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Sketching As A Tool For Numerical Linear Algebra
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Book Synopsis Sketching as a Tool for Numerical Linear Algebra by : David P. Woodruff
Download or read book Sketching as a Tool for Numerical Linear Algebra written by David P. Woodruff and published by Now Publishers. This book was released on 2014-11-14 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sketching as a Tool for Numerical Linear Algebra highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compressed it to a much smaller matrix by multiplying it by a (usually) random matrix with certain properties. Much of the expensive computation can then be performed on the smaller matrix, thereby accelerating the solution for the original problem. It is an ideal primer for researchers and students of theoretical computer science interested in how sketching techniques can be used to speed up numerical linear algebra applications.
Book Synopsis Computer Science – Theory and Applications by : René van Bevern
Download or read book Computer Science – Theory and Applications written by René van Bevern and published by Springer. This book was released on 2019-06-24 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 14th International Computer Science Symposium in Russia, CSR 2019, held in Novosibirsk, Russia, in July 2019. The 31 full papers were carefully reviewed and selected from 71 submissions. The papers cover a wide range of topics such as algorithms and data structures; computational complexity; randomness in computing; approximation algorithms; combinatorial optimization; constraint satisfaction; computational geometry; formal languages and automata; codes and cryptography; combinatorics in computer science; applications of logic to computer science; proof complexity; fundamentals of machine learning; and theoretical aspects of big data.
Book Synopsis The Mathematics of Data by : Michael W. Mahoney
Download or read book The Mathematics of Data written by Michael W. Mahoney and published by American Mathematical Soc.. This book was released on 2018-11-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nothing provided
Book Synopsis Theory and Computation of Complex Tensors and its Applications by : Maolin Che
Download or read book Theory and Computation of Complex Tensors and its Applications written by Maolin Che and published by Springer Nature. This book was released on 2020-04-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective. A systematic description about how to extend the numerical linear algebra to the numerical multi-linear algebra is also delivered in this book. The authors design the neural network model for the computation of the rank-one approximation of real tensors, a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors and a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors, adaptive randomized algorithms for computing the approximate tensor decompositions, and the QR type method for computing U-eigenpairs of complex tensors. This book could be used for the Graduate course, such as Introduction to Tensor. Researchers may also find it helpful as a reference in tensor research.
Book Synopsis Handbook of Big Data by : Peter Bühlmann
Download or read book Handbook of Big Data written by Peter Bühlmann and published by CRC Press. This book was released on 2016-02-22 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Big Data provides a state-of-the-art overview of the analysis of large-scale datasets. Featuring contributions from well-known experts in statistics and computer science, this handbook presents a carefully curated collection of techniques from both industry and academia. Thus, the text instills a working understanding of key statistical
Book Synopsis Topics in Randomized Numerical Linear Algebra by : Alex A. Gittens
Download or read book Topics in Randomized Numerical Linear Algebra written by Alex A. Gittens and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis studies three classes of randomized numerical linear algebra algorithms, namely: (i) randomized matrix sparsification algorithms, (ii) low-rank approximation algorithms that use randomized unitary transformations, and (iii) low-rank approximation algorithms for positive-semidefinite (PSD) matrices. Randomized matrix sparsification algorithms set randomly chosen entries of the input matrix to zero. When the approximant is substituted for the original matrix in computations, its sparsity allows one to employ faster sparsity-exploiting algorithms. This thesis contributes bounds on the approximation error of nonuniform randomized sparsification schemes, measured in the spectral norm and two NP-hard norms that are of interest in computational graph theory and subset selection applications. Low-rank approximations based on randomized unitary transformations have several desirable properties: they have low communication costs, are amenable to parallel implementation, and exploit the existence of fast transform algorithms. This thesis investigates the tradeoff between the accuracy and cost of generating such approximations. State-of-the-art spectral and Frobenius-norm error bounds are provided. The last class of algorithms considered are SPSD "sketching" algorithms. Such sketches can be computed faster than approximations based on projecting onto mixtures of the columns of the matrix. The performance of several such sketching schemes is empirically evaluated using a suite of canonical matrices drawn from machine learning and data analysis applications, and a framework is developed for establishing theoretical error bounds. In addition to studying these algorithms, this thesis extends the Matrix Laplace Transform framework to derive Chernoff and Bernstein inequalities that apply to all the eigenvalues of certain classes of random matrices. These inequalities are used to investigate the behavior of the singular values of a matrix under random sampling, and to derive convergence rates for each individual eigenvalue of a sample covariance matrix.
