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Chordal Graphs and Semidefinite Optimization

Lieven Vandenberghe, Martin S. Andersen
2015 Foundations and Trends® in Optimization  
The first part of this survey (Chapters 2-7) covers the basic theory of chordal graphs and graph elimination, with an emphasis on tree data structures developed in sparse matrix theory (elimination trees  ...  This survey covers the theory and applications of chordal graphs, with an emphasis on algorithms developed in the literature on sparse Cholesky factorization.  ... 
doi:10.1561/2400000006 fatcat:jarefwxrsjdodpyistl2225mte

Structured random measurements in signal processing [article]

Felix Krahmer, Holger Rauhut
2014 arXiv   pre-print
A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a minimal number of samples.  ...  While this was first shown for (unstructured) Gaussian random measurement matrices, applications require certain structure of the measurements leading to structured random measurement matrices.  ...  Based on this work, [54] provides recovery guarantees for sparse vectors with an additional decay condition using a greedy algorithm for a number of measurements on the order of k log(N ).  ... 
arXiv:1401.1106v2 fatcat:ad7lkvnku5cw3f4ofhqosi2kea

An Application of AI Techniques to Structuring Objects into an Optimal Conceptual Hierarchy

Ryszard S. Michalski, Robert E. Stepp
1981 International Joint Conference on Artificial Intelligence  
involving relations on selected object attributes.  ...  Each level of the hierarchy Is determined by an iterative procaaa which repetitively applies a veralon of the A* search algorithm.  ...  Pablo Poveda for providing data used In the muslcologlcal experiment and for many helpful comments.  ... 
dblp:conf/ijcai/MichalskiS81 fatcat:bvs4ldcipffs5hpfrpe4kxlemq

ESSEX: Equipping Sparse Solvers for Exascale [chapter]

Andreas Alvermann, Achim Basermann, Holger Fehske, Martin Galgon, Georg Hager, Moritz Kreutzer, Lukas Krämer, Bruno Lang, Andreas Pieper, Melven Röhrig-Zöllner, Faisal Shahzad, Jonas Thies (+1 others)
2014 Lecture Notes in Computer Science  
This report introduces the project structure and presents selected results which demonstrate the potential impact of ESSEX for efficient sparse solvers on highly scalable heterogeneous supercomputers.  ...  The ESSEX project investigates computational issues arising at exascale for large-scale sparse eigenvalue problems and develops programming concepts and numerical methods for their solution.  ...  This work is supported by the German Research Foundation (DFG) through the Priority Programme 1648 "Software for Exascale Computing" (SPPEXA) under project ESSEX.  ... 
doi:10.1007/978-3-319-14313-2_49 fatcat:57wevi4tuzaejnisisllx4d6be

Page 2021 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
The first algorithm computes a perfect edge without vertex elimination ordering and the second one lists all maximal complete bipartite subgraphs.”  ...  This is the first algorithm for dynamic DFS for nontrivial classes of graphs.”  ... 

Composite Plate Phased Array Structural Health Monitoring Signal Reconstruction Based on Orthogonal Matching Pursuit Algorithm

Yajie Sun, Feihong Gu, Sai Ji, Lihua Wang
2017 Journal of Sensors  
Then, the experiment result indicated that the orthogonal matching pursuit algorithm can reconstruct the signal completely and accurately.  ...  However, a large amount of data will be generated when using ultrasonic phased array with Nyquist sampling theorem for structural health monitoring and is difficult to storage, transmission, and processing  ...  Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant nos. 51405241 and 61672290), the Jiangsu Government Scholarship for Overseas Studies, and the PAPD fund  ... 
doi:10.1155/2017/3157329 fatcat:tky4mnmeqrf43ifi33icvb56sa

Algorithmic Meta Theorems for Sparse Graph Classes [chapter]

Martin Grohe
2014 Lecture Notes in Computer Science  
A well-known example of an algorithmic meta theorem is Courcelle's Theorem, stating that all properties of graphs of bounded tree width that are definable in monadic second-order logic are decidable in  ...  Algorithmic meta theorems give efficient algorithms for classes of algorithmic problems, instead of just individual problems.  ...  Meta Theorems for First-Order Logic For properties definable in first-order logic (FO), we know meta theorems on a much larger variety of graph classes.  ... 
doi:10.1007/978-3-319-06686-8_2 fatcat:cr656t7vjbgxjkdjkcldpksgwm

Scalable Sparse Bayesian Network Learning for Spatial Applications

Thomas Liebig, Christine Körner, Michael May
2008 2008 IEEE International Conference on Data Mining Workshops  
Such patterns exist for instance along streets or between neighbouring street segments.  ...  We introduce and examine a Bayesian Network Learning algorithm enabling us to handle the complexity and performance requirements of the spatial context.  ...  We use this property in our application.  ... 
doi:10.1109/icdmw.2008.124 dblp:conf/icdm/LiebigKM08 fatcat:w3ocuprgprhfninttoyxfugqv4

