Abstract
| Original language | Undefined |
|---|---|
| Pages (from-to) | 1-16 |
| Number of pages | 16 |
| Journal | EURASIP journal on advances in signal processing |
| Volume | 2013 |
| Issue number | 117 |
| DOIs | |
| Publication status | Published - 13 Jun 2013 |
Keywords
- SCS-Safety
- EWI-24408
- IR-89203
- eigenvalue estimation
- METIS-302687
- Eigenvalue correction
Cite this
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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 journal › Article › Academic › peer-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.
KW - SCS-Safety
KW - EWI-24408
KW - IR-89203
KW - eigenvalue estimation
KW - METIS-302687
KW - Eigenvalue correction
U2 - 10.1186/1687-6180-2013-117
DO - 10.1186/1687-6180-2013-117
M3 - Article
VL - 2013
SP - 1
EP - 16
JO - EURASIP journal on advances in signal processing
JF - EURASIP journal on advances in signal processing
SN - 1687-6172
IS - 117
ER -