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

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. ...

##
###
PageRank optimization by edge selection

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. ...

##
###
PageRank Beyond the Web

2015
*
SIAM Review
*

The mathematics of

doi:10.1137/140976649
fatcat:odab3aoaqbfddidyh653kn4oem
*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. ...##
###
Editors' Introduction
[chapter]

2013
*
Lecture Notes in Computer Science
*

using a

doi:10.1007/978-3-642-40935-6_1
fatcat:pchrsvhjezfbvh6dfplqhxhgcy
*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 ...##
###
Semi-supervised learning for graph to signal mapping: A graph signal wiener filter interpretation

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 ...

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

2021
*
arXiv
*
pre-print

We show the framework's generalization power

arXiv:2107.10234v3
fatcat:5pu74kvwf5hnzmsch6hewiydzm
*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). ...##
###
Network Representation
[chapter]

2020
*
Representation Learning for Natural Language Processing
*

measured

doi:10.1007/978-981-15-5573-2_8
fatcat:2fljfkgpozhudbgqr7tgv45vxi
*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 . ...##
###
Fast Algorithms for Game-Theoretic Centrality Measures
[article]

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

arXiv:1512.01764v1
fatcat:tpodgmxjbrampdarikpvhpglx4
*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 . ...##
###
Transforming Graph Data for Statistical Relational Learning

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. ...

##
###
Transforming Graph Representations for Statistical Relational Learning
[article]

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"). ...

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

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. ...

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

2020
*
arXiv
*
pre-print

Part III of this monograph starts

arXiv:2001.00426v1
fatcat:t7323epqsve2na7q7imuyhlkeq
*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 ...##
###
Community detection in graphs

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

doi:10.1016/j.physrep.2009.11.002
fatcat:4ehi6spclncgtevcwxwztmhw4y
*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. ...##
###
Graph Data Management and Mining: A Survey of Algorithms and Applications
[chapter]

2010
*
Managing and Mining Graph Data
*

Finally, we will discuss important avenues of future research

doi:10.1007/978-1-4419-6045-0_2
dblp:series/ads/AggarwalW10a
fatcat:tzo627bhpndl3iedhtru6vv6vy
*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 . ...##
###
Semantic Matching in Search

2014
*
Foundations and Trends in Information Retrieval
*

It has been observed that most of the dissatisfaction cases

doi:10.1561/1500000035
fatcat:ici6lm2fgjfwznnydro5u2s3va
*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. ...
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