Kullback-Leibler distance as a measure of the information filtered from multivariate data

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 76, Issue 3, 2007, Pages

  Tumminello, Michele ^a,b   Lillo, Fabrizio ^a,c   Mantegna, Rosario N ^a  

^a UNIVERSITY OF PALERMO   (Italy)

^b INFM   (Italy)

^c SANTA FE INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTER ANALYSIS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PARAMETER ESTIMATION; SPECTRUM ANALYSIS; UNCERTAINTY ANALYSIS;

GAUSSIAN VARIABLES; HIERARCHICAL CLUSTERING; KULLBACK-LEIBLER DISTANCE; STATISTICAL UNCERTAINTY;

CORRELATION METHODS;

EID: 34648828817     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.031123     Document Type: Article

References (25)

1. P. J. Forrester and T. D. Hughes, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.530639 35, 6736 (1994).
2. Y. Demasure and R. A. Janik, Phys. Lett. B PYLBAJ 0370-2693 10.1016/S0370-2693(02)03189-1 553, 105 (2003).
3. N. S. Holter, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.150242097 97, 8409 (2000).
4. O. Alter, P. O. Brown, and D. Botstein, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.97.18.10101 97, 10101 (2000).
5. N. S. Holter, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.98.4.1693 98, 1693 (2001).
6. L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1467 83, 1467 (1999).
7. V. Plerou, P. Gopikrishnan, B. Rosenow, L. A. Nunes Amaral, and H. E. Stanley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1471 83, 1471 (1999).
8. R. N. Mantegna, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050929 11, 193 (1999).
9. K. V. Mardia, J. T. Kent, and J. M. Bibby, Multivariate Analysis (Academic, San Diego, CA, 1979).
10. M. R. Anderberg, Cluster Analysis for Applications (Academic, New York, 1973).
11. D. B. West, An Introduction to Graph Theory (Prentice-Hall, Englewood Cliffs, NJ, 2001).
12. S. Kullback and R. A. Leibler, Ann. Math. Stat. 22, 79 (1951). 0003-4851
13. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley-Interscience, New York, 1991).
14. H. Jefferys, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 186, 453 (1946).
15. M. S. Bartlett, J. R. Stat. Soc. Ser. B (Methodol.) JSTBAJ 0035-9246 16, 296 (1954).
16. M. Fisz, Probability Theory and Mathematical Statistics (Wiley, New York, 1963).
17. M. L. Metha, Random Matrices (Academic, New York, 1990).
18. B. Rosenow, V. Plerou, P. Gopikrishnan, and H. E. Stanley, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2002-00135-4 59, 500 (2002).
19. M. Potters, J.-P. Bouchaud, and L. Laloux, Acta Phys. Pol. B APOBBB 0587-4254 36, 2767 (2005).
20. M. Tumminello, F. Lillo, and R. N. Mantegna, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/78/30006 78, 30006 (2007).
21. G. E. Johnson, Proc. IEEE IEEPAD 0018-9219 10.1109/5.265353 82, 270 (1994).
22. B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman and Hall/CRC, Boca Raton, FL, 1993).
23. M. Tumminello, C. Coronnello, F. Lillo, S. Miccichè, and R. N. Mantegna, e-print arXiv:physics/0605116, Int. J. Bifurcation Chaos (to be published).
24. R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, 2000).
25. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, London, 1980), p. 576.