Regularization and Interpolation of Positive Matrices

Kaoru Yamamoto; Yongxin Chen; Lipeng Ning; Tryphon T. Georgiou; Allen Tannenbaum

doi:10.1109/TAC.2017.2749258

Regularization and Interpolation of Positive Matrices

Kaoru Yamamoto, Yongxin Chen, Lipeng Ning, Tryphon T. Georgiou, Allen Tannenbaum

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1208-1212
Number of pages	5
Journal	IEEE Transactions on Automatic Control
Volume	63
Issue number	4
DOIs	https://doi.org/10.1109/TAC.2017.2749258
Publication status	Published - Apr 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2017.2749258

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title = "Regularization and Interpolation of Positive Matrices",

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.",

author = "Kaoru Yamamoto and Yongxin Chen and Lipeng Ning and Georgiou, {Tryphon T.} and Allen Tannenbaum",

note = "Funding Information: Manuscript received June 25, 2017; accepted August 10, 2017. Date of publication September 5, 2017; date of current version March 27, 2018. This work was supported in part by the Air Force Office of Scientific Research under Grant FA9550-15-1-0045 and Grant FA9550-17-1-0435, in part by the National Science Foundation under Grant ECCS-1509387, in part by the National Institutes of Health under Grant P41-RR-013218 and Grant P41-EB-015902, and in part by a fellowship through Memorial Sloan Kettering Cancer Center. Recommended by Associate Editor Uday V. Shanbhag. (Corresponding author: Tryphon T. Georgiou.) K. Yamamoto is with the Department of Automatic Control, Lund University, Lund 221 00, Sweden (e-mail: k.yamamoto@ieee.org). Publisher Copyright: {\textcopyright} 2012 IEEE.",

year = "2018",

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doi = "10.1109/TAC.2017.2749258",

language = "English",

volume = "63",

pages = "1208--1212",

journal = "IEEE Transactions on Automatic Control",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

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T1 - Regularization and Interpolation of Positive Matrices

AU - Yamamoto, Kaoru

AU - Chen, Yongxin

AU - Ning, Lipeng

AU - Georgiou, Tryphon T.

AU - Tannenbaum, Allen

N1 - Funding Information: Manuscript received June 25, 2017; accepted August 10, 2017. Date of publication September 5, 2017; date of current version March 27, 2018. This work was supported in part by the Air Force Office of Scientific Research under Grant FA9550-15-1-0045 and Grant FA9550-17-1-0435, in part by the National Science Foundation under Grant ECCS-1509387, in part by the National Institutes of Health under Grant P41-RR-013218 and Grant P41-EB-015902, and in part by a fellowship through Memorial Sloan Kettering Cancer Center. Recommended by Associate Editor Uday V. Shanbhag. (Corresponding author: Tryphon T. Georgiou.) K. Yamamoto is with the Department of Automatic Control, Lund University, Lund 221 00, Sweden (e-mail: k.yamamoto@ieee.org). Publisher Copyright: © 2012 IEEE.

PY - 2018/4

Y1 - 2018/4

N2 - 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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JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 4

ER -

Regularization and Interpolation of Positive Matrices

Abstract

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