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Product Measure Approximation of Symmetric Graph Properties [article]

Dimitris Achlioptas, Paris Siminelakis
2015 arXiv   pre-print
With this in mind, we pursue the following question: What are general sufficient conditions for the uniform measure on a set of graphs S ⊆G_n to be approximable by a product measure?  ...  Let G_n be the set of all graphs on n vertices and let S be an arbitrary subset of G_n, e.g., the set of graphs with m edges.  ...  On one hand was the desire to explore the extent to which symmetric sets (properties) can be studied via product measure approximations (instead of assuming product form and studying properties of the  ... 
arXiv:1502.07787v1 fatcat:itw5tacwdfg6xpfbdgt5atusle

Symmetric Graph Properties Have Independent Edges [chapter]

Dimitris Achlioptas, Paris Siminelakis
2015 Lecture Notes in Computer Science  
With this in mind, we pursue the following question: What are general sufficient conditions for the uniform measure on a set of graphs S ⊆ Gn to be well-approximable by a product measure on the set of  ...  Let Gn be the set of all graphs on n vertices and let S be an arbitrary subset of Gn, e.g., the set of all graphs with m edges.  ...  Conditional on the edge-profile, we can couple the generation of edges in different parts independently, in each part the coupling being identical to that between G(n, m) and G(n, p).  ... 
doi:10.1007/978-3-662-47666-6_37 fatcat:uqf5alercfahjamg2z45olnkau

A New Algorithm to Compute Low T-Transitive Approximation of a Fuzzy Relation Preserving Symmetry. Comparisons with the T-Transitive Closure [chapter]

Luis Garmendia, Adela Salvador
2005 Lecture Notes in Computer Science  
It is given a new algorithm to compute a lower T-transitive approximation of a fuzzy relation that preserves symmetry.  ...  Average distances of the fuzzy relation with the Ttransitive closure are similar than the average distances with the low T-transitive approximation.  ...  Conclusions The T-transitivization algorithm that keeps symmetry, applies to reflexive and symmetric fuzzy relations, computes T-transitive low approximations with similar distances than the T-transitive  ... 
doi:10.1007/11518655_49 fatcat:6uulvhsvinchxgbffj66ugbrji

Inapproximability of actions and Kazhdan's property (T) [article]

Gabor Kun, Andreas Thom
2019 arXiv   pre-print
We construct p.m.p. group actions that are not local-global limits of sequences of finite graphs. Moreover, they do not weakly contain any sequence of finite labeled graphs.  ...  Our methods are based on the study of almost automorphisms of sofic approximations: We show that the set of epsilon-automorphisms of a sufficiently good sofic approximation of a Kazhdan group by expanders  ...  Acknowledgments The work of the authors has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Consolidator Grant No. 681207  ... 
arXiv:1901.03963v2 fatcat:hgrojecj7zhtdjxfkhcknqem3i

A Kernel-Based Framework for Learning Graded Relations From Data

W. Waegeman, T. Pahikkala, A. Airola, T. Salakoski, M. Stock, B. De Baets
2012 IEEE transactions on fuzzy systems  
It extends existing approaches because both crisp and graded relations are considered, and it unifies existing approaches because different types of graded relations can be modeled, including symmetric  ...  Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects  ...  and positive definiteness or transitivity properties for similarity measures.  ... 
doi:10.1109/tfuzz.2012.2194151 fatcat:k5baor5zxzhpbizbusah3kzfze

Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations

Hector Zenil, Narsis Kiani, Jesper Tegnér
2018 Entropy  
We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize spatial, geometric, symmetric and topological properties of mathematical  ...  We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov–Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP  ...  An essential ingredient for a complexity measure is that it integrates all its properties, something that only a noncomputable approximating measure such as CTM/BDM can achieve.  ... 
doi:10.3390/e20070534 pmid:33265623 fatcat:pmg65kxoabaqbadiarbiwzpr3m

Effective Resistance Preserving Directed Graph Symmetrization [article]

Katherine Fitch
2019 arXiv   pre-print
It is shown that the preservation of this metric allows for interpretation of algebraic and spectral properties of the symmetrized graph in the context of the directed graph, due to the relationship between  ...  Additionally, Lyapunov theory is used to demonstrate that the Laplacian matrix of a directed graph can be decomposed into the product of a projection matrix, a skew symmetric matrix, and the Laplacian  ...  Moreover, it is shown that the Laplacian matrix of a directed graph can be decomposed into the product of a projection matrix, a skew symmetric matrix, and the Laplacian matrix of the symmetrized graph  ... 
arXiv:1802.09829v2 fatcat:4x6w47usyrhc3m36ywoqf4xena

Approximate reflectional symmetries of fuzzy objects with an application in model-based object recognition

