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Author : Jason Y. Zien
Publisher :
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.:/5 (321 download)
Download or read book Spectral K-way Ratio-cut Graph Partitioning written by Jason Y. Zien and published by . This book was released on 1993 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pak K. Chan
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (321 download)
Download or read book Spectral K-way Ratio-cut Partitioning written by Pak K. Chan and published by . This book was released on 1992 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Recent research on partitioning has focussed on the ratio-cut cost metric which maintains a balance between the sizes of the edges cut and the sizes of the partitions without fixing the size of the partitions a priori. Iterative approaches and spectral approaches to two- way ratio-cut partitioning have yielded higher quality partitioning results. In this paper we develop a spectral approach to multi-way ratio- cut partitioning which provides a generalization of the ratio-cut cost metric to k-way partitioning and a lower bound on this cost metric. Our approach uses Lanczos algorithm to find the k smallest eigenvalue/eigenvector pairs of the Laplacian of the graph. The eigenvectors are used to construct an orthogonal projection to map a vertex (of the graph) in an n-dimensional space into a k-dimensional subspace. We exploit the (near) orthogonality of the projected points to effect high quality clustering of points in a k-dimensional subspace. An efficient algorithm is presented for coercing the points in the k-dimensional subspace into k-partitions. Advancement over the current work is evidenced by the results of experiments on the standard MCNC benchmarks."
Author : Jos L. Balc Zar
Publisher :
ISBN 13 : 9783642158841
Total Pages : 0 pages
Book Rating : 4.1/5 (588 download)
Download or read book Machine Learning and Knowledge Discovery in Databases written by Jos L. Balc Zar and published by . This book was released on 2011-03-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3322921069
Total Pages : 715 pages
Book Rating : 4.3/5 (229 download)
Download or read book Combinatorial Algorithms for Integrated Circuit Layout written by and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has brought explosive growth in the technology for manufac turing integrated circuits. Integrated circuits with several hundred thousand transistors are now commonplace. This manufacturing capability, combined with the economic benefits of large electronic systems, is forcing a revolution in the design of these systems and providing a challenge to those people in terested in integrated system design. Modern circuits are too complex for an individual to comprehend completely. Managing tremendous complexity and automating the design process have become crucial issues. Two groups are interested in dealing with complexity and in developing algorithms to automate the design process. One group is composed of practi tioners in computer-aided design (CAD) who develop computer programs to aid the circuit-design process. The second group is made up of computer scientists and mathemati'::~l\ns who are interested in the design and analysis of efficient combinatorial aJ::,orithms. These two groups have developed separate bodies of literature and, until recently, have had relatively little interaction. An obstacle to bringing these two groups together is the lack of books that discuss issues of importance to both groups in the same context. There are many instances when a familiarity with the literature of the other group would be beneficial. Some practitioners could use known theoretical results to improve their "cut and try" heuristics. In other cases, theoreticians have published impractical or highly abstracted toy formulations, thinking that the latter are important for circuit layout.
Author : Ravindran Kannan
Publisher : Now Publishers Inc
ISBN 13 : 1601982747
Total Pages : 153 pages
Book Rating : 4.6/5 (19 download)
Download or read book Spectral Algorithms written by Ravindran Kannan and published by Now Publishers Inc. This book was released on 2009 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.
Author : Jason Y. Zien
Publisher :
ISBN 13 :
Total Pages : 332 pages
Book Rating : 4.:/5 (321 download)
Download or read book Multi-level Spectral K-way Graph Partitioning written by Jason Y. Zien and published by . This book was released on 1997 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Te Chiang Hu
Publisher : Institute of Electrical & Electronics Engineers(IEEE)
ISBN 13 :
Total Pages : 286 pages
Book Rating : 4.F/5 ( download)
Download or read book VLSI Circuit Layout written by Te Chiang Hu and published by Institute of Electrical & Electronics Engineers(IEEE). This book was released on 1985 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lasse Kliemann
Publisher : Springer
ISBN 13 : 3319494872
Total Pages : 428 pages
Book Rating : 4.3/5 (194 download)
Download or read book Algorithm Engineering written by Lasse Kliemann and published by Springer. This book was released on 2016-11-10 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithm Engineering is a methodology for algorithmic research that combines theory with implementation and experimentation in order to obtain better algorithms with high practical impact. Traditionally, the study of algorithms was dominated by mathematical (worst-case) analysis. In Algorithm Engineering, algorithms are also implemented and experiments conducted in a systematic way, sometimes resembling the experimentation processes known from fields such as biology, chemistry, or physics. This helps in counteracting an otherwise growing gap between theory and practice.
