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Interactions Between Kernels, Frames, and Persistent Homology

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Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

This contribution discusses interactions between kernel methods, frame analysis, and persistent homology. To this end, we explain recent connections between these research areas, where special emphasis is placed on the discussion of reproducing kernel Hilbert spaces and persistent mechanisms. We show how interactions between these novel methodologies give new opportunities for the construction of numerical algorithms to analyze properties of data that are so far unexplored.

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Author information

Authors and Affiliations

  1. Technische Universität Hamburg, Hamburg, Germany

    Mijail Guillemard

  2. Universität Hamburg, Hamburg, Germany

    Armin Iske

Authors
  1. Mijail Guillemard
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  2. Armin Iske
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Corresponding author

Correspondence to Mijail Guillemard .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Temple University, Philadelphia, Pennsylvania, USA

    Isaac Pesenson

  2. School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia

    Quoc Thong Le Gia

  3. Department of Mathematics, The Graduate Center, CUNY, New York, New York, USA

    Azita Mayeli

  4. Institute of Mathematical Sciences, Claremont Graduate University, Claremont, California, USA

    Hrushikesh Mhaskar

  5. Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong

    Ding-Xuan Zhou

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Guillemard, M., Iske, A. (2017). Interactions Between Kernels, Frames, and Persistent Homology. In: Pesenson, I., Le Gia, Q., Mayeli, A., Mhaskar, H., Zhou, DX. (eds) Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55556-0_14

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