A Bootstrap Approach to Eigenvalue Correction

A.J. Hendrikse; Lieuwe Jan Spreeuwers; Raymond N.J. Veldhuis

doi:10.1109/ICDM.2009.111

A Bootstrap Approach to Eigenvalue Correction

A.J. Hendrikse, Lieuwe Jan Spreeuwers, Raymond N.J. Veldhuis

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

14 Citations (Scopus)

345 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 language	Undefined
Title of host publication	Ninth IEEE International Conference on Data Mining, 2009. ICDM '09.
Place of Publication	Piscataway
Publisher	IEEE
Pages	818-823
Number of pages	6
ISBN (Print)	978-1-4244-5242-2
DOIs	https://doi.org/10.1109/ICDM.2009.111
Publication status	Published - 6 Dec 2009
Event	9th IEEE International Conference on Data Mining, ICDM 2009 - Miami Beach, United States Duration: 6 Dec 2009 → 9 Dec 2009 Conference number: 9

Publication series

Name
Publisher	IEEE Computer Society Press

Workshop

Workshop	9th IEEE International Conference on Data Mining, ICDM 2009
Abbreviated title	ICDM
Country/Territory	United States
City	Miami Beach
Period	6/12/09 → 9/12/09

Keywords

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

Access to Document

10.1109/ICDM.2009.111

Cite this

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title = "A Bootstrap Approach to Eigenvalue Correction",

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.}",

note = "10.1109/ICDM.2009.111 ; null ; Conference date: 06-12-2009 Through 09-12-2009",

year = "2009",

month = dec,

day = "6",

doi = "10.1109/ICDM.2009.111",

language = "Undefined",

isbn = "978-1-4244-5242-2",

publisher = "IEEE",

pages = "818--823",

booktitle = "Ninth IEEE International Conference on Data Mining, 2009. ICDM '09.",

}

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, Piscataway, pp. 818-823, 9th IEEE International Conference on Data Mining, ICDM 2009, Miami Beach, Florida, United States, 6/12/09. https://doi.org/10.1109/ICDM.2009.111

TY - GEN

T1 - A Bootstrap Approach to Eigenvalue Correction

AU - Hendrikse, A.J.

AU - Spreeuwers, Lieuwe Jan

AU - Veldhuis, Raymond N.J.

N1 - Conference code: 9

PY - 2009/12/6

Y1 - 2009/12/6

N2 - 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.

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.

KW - METIS-265783

KW - Bootstrapping

KW - IR-69834

KW - SCS-Safety

KW - isotonic tree method

KW - Eigenvalue correction

KW - General Statistical Analysis

KW - EWI-17390

U2 - 10.1109/ICDM.2009.111

DO - 10.1109/ICDM.2009.111

M3 - Conference contribution

SN - 978-1-4244-5242-2

SP - 818

EP - 823

BT - Ninth IEEE International Conference on Data Mining, 2009. ICDM '09.

PB - IEEE

CY - Piscataway

Y2 - 6 December 2009 through 9 December 2009

ER -