Skip to main content

2010 | OriginalPaper | Buchkapitel

10. Correntropy for Random Variables: Properties and Applications in Statistical Inference

verfasst von : Weifeng Liu, Puskal Pokharel, Jianwu Xu, Sohan Seth

Erschienen in: Information Theoretic Learning

Verlag: Springer New York

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Similarity is a key concept to quantify temporal signals or static measurements. Similarity is difficult to define mathematically, however, one never really thinks too much about this difficulty and naturally translates similarity by correlation. This is one more example of how engrained second-order moment descriptors of the probability density function really are in scientific thinking. Successful engineering or pattern recognition solutions from these methodologies rely heavily on the Gaussianity and linearity assumptions, exactly for the same reasons discussed in Chapter 3.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
7.
Zurück zum Zitat Aronszajn N., The theory of reproducing kernels and their applications, Cambridge Philos. Soc. Proc., vol. 39:133–153, 1943.CrossRefMathSciNet Aronszajn N., The theory of reproducing kernels and their applications, Cambridge Philos. Soc. Proc., vol. 39:133–153, 1943.CrossRefMathSciNet
12.
Zurück zum Zitat Bach F., Jordan M., Kernel independent component analysis, J. Mach. Learn. Res., 3:1–48, 2002.MathSciNet Bach F., Jordan M., Kernel independent component analysis, J. Mach. Learn. Res., 3:1–48, 2002.MathSciNet
65.
94.
Zurück zum Zitat Erdogmus D., Agrawal R., Principe J., A mutual information extension to the matched filter, Signal Process., 85(5):927–935, May 2005.CrossRefMATH Erdogmus D., Agrawal R., Principe J., A mutual information extension to the matched filter, Signal Process., 85(5):927–935, May 2005.CrossRefMATH
107.
Zurück zum Zitat Fukumizu K., Gretton A., Sun X., Scholkopf B., Kernel measures of conditional dependence. In Platt, Koller, Singer, and Roweis Eds., Advances in Neural Information Processing Systems 20, pp. 489–496. MIT Press, Cambridge, MA, 2008. Fukumizu K., Gretton A., Sun X., Scholkopf B., Kernel measures of conditional dependence. In Platt, Koller, Singer, and Roweis Eds., Advances in Neural Information Processing Systems 20, pp. 489–496. MIT Press, Cambridge, MA, 2008.
119.
Zurück zum Zitat Granger C., Maasoumi E., and Racine J., A dependence metric for possibly nonlinear processes. J. Time Series Anal., 25(5):649–669, 2004.CrossRefMATHMathSciNet Granger C., Maasoumi E., and Racine J., A dependence metric for possibly nonlinear processes. J. Time Series Anal., 25(5):649–669, 2004.CrossRefMATHMathSciNet
123.
Zurück zum Zitat Gretton, A., Herbrich R., Smola A., Bousquet O., Schölkopf B., Kernel Methods for Measuring Independence,” J. Mach. Learn. Res., 6:2075–2129, 2005.MATHMathSciNet Gretton, A., Herbrich R., Smola A., Bousquet O., Schölkopf B., Kernel Methods for Measuring Independence,” J. Mach. Learn. Res., 6:2075–2129, 2005.MATHMathSciNet
169.
201.
Zurück zum Zitat Liu W., Pokharel P., Principe J., Correntropy: Properties and applications in non Gaussian signal processing, IEEE Trans. Sig. Proc., 55(11):5286–5298, 2007.CrossRefMathSciNet Liu W., Pokharel P., Principe J., Correntropy: Properties and applications in non Gaussian signal processing, IEEE Trans. Sig. Proc., 55(11):5286–5298, 2007.CrossRefMathSciNet
212.
215.
Zurück zum Zitat McCulloch J., Financial applications of stable distributions. In G. S. Madala and C.R. Rao (Eds.), Handbook of Statistics, vol. 14, pages 393–425. Elsevier, Amsterdam, 1996. McCulloch J., Financial applications of stable distributions. In G. S. Madala and C.R. Rao (Eds.), Handbook of Statistics, vol. 14, pages 393–425. Elsevier, Amsterdam, 1996.
217.
Zurück zum Zitat Mercer J., Functions of positive and negative type, and their connection with the theory of integral equations, Philosoph. Trans. Roy. Soc. Lond., 209:415–446, 1909.CrossRefMATH Mercer J., Functions of positive and negative type, and their connection with the theory of integral equations, Philosoph. Trans. Roy. Soc. Lond., 209:415–446, 1909.CrossRefMATH
218.
231.
Zurück zum Zitat Nikias C. Shao M., Signal Processing with Alpha-Stable Distributions and Applications. John Wiley and Sons, New York, 1995. Nikias C. Shao M., Signal Processing with Alpha-Stable Distributions and Applications. John Wiley and Sons, New York, 1995.
241.
249.
Zurück zum Zitat Pokharel P., Liu W., Principe J., A low complexity robust detector in impulsive noise, Signal Process., 89(10):1902–1909, 2009.CrossRefMATH Pokharel P., Liu W., Principe J., A low complexity robust detector in impulsive noise, Signal Process., 89(10):1902–1909, 2009.CrossRefMATH
250.
Zurück zum Zitat Prichard, D., Theiler, J. (1994). Generating surrogate data for time series with several simultaneously measured variables. Phys. Rev. Lett., 73(7):951–954.CrossRef Prichard, D., Theiler, J. (1994). Generating surrogate data for time series with several simultaneously measured variables. Phys. Rev. Lett., 73(7):951–954.CrossRef
261.
Zurück zum Zitat Rao M., Xu J., Seth S., Chen Y., Tagare M., Principe J., Correntropy dependence measure, submitted to IEEE Trans. Signal Processing. Rao M., Xu J., Seth S., Chen Y., Tagare M., Principe J., Correntropy dependence measure, submitted to IEEE Trans. Signal Processing.
282.
Zurück zum Zitat Santamaría I., Pokharel P., Principe J, Generalized correlation function: Definition, properties and application to blind equalization, IEEE Trans. Signal Process., 54(6):2187–2197, 2006.CrossRef Santamaría I., Pokharel P., Principe J, Generalized correlation function: Definition, properties and application to blind equalization, IEEE Trans. Signal Process., 54(6):2187–2197, 2006.CrossRef
300.
Zurück zum Zitat Silverman B., Density Estimation for Statistics and Data Analysis, Chapman and Hall, London, 1986.CrossRefMATH Silverman B., Density Estimation for Statistics and Data Analysis, Chapman and Hall, London, 1986.CrossRefMATH
344.
Zurück zum Zitat Xu J., Bakardjian H., Cichocki A., Principe J., A new nonlinear similarity measure for multichannel signals, Neural Netw. (invited paper), 21(2–3):222–231, 2008.CrossRefMATH Xu J., Bakardjian H., Cichocki A., Principe J., A new nonlinear similarity measure for multichannel signals, Neural Netw. (invited paper), 21(2–3):222–231, 2008.CrossRefMATH
Metadaten
Titel
Correntropy for Random Variables: Properties and Applications in Statistical Inference
verfasst von
Weifeng Liu
Puskal Pokharel
Jianwu Xu
Sohan Seth
Copyright-Jahr
2010
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4419-1570-2_10