Harmonic analysis of databases and matrices

Ronald R. Coifman; Matan Gavish

doi:10.1007/978-0-8176-8376-4_15

Harmonic analysis of databases and matrices

Ronald R. Coifman^*, Matan Gavish

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

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.

Original language	English
Title of host publication	Applied and Numerical Harmonic Analysis
Publisher	Springer International Publishing
Pages	297-310
Number of pages	14
Edition	9780817683757
DOIs	https://doi.org/10.1007/978-0-8176-8376-4_15
State	Published - 2013
Externally published	Yes

Publication series

Name	Applied and Numerical Harmonic Analysis
Number	9780817683757
Volume	0
ISSN (Print)	2296-5009
ISSN (Electronic)	2296-5017

Bibliographical note

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

Keywords

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

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10.1007/978-0-8176-8376-4_15

Cite this

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Harmonic analysis of databases and matrices

Abstract

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Bibliographical note

Keywords

Access to Document

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