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Regularization and Interpolation of Positive Matrices

Yamamoto, Kaoru LU ; Chen, Yongxin; Ning, Lipeng; Georgiou, Tryphon T. and Tannenbaum, Allen (2017) In IEEE Transactions on Automatic Control
Abstract

We construct certain matricial analogues of mass transport for positive definite matrices of equal trace. The framework aims to devise ways of interpolating positive definite matrices that tradeoff between "aligning up their eigenstructure" and "scaling the corresponding eigenvalues". Motivation for the work is provided by power spectral analysis of multivariate time series where linear interpolation between matrix-valued power spectra generates push-pop unrealistic and undesirable artifacts.

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author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Eigenvalues and eigenfunctions, Electronic mail, Interpolation, Mathematical model, Quantum mechanics, Spectrogram, Time series analysis
in
IEEE Transactions on Automatic Control
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85029155066
ISSN
0018-9286
DOI
10.1109/TAC.2017.2749258
language
English
LU publication?
yes
id
760aaeaa-62a1-4995-b313-241e1234d1a5
date added to LUP
2017-10-02 12:34:53
date last changed
2018-01-07 12:20:06
@article{760aaeaa-62a1-4995-b313-241e1234d1a5,
  abstract     = {<p>We construct certain matricial analogues of mass transport for positive definite matrices of equal trace. The framework aims to devise ways of interpolating positive definite matrices that tradeoff between "aligning up their eigenstructure" and "scaling the corresponding eigenvalues". Motivation for the work is provided by power spectral analysis of multivariate time series where linear interpolation between matrix-valued power spectra generates push-pop unrealistic and undesirable artifacts.</p>},
  author       = {Yamamoto, Kaoru and Chen, Yongxin and Ning, Lipeng and Georgiou, Tryphon T. and Tannenbaum, Allen},
  issn         = {0018-9286},
  keyword      = {Eigenvalues and eigenfunctions,Electronic mail,Interpolation,Mathematical model,Quantum mechanics,Spectrogram,Time series analysis},
  language     = {eng},
  month        = {09},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Automatic Control},
  title        = {Regularization and Interpolation of Positive Matrices},
  url          = {http://dx.doi.org/10.1109/TAC.2017.2749258},
  year         = {2017},
}