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Revealing Structure in Large Graphs: Szemerédi's Regularity Lemma and its Use in Pattern Recognition [article]

Marcello Pelillo, Ismail Elezi, Marco Fiorucci
2016 arXiv   pre-print
In this paper we will provide an overview of the regularity lemma and its algorithmic aspects, and will discuss its relevance in the context of pattern recognition research.  ...  In other words, the result provides us a way to obtain a good description of a large graph using a small amount of data, and can be regarded as a manifestation of the all-pervading dichotomy between structure  ...  Bolla, H, Reittu and F. Bazsó for reading a preliminary version of the paper, and to the anonymous reviewers for their constructive feedback.  ... 
arXiv:1609.06583v1 fatcat:ci24pl24y5ax5dujr4tjmf75xy

Graph Compression Using The Regularity Method [article]

Francesco Pelosin
2018 arXiv   pre-print
In particular, it has been developed a procedure called CoDec (Compression-Decompression) which is based on Alon et al's constructive version of the Regularity Lemma.  ...  The experimental results make us confident that our method can be effectively used as a graph compression technique able to preserve meaningful patterns of the original graph.  ...  Acknowledgements I would like to express my gratitude to my supervisor Marcello Pelillo for accepting me as a candidate and assigning me such stimulating research topic for my thesis.  ... 
arXiv:1810.07275v2 fatcat:e6cqxv4lb5asrinacz6t3xlbrq

Regular Partitions and Their Use in Structural Pattern Recognition [article]

Marco Fiorucci
2020 arXiv   pre-print
In this thesis, we tackle this challenge by introducing a framework to summarize large graphs based on Szemer\'edi's Regularity Remma (RL), which roughly states that any sufficiently large graph can almost  ...  We first extend an heuristic version of the RL to improve its efficiency and its robustness. We use the proposed algorithm to address graph-based clustering and image segmentation tasks.  ...  Hence, in this thesis, we posit that the regularity lemma can be used to summarize large graphs revealing its main structural patterns, while filtering out noise, which is common in any real-world networks  ... 
arXiv:1909.07420v2 fatcat:yconxoyh4ffezb6ahglrdbnruy

Exploiting Contextual Information with Deep Neural Networks [article]

Ismail Elezi
2020 arXiv   pre-print
In parallel, we show that by explicitly designing algorithms (motivated from graph theory and game theory) that take into considerations the entire structure of the dataset, we can achieve state-of-the-art  ...  results in different topics like semi-supervised learning and similarity learning.  ...  The first two papers contain the part about the explicit usage of contextual information and are the core of the thesis: Szemeredi's regularity lemma and its use in pattern recognition [143] ; Pattern  ... 
arXiv:2006.11706v2 fatcat:bzaghxubbzcftdsvv4ogk3tfxe

Nonmonotonic and Paraconsistent Reasoning: From Basic Entailments to Plausible Relations [chapter]

Ofer Arieli, Arnon Avron
1999 Lecture Notes in Computer Science  
This is proved by establishing a directed version of Szemerédi's regularity lemma, and implies that for every H there is a one-sided error property tester whose query complexity is bounded by a function  ...  Abstract An IR image of the human face presents its unique heat-signature and can be used for recognition.  ...  In providing this we also prove a result about random walks on the group Z q 2 that may be interesting in its own right.  ... 
doi:10.1007/3-540-48747-6_2 fatcat:nbkzf3rldrhk5pim4nzehnplom

Szemerédi's Regularity Lemma and Its Applications to Pairwise Clustering and Segmentation [chapter]

Anna Sperotto, Marcello Pelillo
Lecture Notes in Computer Science  
This paper reports a first attempt at applying Szemerédi's result to computer vision and pattern recognition problems.  ...  Szemerédi's regularity lemma is a deep result from extremal graph theory which states that every graph can be well-approximated by the union of a constant number of random-like bipartite graphs, called  ...  recognition problems, whenever large and dense graphs arise.  ... 
doi:10.1007/978-3-540-74198-5_2 fatcat:uog4dpgnkfc7lhjjehmpizfqqi

Ronald Lewis Graham (1935–2020)

Joe Buhler, Steve Butler, Joel Spencer, Persi Diaconis, Henry Pollak, Solomon A Garfunkel, Andrew Odlyzko, Jeffrey C Lagarias, Donald E Knuth, Carl Pomerance, Carla Savage, László Lovász (+7 others)
2021 Notices of the American Mathematical Society  
Ramsey's Theorem guarantees certain regularity in large structures. For graphs this regularity is a complete graph or an empty graph.  ...  It was also useful because graphs that arise in deterministic contexts are often quasirandom, and the theory of quasirandomness immediately gives us a great deal of information about any such graph.  ... 
doi:10.1090/noti2382 fatcat:r3lc5ueyxrcwfnmhicdt3lp2im

Problems of unknown complexity : graph isomorphism and Ramsey theoretic numbers [article]

Pascal Schweitzer, Universität Des Saarlandes, Universität Des Saarlandes
2009
Finally, I am greatly in debt and most thankful to my brother Patrick Schweitzer, who persistently improved the quality of my dissertation in virtually every aspect.  ...  For the unions and joins, Nauty does not benefit from the cellfano option. Presumably, it is possible to create a new invariant which helps in the recognition of this particular graph family.  ...  different when it is used to sample in the two input graphs.  ... 
doi:10.22028/d291-25946 fatcat:ff66x4zhlzaghlr4visddjomkq

Symmetry, Almost

Amanda Folsom
2019 Notices of the American Mathematical Society  
Rates quoted do not include the Alabama state hotel tax (13%), local taxes and hotel fees may apply.  ...  Invited Addresses Special Sessions If you are volunteering to speak in a Special Session, you should send your abstract as early as possible via the abstract submission form found at http://www.ams.org  ...  This is a fascinating subject in its own right, not least for the connections it reveals between Bernoulli numbers and the structure of cyclotomic class groups.  ... 
doi:10.1090/noti1775 fatcat:xwrijzvqazg7bdym7un5qq2jjq