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Frame Theory in Data Science

  • Book
  • © 2024

Overview

Authors:
  1. Zhihua Zhang

    1. Shandong University, Jinan, China

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    You can also search for this author in PubMed   Google Scholar

  2. Palle E. T. Jorgensen

    1. Department of Mathematics, The University of Iowa, Iowa City, USA

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    You can also search for this author in PubMed   Google Scholar

  • The internationally first book on systematic frame theory and algorithms
  • Novel applications of frame theory in big data, deep learning and climate diagnosis & prediction
  • Includes the authors' frame research in the past twenty years

Part of the book series: Advances in Science, Technology & Innovation (ASTI)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Abstract Frames

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 1-22

  3. Harmonic Frames

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 23-38

  4. Polynomial Frames

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 39-54

  5. Analytic Extension of Frames

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 55-63

  6. Quasi-Orthogonal Frames

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 65-102

  7. Affine Frames

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 103-136

  8. Spectral Domain of Frames

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 137-166

  9. Periodic Frames

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 167-190

  10. Frame Spectral Energy Distribution

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 191-208

  11. Sparse Frame-Polynomial Coupling Representation

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 209-221

  12. Object-Oriented Frame Analysis

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 223-240

  13. Frame Networks

    • Zhihua Zhang, Palle E. T. Jorgensen
    Pages 241-252

  14. Back Matter

    Pages 253-255
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Keywords

About this book

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. 

Authors and Affiliations

  • Shandong University, Jinan, China

    Zhihua Zhang

  • Department of Mathematics, The University of Iowa, Iowa City, USA

    Palle E. T. Jorgensen

About the authors

Zhihua Zhang is a Taishan Distinguished Professor at Shandong University, China and is leading an interdisciplinary big data mining research group. His long-standing researches focus on big data, climate change mechanisms, environmental evolution and sustainability. He has published 8 books (2 with Elsevier, 5 with Springer, and 1 with DeGruyter) and more than 70 articles. He is a chief editor, associate editor, or editorial board member of many global known journals on applied mathematics, climate and environmental science, as well as the first-track chair and plenary speaker of Mediterranean Geosciences Union Annual Meeting.


Palle E.T. Jorgensen is a Professor at the University of Iowa. His prior academic/teaching positions include the University of Pennsylvania, Stanford University, and Aarhus University (Denmark.) He has authored more than 300 highly cited research papers, and more than 10 books. He has received numerous honors and awards, including in 2018 Jorgensen being the NSF/CBMS speaker, giving 10 lectures; titled Harmonic Analysis: Smooth and Non-smooth, published as vol. 128, in the AMS/CBMS book series. He is a frequent invited speaker, giving colloquium and conference presentations at universities in the US, and around the World. 




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