Harmonic analysis of databases and matrices

Ronald R. Coifman*, Matan Gavish

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations


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.

Original languageAmerican English
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Number of pages14
StatePublished - 2013
Externally publishedYes

Publication series

NameApplied and Numerical Harmonic Analysis
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media New York 2013.


  • Bi-Holder
  • Databases
  • Diffusion geometry
  • Machine learning
  • Partition trees
  • Tensor Haar
  • Tensor harmonic Analysis


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