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Inexact Matching of Large and Sparse Graphs Using Laplacian Eigenvectors [chapter]

David Knossow, Avinash Sharma, Diana Mateus, Radu Horaud
2009 Lecture Notes in Computer Science  
In this paper we propose an inexact spectral matching algorithm that embeds large graphs on a low-dimensional isometric space spanned by a set of eigenvectors of the graph Laplacian.  ...  This results in an inexact graph matching solution that can be improved using a rigid point registration algorithm. We apply the proposed methodology to match surfaces represented by meshes.  ...  The link between spectral matching and spectral clustering has not yet been Inexact Matching of Large and Sparse Graphs Using Laplacian Eigenvectors 3 thoroughly investigated.  ... 
doi:10.1007/978-3-642-02124-4_15 fatcat:3l4hdkupurg2hjsjxo6kcaiqaa

GRASP: Graph Alignment through Spectral Signatures [article]

Judith Hermanns, Anton Tsitsulin, Marina Munkhoeva, Alex Bronstein, Davide Mottin, Panagiotis Karras
2021 arXiv   pre-print
What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics.  ...  Our experimental study, featuring noise levels higher than anything used in previous studies, shows that GRASP outperforms state-of-the-art methods for graph alignment across noise levels and graph types  ...  The eigenvectors form an orthogonal basis, which we use a standard basis. We use φ (ψ) to indicate the eigenvectors of the Laplacian of graph G 1 (G 2 ).  ... 
arXiv:2106.05729v2 fatcat:gjn3jf3ivjgk7gzfbnm4tai6wa

Spectral Projector-Based Graph Fourier Transforms

Joya A. Deri, Jose M. F. Moura
2017 IEEE Journal on Selected Topics in Signal Processing  
Many real world large sparse graphs have defective adjacency matrices.  ...  This is particularly meaningful when A has repeated eigenvalues, and it is very useful when A is defective or not diagonalizable (as it may be the case with directed graphs).  ...  In many of these, the graphs are large and sparse and their adjacency matrix is defective. This paper addresses these issues.  ... 
doi:10.1109/jstsp.2017.2731599 fatcat:o5lmtypxbjdfnckucpe66vvgwm

Edit distance from graph spectra

Robles-Kelly, Hancock
2003 Proceedings Ninth IEEE International Conference on Computer Vision  
We pose the problem of graph-matching as maximum a posteriori probability alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression for the edit costs.  ...  One of the criticisms that can be leveled at existing methods for computing graph edit distance is that it lacks the formality and rigour of the computation of string edit distance.  ...  The edit sequence delivers correspondences that are robust to structural error and can be used to cluster graphs into meaningful classes for purposes of image-database indexing and retrieval.  ... 
doi:10.1109/iccv.2003.1238347 dblp:conf/iccv/Robles-KellyH03 fatcat:ktrmlhn33jg5tn54b2ktwgkpze

Identifying network structure similarity using spectral graph theory

Ralucca Gera, L. Alonso, Brian Crawford, Jeffrey House, J. A. Mendez-Bermudez, Thomas Knuth, Ryan Miller
2018 Applied Network Science  
To test the scalability of our metric we use a random matrix theory approach while discovering Erdös-Rényi graphs.  ...  We introduce and test our metric on the consecutive snapshots of a network, and against the ground truth.  ...  Feasible inexact matching of different size graphs use spectral analysis.  ... 
doi:10.1007/s41109-017-0042-3 pmid:30839726 pmcid:PMC6214265 fatcat:6yaabbsbpvg3xpcq65eb3euu2q

Pseudo-Aligned Multilingual Corpora

Fernando Diaz, Donald Metzler
2007 International Joint Conference on Artificial Intelligence  
Specifically, we construct a topicbased graph for each language.  ...  Experimental results show that pseudo-alignment of multilingual corpora is feasible and that the document alignments produced are qualitatively sound.  ...  Any opinions, findings and conclusions or recommendations expressed in this material are the authors' and do not necessarily reflect those of the sponsor.  ... 
dblp:conf/ijcai/DiazM07 fatcat:3fdipgp2wveqhpfddgohhznecu

Node Embeddings and Exact Low-Rank Representations of Complex Networks [article]

Sudhanshu Chanpuriya, Cameron Musco, Konstantinos Sotiropoulos, Charalampos E. Tsourakakis
2020 arXiv   pre-print
Specifically, we prove that a minor relaxation of their model can generate sparse graphs with high triangle density.  ...  In particular, they show that any network generated from a natural low-dimensional model cannot be both sparse and have high triangle density (high clustering coefficient), two hallmark properties of many  ...  a small number of extremal eigenvectors of a matrix representation of the graph (e.g., top eigenvectors of the adjacency matrix [McS01] , or bottom eigenvectors of the Laplacian [AM85] ) to find good  ... 
arXiv:2006.05592v2 fatcat:jny4y4eeyneq7dxddhjjawfyte

The Principal Components Analysis of a Graph, and Its Relationships to Spectral Clustering [chapter]

Marco Saerens, Francois Fouss, Luh Yen, Pierre Dupont
2004 Lecture Notes in Computer Science  
The ECTD can be computed from the pseudoinverse of the Laplacian matrix of the graph, which is a kernel.  ...  This work presents a novel procedure for computing (1) distances between nodes of a weighted, undirected, graph, called the Euclidean Commute Time Distance (ECTD), and (2) a subspace projection of the  ...  Van Dooren and Prof. Blondel, from the "Département d'Ingénierie Mathématique" of the Université catholique de Louvain, for insightful discussions.  ... 
doi:10.1007/978-3-540-30115-8_35 fatcat:l3p6o3azubc3lmlgz5zdccyphq