Book Synopsis Information-Theoretic Methods in Data Science by : Miguel R. D. Rodrigues
Download or read book Information-Theoretic Methods in Data Science written by Miguel R. D. Rodrigues and published by Cambridge University Press. This book was released on 2021-04-08 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified treatment of the interface between information theory and emerging topics in data science, written in a clear, tutorial style. Covering topics such as data acquisition, representation, analysis, and communication, it is ideal for graduate students and researchers in information theory, signal processing, and machine learning.
Book Synopsis Fast Direct Solvers for Elliptic PDEs by : Per-Gunnar Martinsson
Download or read book Fast Direct Solvers for Elliptic PDEs written by Per-Gunnar Martinsson and published by SIAM. This book was released on 2019-12-16 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.
Book Synopsis Foundations of Vector Retrieval by : Sebastian Bruch
Download or read book Foundations of Vector Retrieval written by Sebastian Bruch and published by Springer Nature. This book was released on 2024 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computing and Combinatorics by : Donghyun Kim
Download or read book Computing and Combinatorics written by Donghyun Kim and published by Springer Nature. This book was released on 2020-08-27 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 26th International Conference on Computing and Combinatorics, COCOON 2020, held in Atlanta, GA, USA, in August 2020. Due to the COVID-19 pandemic COCOON 2020 was organized as a fully online conference. The 54 papers presented in this volume were carefully reviewed and selected from 126 submissions. The papers cover various topics, including algorithm design, approximation algorithm, graph theory, complexity theory, problem solving, optimization, computational biology, computational learning, communication network, logic, and game theory.
Book Synopsis Tensor Computation for Data Analysis by : Yipeng Liu
Download or read book Tensor Computation for Data Analysis written by Yipeng Liu and published by Springer Nature. This book was released on 2021-08-31 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor is a natural representation for multi-dimensional data, and tensor computation can avoid possible multi-linear data structure loss in classical matrix computation-based data analysis. This book is intended to provide non-specialists an overall understanding of tensor computation and its applications in data analysis, and benefits researchers, engineers, and students with theoretical, computational, technical and experimental details. It presents a systematic and up-to-date overview of tensor decompositions from the engineer's point of view, and comprehensive coverage of tensor computation based data analysis techniques. In addition, some practical examples in machine learning, signal processing, data mining, computer vision, remote sensing, and biomedical engineering are also presented for easy understanding and implementation. These data analysis techniques may be further applied in other applications on neuroscience, communication, psychometrics, chemometrics, biometrics, quantum physics, quantum chemistry, etc. The discussion begins with basic coverage of notations, preliminary operations in tensor computations, main tensor decompositions and their properties. Based on them, a series of tensor-based data analysis techniques are presented as the tensor extensions of their classical matrix counterparts, including tensor dictionary learning, low rank tensor recovery, tensor completion, coupled tensor analysis, robust principal tensor component analysis, tensor regression, logistical tensor regression, support tensor machine, multilinear discriminate analysis, tensor subspace clustering, tensor-based deep learning, tensor graphical model and tensor sketch. The discussion also includes a number of typical applications with experimental results, such as image reconstruction, image enhancement, data fusion, signal recovery, recommendation system, knowledge graph acquisition, traffic flow prediction, link prediction, environmental prediction, weather forecasting, background extraction, human pose estimation, cognitive state classification from fMRI, infrared small target detection, heterogeneous information networks clustering, multi-view image clustering, and deep neural network compression.
