Interactions between kernels, frames, and persistent homology. (English) Zbl 1404.42056
Pesenson, Isaac (ed.) et al., Recent applications of harmonic analysis to function spaces, differential equations, and data science. Novel methods in harmonic analysis. Volume 2. Cham: Birkhäuser/Springer (ISBN 978-3-319-55555-3/hbk; 978-3-319-55556-0/ebook; 978-3-319-55860-8/set). Applied and Numerical Harmonic Analysis, 861-888 (2017).
Summary: 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.
For the entire collection see [Zbl 1378.42001].
For the entire collection see [Zbl 1378.42001].
MSC:
| 42C15 | General harmonic expansions, frames |
| 55N35 | Other homology theories in algebraic topology |
| 41A30 | Approximation by other special function classes |
| 94A20 | Sampling theory in information and communication theory |
| 13P25 | Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) |
Software:
PersistenceImagesReferences:
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