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Excursions in Harmonic Analysis, Volume 1 pp 297–310Cite as

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Harmonic Analysis of Databases and Matrices

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

Abstract

We describe methods to organize and process matrices/databases through a bi-multiscale tensor product harmonic Analysis on row and column functions. The goal is to reorganize the matrix so that its entries exhibit smoothness or predictability relative to the tensor row column geometry. In particular we show that approximate bi-Holder smoothness follows from simple l p entropy conditions. We describe various applications both for the analysis of matrices of linear transformations, as well for the extraction of information and structure in document databases.

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Acknowledgements

MG is supported by a William R. and Sara Hart Kimball Stanford Graduate Fellowship.

Author information

Authors and Affiliations

  1. Program in Applied Mathematics, Yale University, New Haven, UK

    Ronald R. Coifman

  2. Department of Statistics, Stanford University, Stanford, CA, 94305, USA

    Matan Gavish

Authors
  1. Ronald R. Coifman
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  2. Matan Gavish
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Corresponding author

Correspondence to Ronald R. Coifman .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Maryland, Norbert Wiener Center, College Park, 20742-0001, Maryland, USA

    Travis D. Andrews

  2. Norbert Wiener Center, Department of Mathematics, University of Maryland, College Park, 20742, Maryland, USA

    Radu Balan

  3. Department of Mathematics, University of Maryland, College Park, 20742-4015, Maryland, USA

    John J. Benedetto

  4. Department of Mathematics, University of Maryland, College Park, 20742-4015, Maryland, USA

    Wojciech Czaja

  5. , Department of Mathematics, University of Maryland, College Park, 20742, Maryland, USA

    Kasso A. Okoudjou

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Coifman, R.R., Gavish, M. (2013). Harmonic Analysis of Databases and Matrices. In: Andrews, T., Balan, R., Benedetto, J., Czaja, W., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 1. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8376-4_15

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