Book Synopsis Sampling Techniques for Supervised or Unsupervised Tasks by : Frédéric Ros
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 232 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
Book Synopsis Inference and Learning from Data: Volume 3 by : Ali H. Sayed
Download or read book Inference and Learning from Data: Volume 3 written by Ali H. Sayed and published by Cambridge University Press. This book was released on 2022-12-22 with total page 1082 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extraordinary three-volume work, written in an engaging and rigorous style by a world authority in the field, provides an accessible, comprehensive introduction to the full spectrum of mathematical and statistical techniques underpinning contemporary methods in data-driven learning and inference. This final volume, Learning, builds on the foundational topics established in volume I to provide a thorough introduction to learning methods, addressing techniques such as least-squares methods, regularization, online learning, kernel methods, feedforward and recurrent neural networks, meta-learning, and adversarial attacks. A consistent structure and pedagogy is employed throughout this volume to reinforce student understanding, with over 350 end-of-chapter problems (including complete solutions for instructors), 280 figures, 100 solved examples, datasets and downloadable Matlab code. Supported by sister volumes Foundations and Inference, and unique in its scale and depth, this textbook sequence is ideal for early-career researchers and graduate students across many courses in signal processing, machine learning, data and inference.
Book Synopsis High-Dimensional Statistics by : Martin J. Wainwright
Download or read book High-Dimensional Statistics written by Martin J. Wainwright and published by Cambridge University Press. This book was released on 2019-02-21 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.
Book Synopsis Structural Information and Communication Complexity by : Sergio Rajsbaum
Download or read book Structural Information and Communication Complexity written by Sergio Rajsbaum and published by Springer Nature. This book was released on 2023-05-24 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 30th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2023, held in Alcalá de Henares, Spain, during June 6–9, 2023. The 26 full papers presented in this book were carefully reviewed and selected from 48 submissions. SIROCCO is devoted to the study of the interplay between structural knowledge, communication, and computing in decentralized systems of multiple communicating entities. Special emphasis is given to innovative approaches leading to better understanding of the relationship between computing and communication. This is the 30th edition of SIROCCO, and 3 of the 26 papers in this book are devoted to celebrating this fact, plus an additional paper about a recent trend to study special models of computation.
Book Synopsis Introduction to Property Testing by : Oded Goldreich
Download or read book Introduction to Property Testing written by Oded Goldreich and published by Cambridge University Press. This book was released on 2017-11-23 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Property testing is concerned with the design of super-fast algorithms for the structural analysis of large quantities of data. The aim is to unveil global features of the data, such as determining whether the data has a particular property or estimating global parameters. Remarkably, it is possible for decisions to be made by accessing only a small portion of the data. Property testing focuses on properties and parameters that go beyond simple statistics. This book provides an extensive and authoritative introduction to property testing. It provides a wide range of algorithmic techniques for the design and analysis of tests for algebraic properties, properties of Boolean functions, graph properties, and properties of distributions.
Book Synopsis Adversarial and Uncertain Reasoning for Adaptive Cyber Defense by : Sushil Jajodia
Download or read book Adversarial and Uncertain Reasoning for Adaptive Cyber Defense written by Sushil Jajodia and published by Springer Nature. This book was released on 2019-08-30 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today’s cyber defenses are largely static allowing adversaries to pre-plan their attacks. In response to this situation, researchers have started to investigate various methods that make networked information systems less homogeneous and less predictable by engineering systems that have homogeneous functionalities but randomized manifestations. The 10 papers included in this State-of-the Art Survey present recent advances made by a large team of researchers working on the same US Department of Defense Multidisciplinary University Research Initiative (MURI) project during 2013-2019. This project has developed a new class of technologies called Adaptive Cyber Defense (ACD) by building on two active but heretofore separate research areas: Adaptation Techniques (AT) and Adversarial Reasoning (AR). AT methods introduce diversity and uncertainty into networks, applications, and hosts. AR combines machine learning, behavioral science, operations research, control theory, and game theory to address the goal of computing effective strategies in dynamic, adversarial environments.