Nearly Optimal Preconditioned Methods for Hermitian Eigenproblems Under Limited Memory. Part II: Seeking Many Eigenvalues

Andreas Stathopoulos, James R. McCombs
2007 SIAM Journal on Scientific Computing  
In this paper, we seek nearly optimal methods for a large number, nev, of eigenpairs, that work with a search space whose size is O(1), independent from nev.  ...  Third, we perform an extensive set of experiments with our methods and against other state-of-the-art software that validate our models, and confirm our GD+k and JDQMR methods as nearly optimal within  ...  The numerical solution of large, sparse, Hermitian or real symmetric eigenvalue problems is one of the most computationally intensive tasks in a variety of applications.  ... 
doi:10.1137/060661910 fatcat:7dfr6h6vcbhbpnbqppto7rkrcy

A Unified Framework for Structured Graph Learning via Spectral Constraints [article]

Sandeep Kumar, Jiaxi Ying, José Vinícius de M. Cardoso, Daniel Palomar
2019 arXiv   pre-print
Useful structured graphs include the multi-component graph, bipartite graph, connected graph, sparse graph, and regular graph.  ...  In this paper, we introduce a unified graph learning framework lying at the integration of Gaussian graphical models and spectral graph theory.  ...  For example, sparse eigenvectors of the graph matrices are important to investigate the uncertainty principle over graphs (Teke and Vaidyanathan, 2017) .  ... 
arXiv:1904.09792v1 fatcat:oyeulr5bcjasbhs2cbeixvk2fu

Distributed Graph Isomorphism using Quantum Walks

Jayaprabha Yadav
2015 International Journal on Recent and Innovation Trends in Computing and Communication  
To show the effectiveness of the technique, we applied it to the large graphs derived from images using Delauney triangulation. The results show a remarkable speedup for large data.  ...  Graph isomorphism being an NP problem, most of the systems that solves the graph isomorphism are constrained with some classes of the graph, and do not work for all types of graphs in polynomial time.  ...  There are of course more sophisticated inexact graph matching algorithms available. Douglas and Wang [9] have recently explored the use of discrete quantum walks for graph isomorphism.  ... 
doi:10.17762/ijritcc2321-8169.150212 fatcat:6st723fggbf6tc6eihsu56vzv4

Accelerated Dual Descent for Network Optimization [article]

M. Zargham, A. Ribeiro, A. Jadbabaie, A. Ozdaglar
2011 arXiv   pre-print
The approximate Newton directions are obtained through matrix splitting techniques and sparse Taylor approximations of the inverse Hessian.We show that, similarly to conventional Newton methods, the proposed  ...  This paper introduces a family of dual descent algorithms that use approximate Newton directions to accelerate the convergence rate of conventional dual descent.  ...  The other eigenvectors of the normalized Laplacian necessarily lie in (−1, 1). Suppose µ ∈ (−1, 1) is one such eigenvalue of I −L k , associated with eigenvector ν.  ... 
arXiv:1104.1157v1 fatcat:xgbngm4mwbcuha7mfajsufknae

Accelerated dual descent for network optimization

Michael Zargham, Alejandro Ribeiro, Asuman Ozdaglar, Ali Jadbabaie
2011 Proceedings of the 2011 American Control Conference  
The approximate Newton directions are obtained through matrix splitting techniques and sparse Taylor approximations of the inverse Hessian.  ...  This paper introduces a family of dual descent algorithms that use approximate Newton directions to accelerate the convergence rate of conventional dual descent.  ...  The other eigenvectors of the normalized Laplacian necessarily lie in (−1, 1). Suppose µ ∈ (−1, 1) is one such eigenvalue of I −L k , associated with eigenvector ν.  ... 
doi:10.1109/acc.2011.5991367 fatcat:bmmswhe2x5fzbi776jhrmyy3za

Does the ℓ_1-norm Learn a Sparse Graph under Laplacian Constrained Graphical Models? [article]

Jiaxi Ying, José Vinícius de M. Cardoso, Daniel P. Palomar
2020 arXiv   pre-print
We consider the problem of learning a sparse graph under Laplacian constrained Gaussian graphical models.  ...  To address this issue, we propose a nonconvex estimation method by solving a sequence of weighted ℓ_1-norm penalized sub-problems and prove that the statistical error of the proposed estimator matches  ...  We will prove that a large regularization parameter of the 1 -norm will lead to a solution that represents a fully connected graph instead of a sparse graph.  ... 
arXiv:2006.14925v1 fatcat:cgyc34j2mnbgzg7xncrmbqftzu

A Bayesian network framework for relational shape matching

Rangarajan, Coughlan, Yuille
2003 Proceedings Ninth IEEE International Conference on Computer Vision  
The new Bethe free energy approach is used to estimate the pairwise correspondences between links of the template graphs and the data.  ...  The main advantage of the relational shape matching approach is the obviation of the non-rigid spatial mappings used by recent non-rigid matching approaches.  ...  The Laplacian of a graph is a non-negative definite matrix. The first zero eigenvalue along with the eigenvector e = 1 N1 [1, 1, . . . , 1] T corresponds to the translation invariance of U.  ... 
doi:10.1109/iccv.2003.1238412 dblp:conf/iccv/RangarajanCY03 fatcat:ru53mcjtvfbkvdv6goxby5zmza
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