Olivier Colliot, Alexander V. Tuzikov, Roberto M. Cesar, Isabelle Bloch
2004 Fuzzy sets and systems (Print)  
The choice of an appropriate measure of comparison is based on the desired properties of the symmetry measure. Then, an algorithm for computing the symmetry plane of fuzzy objects is proposed.  ...  Approximate reflectional symmetries of fuzzy objects with an application in model-based object recognition. Abstract This paper is devoted to the study of reflectional symmetries of fuzzy objects.  ...  One important property of the symmetry attribute s(a, b) is that it will be zero for most pairs of regions which are not symmetrical, and non-zero only for a small group of approximately symmetrical pairs  ... 
doi:10.1016/j.fss.2003.07.003 fatcat:qylaeuftxja7zpc7hu4lg3ax2e

Splines and wavelets on circulant graphs

M.S. Kotzagiannidis, P.L. Dragotti
2017 Applied and Computational Harmonic Analysis  
Ultimately, we consider generalizations to arbitrary graphs in the form of graph approximations, with focus on graph product decompositions.  ...  In particular, we proceed to show how the use of graph products facilitates a multi-dimensional extension of the proposed constructions and properties.  ...  In particular, given an arbitrary undirected graph, we consider its approximation as the graph product of circulant graphs.  ... 
doi:10.1016/j.acha.2017.10.002 fatcat:c2lxgxxz4vdhld4ryxgr62sjcu

Learning Valued Relations from Data [chapter]

Willem Waegeman, Tapio Pahikkala, Antti Airola, Tapio Salakoski, Bernard De Baets
2011 Advances in Intelligent and Soft Computing  
It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types of valued relations can be modeled, including symmetric  ...  Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects  ...  A Kronecker product feature mapping was proposed for combining the features of pairs of objects that constitute a relation (edge level in a graph).  ... 
doi:10.1007/978-3-642-24001-0_24 dblp:conf/eurofuse/WaegemanPASB11 fatcat:fid63q7ofbgytnemxwlxukfiia

Subgraph densities in Markov spaces [article]

Dávid Kunszenti-Kovács, László Lovász, Balázs Szegedy
2022 arXiv   pre-print
We generalize subgraph densities, arising in dense graph limit theory, to Markov spaces (symmetric measures on the square of a standard Borel space).  ...  More generally, we define an analogue of the set of homomorphisms in the form of a measure on maps of a finite graph into a Markov space.  ...  Since graphons can be approximated by finite graphs via sampling, and the homomorphism measures of these finite graphs approximate the homomorphism measure of the graphon, we obtain a partial answer to  ... 
arXiv:2206.04493v1 fatcat:gdartabb3zeqdcba2m7a3e46vq

Deterministic Approximation of Random Walks in Small Space

Jack Murtagh, Omer Reingold, Aaron Sidford, Salil Vadhan, Michael Wagner
2019 International Workshop on Approximation Algorithms for Combinatorial Optimization  
Second, we define and analyze a generalization of the derandomized square for irregular graphs and for sparsifying the product of two distinct graphs.  ...  We give a deterministic, nearly logarithmic-space algorithm that given an undirected graph G, a positive integer r, and a set S of vertices, approximates the conductance of S in the r-step random walk  ...  To measure the approximation between graphs we use spectral approximation 2 [23]: Definition 5. Let L, L ∈ R n×n be symmetric PSD matrices.  ... 
doi:10.4230/lipics.approx-random.2019.42 dblp:conf/approx/MurtaghRSV19 fatcat:qbobogy745ds7b43u23fx3oj4y

Spectral clustering with epidemic diffusion

Laura M. Smith, Kristina Lerman, Cristina Garcia-Cardona, Allon G. Percus, Rumi Ghosh
2013 Physical Review E  
We show that the replicator, an operator describing epidemic diffusion, is equivalent to the symmetric normalized Laplacian of a reweighted graph with edges reweighted by the eigenvector centralities of  ...  We propose a new spectral partitioning method that exploits the properties of epidemic diffusion.  ...  This work has been funded by the Air Force Office of Scientific Research under contracts  ... 
doi:10.1103/physreve.88.042813 pmid:24229231 fatcat:bn3xge357rbshijkt277n37tte

Page 2095 of Mathematical Reviews Vol. , Issue 90D [page]

1990 Mathematical Reviews  
For a measurable function f on [0,1] let AC(/) = {x:f is ap- proximately continuous at x}, AS(/) = {x:f is approximately symmetric at x}, ASC(/) = {x: f is approximately symmetrically continuous at x},  ...  [Evans, Michael Jon] (1-NCS); Humke, Paul D. (1-OLAF) The approximate symmetric behavior of real functions. Real Anal. Exchange 14 (1988/89), no. 2, 375-392.  ... 

Asymmetric Transitivity Preserving Graph Embedding

Mingdong Ou, Peng Cui, Jian Pei, Ziwei Zhang, Wenwu Zhu
2016 Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '16  
Graph embedding algorithms embed a graph into a vector space where the structure and the inherent properties of the graph are preserved.  ...  The existing graph embedding methods cannot preserve the asymmetric transitivity well, which is a critical property of directed graphs.  ...  Preserving the symmetric transitivity in undirected graphs in an embedding space is natural and straightforward, as most of the distance metrics defined in the vector space possess the property of symmetric  ... 
doi:10.1145/2939672.2939751 dblp:conf/kdd/OuCPZ016 fatcat:qrhtrbyvlbbrvf53fdbcso3p7a
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