Author : Frédéric Ros
Publisher : Springer Nature
ISBN 13 : 3030293491
Total Pages : 239 pages
Book Rating : 4.0/5 (32 download)
Download or read book Sampling Techniques for Supervised or Unsupervised Tasks written by Frédéric Ros and published by Springer Nature. This book was released on 2019-10-26 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes in detail sampling techniques that can be used for unsupervised and supervised cases, with a focus on sampling techniques for machine learning algorithms. It covers theory and models of sampling methods for managing scalability and the “curse of dimensionality”, their implementations, evaluations, and applications. A large part of the book is dedicated to database comprising standard feature vectors, and a special section is reserved to the handling of more complex objects and dynamic scenarios. The book is ideal for anyone teaching or learning pattern recognition and interesting teaching or learning pattern recognition and is interested in the big data challenge. It provides an accessible introduction to the field and discusses the state of the art concerning sampling techniques for supervised and unsupervised task. Provides a comprehensive description of sampling techniques for unsupervised and supervised tasks; Describe implementation and evaluation of algorithms that simultaneously manage scalable problems and curse of dimensionality; Addresses the role of sampling in dynamic scenarios, sampling when dealing with complex objects, and new challenges arising from big data. "This book represents a timely collection of state-of-the art research of sampling techniques, suitable for anyone who wants to become more familiar with these helpful techniques for tackling the big data challenge." M. Emre Celebi, Ph.D., Professor and Chair, Department of Computer Science, University of Central Arkansas "In science the difficulty is not to have ideas, but it is to make them work" From Carlo Rovelli
Author : Marianna Bolla
Publisher : John Wiley & Sons
ISBN 13 : 1118650719
Total Pages : 229 pages
Book Rating : 4.1/5 (186 download)
Download or read book Spectral Clustering and Biclustering written by Marianna Bolla and published by John Wiley & Sons. This book was released on 2013-06-27 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores regular structures in graphs and contingency tables by spectral theory and statistical methods This book bridges the gap between graph theory and statistics by giving answers to the demanding questions which arise when statisticians are confronted with large weighted graphs or rectangular arrays. Classical and modern statistical methods applicable to biological, social, communication networks, or microarrays are presented together with the theoretical background and proofs. This book is suitable for a one-semester course for graduate students in data mining, multivariate statistics, or applied graph theory; but by skipping the proofs, the algorithms can also be used by specialists who just want to retrieve information from their data when analysing communication, social, or biological networks. Spectral Clustering and Biclustering: Provides a unified treatment for edge-weighted graphs and contingency tables via methods of multivariate statistical analysis (factoring, clustering, and biclustering). Uses spectral embedding and relaxation to estimate multiway cuts of edge-weighted graphs and bicuts of contingency tables. Goes beyond the expanders by describing the structure of dense graphs with a small spectral gap via the structural eigenvalues and eigen-subspaces of the normalized modularity matrix. Treats graphs like statistical data by combining methods of graph theory and statistics. Establishes a common outline structure for the contents of each algorithm, applicable to networks and microarrays, with unified notions and principles.
Author : Wei Zhang
Publisher : Springer Science & Business Media
ISBN 13 : 3642294553
Total Pages : 848 pages
Book Rating : 4.6/5 (422 download)
Download or read book Software Engineering and Knowledge Engineering: Theory and Practice written by Wei Zhang and published by Springer Science & Business Media. This book was released on 2012-06-30 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2012 International Conference on Software Engineering, Knowledge Engineering and Information Engineering (SEKEIE 2012) will be held in Macau, April 1-2, 2012 . This conference will bring researchers and experts from the three areas of Software Engineering, Knowledge Engineering and Information Engineering together to share their latest research results and ideas. This volume book covered significant recent developments in the Software Engineering, Knowledge Engineering and Information Engineering field, both theoretical and applied. We are glad this conference attracts your attentions, and thank your support to our conference. We will absorb remarkable suggestion, and make our conference more successful and perfect.
Author : William L. William L. Hamilton
Publisher : Springer Nature
ISBN 13 : 3031015886
Total Pages : 141 pages
Book Rating : 4.0/5 (31 download)
Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
Author : P.-A. Absil
Publisher : Princeton University Press
ISBN 13 : 1400830249
Total Pages : 240 pages
Book Rating : 4.4/5 (8 download)
Download or read book Optimization Algorithms on Matrix Manifolds written by P.-A. Absil and published by Princeton University Press. This book was released on 2009-04-11 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
Author : Krishnaiyan "KT" Thulasiraman
Publisher : CRC Press
ISBN 13 : 1420011073
Total Pages : 1217 pages
Book Rating : 4.4/5 (2 download)
Download or read book Handbook of Graph Theory, Combinatorial Optimization, and Algorithms written by Krishnaiyan "KT" Thulasiraman and published by CRC Press. This book was released on 2016-01-05 with total page 1217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and c
Author : Andries E. Brouwer
Publisher : Springer Science & Business Media
ISBN 13 : 1461419395
Total Pages : 254 pages
Book Rating : 4.4/5 (614 download)
Download or read book Spectra of Graphs written by Andries E. Brouwer and published by Springer Science & Business Media. This book was released on 2011-12-17 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.
Author : Charles-Edmond Bichot
Publisher : John Wiley & Sons
ISBN 13 : 1118601254
Total Pages : 301 pages
Book Rating : 4.1/5 (186 download)
Download or read book Graph Partitioning written by Charles-Edmond Bichot and published by John Wiley & Sons. This book was released on 2013-01-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph partitioning is a theoretical subject with applications in many areas, principally: numerical analysis, programs mapping onto parallel architectures, image segmentation, VLSI design. During the last 40 years, the literature has strongly increased and big improvements have been made. This book brings together the knowledge accumulated during many years to extract both theoretical foundations of graph partitioning and its main applications.
Author : Guojun Gan
Publisher : SIAM
ISBN 13 : 1611976332
Total Pages : 430 pages
Book Rating : 4.6/5 (119 download)
Download or read book Data Clustering: Theory, Algorithms, and Applications, Second Edition written by Guojun Gan and published by SIAM. This book was released on 2020-11-10 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data clustering, also known as cluster analysis, is an unsupervised process that divides a set of objects into homogeneous groups. Since the publication of the first edition of this monograph in 2007, development in the area has exploded, especially in clustering algorithms for big data and open-source software for cluster analysis. This second edition reflects these new developments, covers the basics of data clustering, includes a list of popular clustering algorithms, and provides program code that helps users implement clustering algorithms. Data Clustering: Theory, Algorithms and Applications, Second Edition will be of interest to researchers, practitioners, and data scientists as well as undergraduate and graduate students.
