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Frame Theory In Data Science

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Frame Theory In Data Science

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Author : Zhihua Zhang
language : en
Publisher: Springer Nature
Release Date : 2024-04-10

Frame Theory In Data Science written by Zhihua Zhang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-10 with Computers categories.

This book establishes brand-new frame theory and technical implementation in data science, with a special focus on spatial-scale feature extraction, network dynamics, object-oriented analysis, data-driven environmental prediction, and climate diagnosis. Given that data science is unanimously recognized as a core driver for achieving Sustainable Development Goals of the United Nations, these frame techniques bring fundamental changes to multi-channel data mining systems and support the development of digital Earth platforms. This book integrates the authors' frame research in the past twenty years and provides cutting-edge techniques and depth for scientists, professionals, and graduate students in data science, applied mathematics, environmental science, and geoscience.

Finite Frames

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Author : Peter G. Casazza
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-14

Finite Frames written by Peter G. Casazza and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.

Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.

Frame Theory In Data Science

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Author : Zhihua Zhang
language : en
Publisher: Springer
Release Date : 2024-03-03

Frame Theory In Data Science written by Zhihua Zhang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-03 with Computers categories.

Library Of Congress Subject Headings

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Author : Library of Congress
language : en
Publisher:
Release Date : 2001

Library Of Congress Subject Headings written by Library of Congress and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Subject headings, Library of Congress categories.

New Trends In Applied Harmonic Analysis

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Author : Akram Aldroubi
language : en
Publisher: Birkhäuser
Release Date : 2016-04-21

New Trends In Applied Harmonic Analysis written by Akram Aldroubi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-21 with Mathematics categories.

This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.

Morrey Spaces

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Author : David Adams
language : en
Publisher: Birkhäuser
Release Date : 2015-12-31

Morrey Spaces written by David Adams and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-31 with Mathematics categories.

In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any “full” interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory.

Generalized Multiresolution Analyses

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Author : Kathy D. Merrill
language : en
Publisher: Springer
Release Date : 2018-10-11

Generalized Multiresolution Analyses written by Kathy D. Merrill and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-11 with Mathematics categories.

This monograph presents the first unified exposition of generalized multiresolution analyses. Expanding on the author’s pioneering work in the field, these lecture notes provide the tools and framework for using GMRAs to extend results from classical wavelet analysis to a more general setting. Beginning with the basic properties of GMRAs, the book goes on to explore the multiplicity and dimension functions of GMRA, wavelet sets, and generalized filters. The author’s constructions of wavelet sets feature prominently, with figures to illustrate their remarkably simple geometric form. The last three chapters exhibit extensions of wavelet theory and GMRAs to other settings. These include fractal spaces, wavelets with composite dilations, and abstract constructions of GMRAs beyond the usual setting of L2(Rn). This account of recent developments in wavelet theory will appeal to researchers and graduate students with an interest in multiscale analysis from a pure or applied perspective. Familiarity with harmonic analysis and operator theory will be helpful to the reader, though the only prerequisite is graduate level experience with real and functional analysis.

Machine Learning Optimization And Data Science

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Author : Giuseppe Nicosia
language : en
Publisher: Springer Nature
Release Date : 2023-03-09

Machine Learning Optimization And Data Science written by Giuseppe Nicosia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-09 with Computers categories.

This two-volume set, LNCS 13810 and 13811, constitutes the refereed proceedings of the 8th International Conference on Machine Learning, Optimization, and Data Science, LOD 2022, together with the papers of the Second Symposium on Artificial Intelligence and Neuroscience, ACAIN 2022. The total of 84 full papers presented in this two-volume post-conference proceedings set was carefully reviewed and selected from 226 submissions. These research articles were written by leading scientists in the fields of machine learning, artificial intelligence, reinforcement learning, computational optimization, neuroscience, and data science presenting a substantial array of ideas, technologies, algorithms, methods, and applications.

Counting Lattice Paths Using Fourier Methods

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Author : Shaun Ault
language : en
Publisher: Springer Nature
Release Date : 2019-08-30

Counting Lattice Paths Using Fourier Methods written by Shaun Ault and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-30 with Mathematics categories.

This monograph introduces a novel and effective approach to counting lattice paths by using the discrete Fourier transform (DFT) as a type of periodic generating function. Utilizing a previously unexplored connection between combinatorics and Fourier analysis, this method will allow readers to move to higher-dimensional lattice path problems with ease. The technique is carefully developed in the first three chapters using the algebraic properties of the DFT, moving from one-dimensional problems to higher dimensions. In the following chapter, the discussion turns to geometric properties of the DFT in order to study the corridor state space. Each chapter poses open-ended questions and exercises to prompt further practice and future research. Two appendices are also provided, which cover complex variables and non-rectangular lattices, thus ensuring the text will be self-contained and serve as a valued reference. Counting Lattice Paths Using Fourier Methods is ideal for upper-undergraduates and graduate students studying combinatorics or other areas of mathematics, as well as computer science or physics. Instructors will also find this a valuable resource for use in their seminars. Readers should have a firm understanding of calculus, including integration, sequences, and series, as well as a familiarity with proofs and elementary linear algebra.

Foundations Of Discrete Harmonic Analysis

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Author : Vasily N. Malozemov
language : en
Publisher: Springer Nature
Release Date : 2020-06-24

Foundations Of Discrete Harmonic Analysis written by Vasily N. Malozemov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-24 with Mathematics categories.

This book provides an introduction to discrete harmonic analysis (DHA) with a view towards applications to digital signal processing. In a nutshell, DHA is used to determine the time-frequency structure of a digitized signal, providing a representation of the signal as a sum of spectral components that can then be analyzed. The main methods of DHA are discrete Fourier transform and other discrete orthogonal transforms such as the Walsh and Haar transforms. Fast algorithms are used to process signals in real time, while additional options are provided by spline harmonic analysis. These topics are carefully covered in the book. With only modest prerequisites, some of which are recalled at the beginning, a profound mathematical theory is built almost from scratch. The 150 exercises included form an integral part of the text. Based decades of teaching experience, this book provides a basis for lecture courses starting at the upper undergraduate level, and will also prove a valuable resource for mathematicians and engineers interested in digital signal processing.

Frame Theory In Data Science

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