Encyclopedia of Machine Learning

2010 Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Covariance Matrix

  • Xinhua Zhang
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30164-8_183


It is convenient to define a covariance matrix by using multi-variate random variables ( mrv): X = ( X 1, , X d) ​. For univariate random variables X i and X j, their covariance is defined as:
$$\textrm{ Cov}({X}_{i},{X}_{j}) = \mathbb{E}\left [({X}_{i} - {\mu }_{i})({X}_{j} - {\mu }_{j})\right ],$$
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Recommended Reading

  1. Casella, G., & Berger, R. (2002). Statistical inference (2nd ed.). Pacific Grove, CA: Duxbury.Google Scholar
  2. Gretton, A., Herbrich, R., Smola, A., Bousquet, O., & Schölkopf, B. (2005). Kernel methods for measuring independence. Journal of Machine Learning Research, 6, 2075–2129.Google Scholar
  3. Jolliffe, I. T. (2002) Principal component analysis (2nd ed.). Springer series in statistics. New York: Springer.zbMATHGoogle Scholar
  4. Mardia, K. V., Kent, J. T., & Bibby, J. M. (1979). Multivariate analysis. London: Academic Press.zbMATHGoogle Scholar
  5. Schölkopf, B., & Smola, A. (2002). Learning with kernels. Cambridge, MA: MIT Press.Google Scholar
  6. Williams, C. K. I., & Rasmussen, C. E. (2006). Gaussian processes for regression. Cambridge, MA: MIT Press.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Xinhua Zhang

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