhiyuan Liu, Yankai Lin, Maosong Sun
2020 Representation Learning for Natural Language Processing  
measured by cosine similarity or Euclidean distance of their representations).  ...  Network representation learning aims to embed the vertexes in a network into low-dimensional dense representations, in which similar vertices in the network should have "close" representations (usually  ...  of vertex v i and l i j is the length of shortest path between vertex v i and v j .  ... 
doi:10.1007/978-981-15-5573-2_8 fatcat:2fljfkgpozhudbgqr7tgv45vxi

Fast Algorithms for Game-Theoretic Centrality Measures [article]

Piotr Lech Szczepański
2015 arXiv   pre-print
The main contribution of this dissertation is that we show that a wide variety of game-theoretic solution concepts on networks can be computed in polynomial time.  ...  Next, the centrality of any individual node is determined by a chosen game-theoretic solution concept (notably, the Shapley value) in the same way as the payoff of a player in a cooperative game.  ...  If vertex u immediately precedes vertex v on some shortest path from source s, all shortest paths stored in T su extended by vertex v are part of the set of shortest paths stored in T sv .  ... 
arXiv:1512.01764v1 fatcat:tpodgmxjbrampdarikpvhpglx4

Transforming Graph Data for Statistical Relational Learning

R. A. Rossi, L. K. McDowell, D. W. Aha, J. Neville
2012 The Journal of Artificial Intelligence Research  
In this article, we examine and categorize techniques for transforming graph-based relational data to improve SRL algorithms.  ...  ., social, biological, information networks) and a corresponding increase in the application of Statistical Relational Learning (SRL) algorithms to these domains.  ...  Luke McDowell was supported in part by NSF award number 1116439 and by a grant from ONR. This research was also partly supported by the NSF under the contract number IIS-1149789.  ... 
doi:10.1613/jair.3659 fatcat:tumtadmqgven3jevn6ywcqiuka

Transforming Graph Representations for Statistical Relational Learning [article]

Ryan A. Rossi, Luke K. McDowell, David W. Aha, Jennifer Neville
2012 arXiv   pre-print
In this article, we examine a range of representation issues for graph-based relational data.  ...  ., social, biological, information networks) and a corresponding increase in the application of statistical relational learning (SRL) algorithms to these domains.  ...  They show how to compute such relative rankings both for metrics based on shortest paths as well as for Markov chain-based techniques (e.g., to produce "PageRank with priors").  ... 
arXiv:1204.0033v1 fatcat:32zwr7gadfbo5kvsdh57w3gtci

A Survey of Computational Approaches to Reconstruct and Partition Biological Networks [chapter]

Lipi Acharya, Thair Judeh, Dongxiao Zhu
2012 Statistical and Machine Learning Approaches for Network Analysis  
polynomial time convergence of the EM algorithm.  ...  Recompute the shortest-path betweenness scores for all edges affected by the removal. } The most important step in the Girvan-Newman algorithm is to recalculate the shortest-path betweenness scores.  ... 
doi:10.1002/9781118346990.ch1 fatcat:nxykyfoherf6fpzfpwo5acyy6a

Graph Signal Processing – Part III: Machine Learning on Graphs, from Graph Topology to Applications [article]

Ljubisa Stankovic, Danilo Mandic, Milos Dakovic, Milos Brajovic, Bruno Scalzo, Shengxi Li, Anthony G. Constantinides
2020 arXiv   pre-print
Part III of this monograph starts by addressing ways to learn graph topology, from the case where the physics of the problem already suggest a possible topology, through to most general cases where the  ...  For completeness, both variants of LASSO are derived in an intuitive way, and explained.  ...  or groups of other vertices of the graph, and is given by where σ(k, m) denotes the number of shortest paths between vertices k and m, and σ(k, m|n) the number of those paths passing through vertex n  ... 
arXiv:2001.00426v1 fatcat:t7323epqsve2na7q7imuyhlkeq

Community detection in graphs

Santo Fortunato
2010 Physics reports  
We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by  ...  Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs.  ...  distribution of shortest path lengths.  ... 
doi:10.1016/j.physrep.2009.11.002 fatcat:4ehi6spclncgtevcwxwztmhw4y

Graph Data Management and Mining: A Survey of Algorithms and Applications [chapter]

Charu C. Aggarwal, Haixun Wang
2010 Managing and Mining Graph Data  
Finally, we will discuss important avenues of future research in the area.  ...  Graph mining and management has become a popular area of research in recent years because of its numerous applications in a wide variety of practical fields, including computational biology, software bug  ...  Clearly, the hitting time is a function of not just the length of the shortest paths, but also the number of possible paths which exist from node to node .  ... 
doi:10.1007/978-1-4419-6045-0_2 dblp:series/ads/AggarwalW10a fatcat:tzo627bhpndl3iedhtru6vv6vy

Semantic Matching in Search

Hang Li, Jun Xu
2014 Foundations and Trends in Information Retrieval  
It has been observed that most of the dissatisfaction cases in relevance are due to term mismatch between queries and documents (e.g., query "ny times" does not match well with a document only containing  ...  "New York Times"), because term matching, i.e., the bag-of-words approach, still functions as the main mechanism of modern search engines.  ...  This work is supported in part by China National 973 project 2014CB340301.  ... 
doi:10.1561/1500000035 fatcat:ici6lm2fgjfwznnydro5u2s3va
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