Smooth eigenvalue correction

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

Second-order statistics play an important role in data modeling. Nowadays, there is a tendency toward measuring more signals with higher resolution (e.g., high-resolution video), causing a rapid increase of dimensionality of the measured samples, while the number of samples remains more or less the same. As a result the eigenvalue estimates are significantly biased as described by the MarĿenko Pastur equation for the limit of both the number of samples and their dimensionality going to infinity. By introducing a smoothness factor, we show that the MarĿenko Pastur equation can be used in practical situations where both the number of samples and their dimensionality remain finite. Based on this result we derive methods, one already known and one new to our knowledge, to estimate the sample eigenvalues when the population eigenvalues are known. However, usually the sample eigenvalues are known and the population eigenvalues are required. We therefore applied one of the these methods in a feedback loop, resulting in an eigenvalue bias correction method. We compare this eigenvalue correction method with the state-of-the-art methods and show that our method outperforms other methods particularly in real-life situations often encountered in biometrics: underdetermined configurations, high-dimensional configurations, and configurations where the eigenvalues are exponentially distributed.
Original languageUndefined
Pages (from-to)1-16
Number of pages16
JournalEURASIP journal on advances in signal processing
Volume2013
Issue number117
DOIs
Publication statusPublished - 13 Jun 2013

Keywords

  • SCS-Safety
  • EWI-24408
  • IR-89203
  • eigenvalue estimation
  • METIS-302687
  • Eigenvalue correction

Cite this

@article{a8700023108349c897124f3bd35a0775,
title = "Smooth eigenvalue correction",
abstract = "Second-order statistics play an important role in data modeling. Nowadays, there is a tendency toward measuring more signals with higher resolution (e.g., high-resolution video), causing a rapid increase of dimensionality of the measured samples, while the number of samples remains more or less the same. As a result the eigenvalue estimates are significantly biased as described by the MarĿenko Pastur equation for the limit of both the number of samples and their dimensionality going to infinity. By introducing a smoothness factor, we show that the MarĿenko Pastur equation can be used in practical situations where both the number of samples and their dimensionality remain finite. Based on this result we derive methods, one already known and one new to our knowledge, to estimate the sample eigenvalues when the population eigenvalues are known. However, usually the sample eigenvalues are known and the population eigenvalues are required. We therefore applied one of the these methods in a feedback loop, resulting in an eigenvalue bias correction method. We compare this eigenvalue correction method with the state-of-the-art methods and show that our method outperforms other methods particularly in real-life situations often encountered in biometrics: underdetermined configurations, high-dimensional configurations, and configurations where the eigenvalues are exponentially distributed.",
keywords = "SCS-Safety, EWI-24408, IR-89203, eigenvalue estimation, METIS-302687, Eigenvalue correction",
author = "A.J. Hendrikse and Veldhuis, {Raymond N.J.} and Spreeuwers, {Lieuwe Jan}",
note = "eemcs-eprint-24408",
year = "2013",
month = "6",
day = "13",
doi = "10.1186/1687-6180-2013-117",
language = "Undefined",
volume = "2013",
pages = "1--16",
journal = "EURASIP journal on advances in signal processing",
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Smooth eigenvalue correction. / Hendrikse, A.J.; Veldhuis, Raymond N.J.; Spreeuwers, Lieuwe Jan.

In: EURASIP journal on advances in signal processing, Vol. 2013, No. 117, 13.06.2013, p. 1-16.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Smooth eigenvalue correction

AU - Hendrikse, A.J.

AU - Veldhuis, Raymond N.J.

AU - Spreeuwers, Lieuwe Jan

N1 - eemcs-eprint-24408

PY - 2013/6/13

Y1 - 2013/6/13

N2 - Second-order statistics play an important role in data modeling. Nowadays, there is a tendency toward measuring more signals with higher resolution (e.g., high-resolution video), causing a rapid increase of dimensionality of the measured samples, while the number of samples remains more or less the same. As a result the eigenvalue estimates are significantly biased as described by the MarĿenko Pastur equation for the limit of both the number of samples and their dimensionality going to infinity. By introducing a smoothness factor, we show that the MarĿenko Pastur equation can be used in practical situations where both the number of samples and their dimensionality remain finite. Based on this result we derive methods, one already known and one new to our knowledge, to estimate the sample eigenvalues when the population eigenvalues are known. However, usually the sample eigenvalues are known and the population eigenvalues are required. We therefore applied one of the these methods in a feedback loop, resulting in an eigenvalue bias correction method. We compare this eigenvalue correction method with the state-of-the-art methods and show that our method outperforms other methods particularly in real-life situations often encountered in biometrics: underdetermined configurations, high-dimensional configurations, and configurations where the eigenvalues are exponentially distributed.

AB - Second-order statistics play an important role in data modeling. Nowadays, there is a tendency toward measuring more signals with higher resolution (e.g., high-resolution video), causing a rapid increase of dimensionality of the measured samples, while the number of samples remains more or less the same. As a result the eigenvalue estimates are significantly biased as described by the MarĿenko Pastur equation for the limit of both the number of samples and their dimensionality going to infinity. By introducing a smoothness factor, we show that the MarĿenko Pastur equation can be used in practical situations where both the number of samples and their dimensionality remain finite. Based on this result we derive methods, one already known and one new to our knowledge, to estimate the sample eigenvalues when the population eigenvalues are known. However, usually the sample eigenvalues are known and the population eigenvalues are required. We therefore applied one of the these methods in a feedback loop, resulting in an eigenvalue bias correction method. We compare this eigenvalue correction method with the state-of-the-art methods and show that our method outperforms other methods particularly in real-life situations often encountered in biometrics: underdetermined configurations, high-dimensional configurations, and configurations where the eigenvalues are exponentially distributed.

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KW - IR-89203

KW - eigenvalue estimation

KW - METIS-302687

KW - Eigenvalue correction

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