Deconstructing the Structure of Sparse Neural Networks [article]

Maxwell Van Gelder, Mitchell Wortsman, Kiana Ehsani
2020 arXiv   pre-print
In looking back at algorithms for sparse neural networks and analyzing their performance from a different lens, we uncover several interesting properties and promising directions for future research.  ...  Although sparse neural networks have been studied extensively, the focus has been primarily on accuracy. In this work, we focus instead on network structure, and analyze three popular algorithms.  ...  Performance of ResNet-18 on CIFAR-10 when trained with the structure found by sparsity algorithms but with weights reset randomly.  ... 
arXiv:2012.00172v1 fatcat:egi6pmin2jef3pfu3r2am4av5a

Computationally efficient sup-t transitive closure for sparse fuzzy binary relations

Manolis Wallace, Yannis Avrithis, Stefanos Kollias
2006 Fuzzy sets and systems (Print)  
The property of transitivity is one of the most important for fuzzy binary relations, especially in the cases when they are used for the representation of real life similarity or ordering information.  ...  In this paper, after formalizing the notion of sparseness and providing a representation model for sparse relations that displays both computational and storage merits, we propose an algorithm for the  ...  Thus, the same complexity holds for the reflexive case as well. 2 Of course, it is easy to extend algorithm ITU in order to make it applicable to the case of complete representation as well: Algorithm  ... 
doi:10.1016/j.fss.2005.06.005 fatcat:cg2x4vs4jjdqnewkeaseeo3swq

Three-dimensional SAR imaging with sparse linear array using tensor completion in embedded space

Siqian Zhang, Ding Ding, Chenxi Zhao, Lingjun Zhao
2022 EURASIP Journal on Advances in Signal Processing  
Then, the tucker decomposition with incremental rank has been applied for completion.  ...  With the help of sparsity and low-rank property hidden in the 3D radar signal, the incomplete tensor data is taken as the input and converted into a higher order incomplete Hankel tensor by multiway delay  ...  Acknowledgements The authors thank the corresponding editors and reviewers for providing valuable comments and suggestions for this article.  ... 
doi:10.1186/s13634-022-00896-x fatcat:wmt5m5t77zgpbjto6ajet62ube

Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications [article]

Qing Qu, Zhihui Zhu, Xiao Li, Manolis C. Tsakiris, John Wright, and René Vidal
2020 arXiv   pre-print
In this paper, we overview recent advances on global nonconvex optimization theory for solving this problem, ranging from geometric analysis of its optimization landscapes, to efficient optimization algorithms  ...  for solving the associated nonconvex optimization problem, to applications in machine intelligence, representation learning, and imaging sciences.  ...  First, let us start with first-order iterative methods for solving the optimization problem (III.2) constrained over the sphere.  ... 
arXiv:2001.06970v1 fatcat:zluhhl3635bzrnnk7fjw5tvi7a

Structure-adaptive parallel solution of sparse triangular linear systems

Ehsan Totoni, Michael T. Heath, Laxmikant V. Kale
2014 Parallel Computing  
We describe the implementation of our algorithm in Charm++ and MPI and present promising results on up to 512 cores of BlueGene/P, using numerous sparse matrices from real applications.  ...  We develop a novel parallel algorithm based on various heuristics that adapts to the structure of the matrix and extracts parallelism that is unexploited by conventional methods.  ...  Even for applications with only one solution iteration, our algorithm (with the analysis time added) performs much better than the packages we compared with here.  ... 
doi:10.1016/j.parco.2014.06.006 fatcat:emxx7wcn4vceflpomruuw7mw4m

Sparse Representation for Wireless Communications: A Compressive Sensing Approach

Zhijin Qin, Jiancun Fan, Yuanwei Liu, Yue Gao, Geoffrey Ye Li
2018 IEEE Signal Processing Magazine  
Moreover, other potential applications and research challenges on sparse representation for 5G and IoT networks are identified.  ...  In this article, we will discuss various applications of sparse representation in wireless communications, with focus on the most recent compressive sensing (CS) enabled approaches.  ...  First, the abnormal values are detected with the help of recovering signal from an over-complete dictionary.  ... 
doi:10.1109/msp.2018.2789521 fatcat:wamvxn7kebavtjroau4ksfbwea

Optimally Sparse Frames [article]

Peter G. Casazza, Andreas Heinecke, Felix Krahmer, Gitta Kutyniok
2011 arXiv   pre-print
We then analyze the recently introduced algorithm Spectral Tetris for construction of unit norm tight frames and prove that the tight frames generated by this algorithm are in fact optimally sparse with  ...  Finally, we show that even the generalization of Spectral Tetris for the construction of unit norm frames associated with a given frame operator produces optimally sparse frames.  ...  Acknowledgement The authors would like to thank Ali Pezeshki for enlightening discussions on this topic. We are also grateful to the anonymous referees for valuable comments and suggestions.  ... 
arXiv:1009.3663v3 fatcat:h6cj5zskerc7dd5jhistrwt7o4
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