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Numerical Study of Random Correlation Matrices: Finite-Size Effects

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Intelligent Decision Technologies

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 10))

Abstract

We report the numerical calculations of the distribution of maximal eigenvalue for various size of random correlation matrices. Such an extensive study enables us to work out empirical formulas for the average and standard deviation of the maximal eigenvalue, which are accurate in a wide range of parameters. As an application of those formulas, we propose a criterion to single out statistically meaningful correlations in the principal component analysis. The new criterion incorporates finite-size effects into the current method based on the random matrix theory, which gives the exact results in the infinite-size limit.

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Author information

Authors and Affiliations

  1. Graduate School of Science and Technology, Niigata University, Ikarashi, Niigata, 950-2181, Japan

    Yuta Arai

  2. Faculty of Science, Niigata University, Ikarashi, Niigata, 950-2181, Japan

    Kouichi Okunishi & Hiroshi Iyetomi

Authors
  1. Yuta Arai
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  2. Kouichi Okunishi
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  3. Hiroshi Iyetomi
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Editor information

Editors and Affiliations

  1. Graduate School of Information, Production and Systems (IPS), Waseda University, 2-7 Hibikino Wakamatsuku, 808-0135, Fukuoka, Kitakyushu, Japan

    Junzo Watada

  2. Sellinger School of Business and Management, Loyola University Maryland, 4501 N Charles Street, 21210, Baltimore, MD, USA

    Gloria Phillips-Wren

  3. School of Electrical and Information Engineering, University of South Australia, Mawson Lakes Campus Adelaide, 5095, South Australia, SA, Australia

    Lakhmi C. Jain

  4. KES International, Shoreham-by-seaWest Sussex, PO Box 2115, BN43 9AF, United Kingdom

    Robert J. Howlett

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© 2011 Springer-Verlag Berlin Heidelberg

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Arai, Y., Okunishi, K., Iyetomi, H. (2011). Numerical Study of Random Correlation Matrices: Finite-Size Effects. In: Watada, J., Phillips-Wren, G., Jain, L.C., Howlett, R.J. (eds) Intelligent Decision Technologies. Smart Innovation, Systems and Technologies, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22194-1_55

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  • DOI: https://doi.org/10.1007/978-3-642-22194-1_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22193-4

  • Online ISBN: 978-3-642-22194-1

  • eBook Packages: EngineeringEngineering (R0)

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