Smooth eigenvalue correction

Anne Hendrikse*, Raymond Veldhuis, Luuk Spreeuwers

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    2 Citations (Scopus)
    115 Downloads (Pure)


    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 languageEnglish
    Article number117
    Number of pages16
    JournalEURASIP journal on advances in signal processing
    Publication statusPublished - 2013


    • SCS-Safety
    • Eigenvalue estimation
    • Eigenvalue correction


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