A Bootstrap Approach to Eigenvalue Correction

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

10 Citations (Scopus)
61 Downloads (Pure)

Abstract

Eigenvalue analysis is an important aspect in many data modeling methods. Unfortunately, the eigenvalues of the sample covariance matrix (sample eigenvalues) are biased estimates of the eigenvalues of the covariance matrix of the data generating process (population eigenvalues). We present a new method based on bootstrapping to reduce the bias in the sample eigenvalues: the eigenvalue estimates are updated in several iterations, where in each iteration synthetic data is generated to determine how to update the population eigenvalue estimates. Comparison of the bootstrap eigenvalue correction with a state of the art correction method by Karoui shows that depending on the type of population eigenvalue distribution, sometimes the Karoui method performs better and sometimes our bootstrap method.
Original languageUndefined
Title of host publicationNinth IEEE International Conference on Data Mining, 2009. ICDM '09.
Place of PublicationPiscataway
PublisherIEEE Computer Society
Pages818-823
Number of pages6
ISBN (Print)978-1-4244-5242-2
DOIs
Publication statusPublished - 6 Dec 2009
Event9th IEEE International Conference on Data Mining, ICDM 2009 - Miami Beach, United States
Duration: 6 Dec 20099 Dec 2009
Conference number: 9

Publication series

Name
PublisherIEEE Computer Society Press

Workshop

Workshop9th IEEE International Conference on Data Mining, ICDM 2009
Abbreviated titleICDM
CountryUnited States
CityMiami Beach
Period6/12/099/12/09

Keywords

  • METIS-265783
  • Bootstrapping
  • IR-69834
  • SCS-Safety
  • isotonic tree method
  • Eigenvalue correction
  • General Statistical Analysis
  • EWI-17390

Cite this

Hendrikse, A. J., Spreeuwers, L. J., & Veldhuis, R. N. J. (2009). A Bootstrap Approach to Eigenvalue Correction. In Ninth IEEE International Conference on Data Mining, 2009. ICDM '09. (pp. 818-823). [10.1109/ICDM.2009.111] Piscataway: IEEE Computer Society. https://doi.org/10.1109/ICDM.2009.111
Hendrikse, A.J. ; Spreeuwers, Lieuwe Jan ; Veldhuis, Raymond N.J. / A Bootstrap Approach to Eigenvalue Correction. Ninth IEEE International Conference on Data Mining, 2009. ICDM '09.. Piscataway : IEEE Computer Society, 2009. pp. 818-823
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abstract = "Eigenvalue analysis is an important aspect in many data modeling methods. Unfortunately, the eigenvalues of the sample covariance matrix (sample eigenvalues) are biased estimates of the eigenvalues of the covariance matrix of the data generating process (population eigenvalues). We present a new method based on bootstrapping to reduce the bias in the sample eigenvalues: the eigenvalue estimates are updated in several iterations, where in each iteration synthetic data is generated to determine how to update the population eigenvalue estimates. Comparison of the bootstrap eigenvalue correction with a state of the art correction method by Karoui shows that depending on the type of population eigenvalue distribution, sometimes the Karoui method performs better and sometimes our bootstrap method.",
keywords = "METIS-265783, Bootstrapping, IR-69834, SCS-Safety, isotonic tree method, Eigenvalue correction, General Statistical Analysis, EWI-17390",
author = "A.J. Hendrikse and Spreeuwers, {Lieuwe Jan} and Veldhuis, {Raymond N.J.}",
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booktitle = "Ninth IEEE International Conference on Data Mining, 2009. ICDM '09.",
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}

Hendrikse, AJ, Spreeuwers, LJ & Veldhuis, RNJ 2009, A Bootstrap Approach to Eigenvalue Correction. in Ninth IEEE International Conference on Data Mining, 2009. ICDM '09.., 10.1109/ICDM.2009.111, IEEE Computer Society, Piscataway, pp. 818-823, 9th IEEE International Conference on Data Mining, ICDM 2009, Miami Beach, United States, 6/12/09. https://doi.org/10.1109/ICDM.2009.111

A Bootstrap Approach to Eigenvalue Correction. / Hendrikse, A.J.; Spreeuwers, Lieuwe Jan; Veldhuis, Raymond N.J.

Ninth IEEE International Conference on Data Mining, 2009. ICDM '09.. Piscataway : IEEE Computer Society, 2009. p. 818-823 10.1109/ICDM.2009.111.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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T1 - A Bootstrap Approach to Eigenvalue Correction

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AB - Eigenvalue analysis is an important aspect in many data modeling methods. Unfortunately, the eigenvalues of the sample covariance matrix (sample eigenvalues) are biased estimates of the eigenvalues of the covariance matrix of the data generating process (population eigenvalues). We present a new method based on bootstrapping to reduce the bias in the sample eigenvalues: the eigenvalue estimates are updated in several iterations, where in each iteration synthetic data is generated to determine how to update the population eigenvalue estimates. Comparison of the bootstrap eigenvalue correction with a state of the art correction method by Karoui shows that depending on the type of population eigenvalue distribution, sometimes the Karoui method performs better and sometimes our bootstrap method.

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Hendrikse AJ, Spreeuwers LJ, Veldhuis RNJ. A Bootstrap Approach to Eigenvalue Correction. In Ninth IEEE International Conference on Data Mining, 2009. ICDM '09.. Piscataway: IEEE Computer Society. 2009. p. 818-823. 10.1109/ICDM.2009.111 https://doi.org/10.1109/ICDM.2009.111