Tsallis kernels on measures

2008 IEEE Information Theory Workshop, ITW

Volumn , Issue , 2008, Pages 298-302

  Martins, André F T ^a,b   Aguiar, Pedro M Q ^b   Figueiredo, Mário A T ^b  

^a Carnegie Mellon University   (United States)

^b INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Convexity; Jensen Shannon divergence; Nonextensive entropy; Positive definite kernels; Tsallis entropy

Indexed keywords

CLASSIFICATION (OF INFORMATION); CYBERNETICS; ENTROPY; RISK ASSESSMENT; TEXT PROCESSING;

BUILDING BLOCKS; CONVEXITY; JENSEN-SHANNON DIVERGENCE; KERNELS ON MEASURES; NEW CONCEPT; NONEXTENSIVE ENTROPY; POSITIVE DEFINITE; POSITIVE DEFINITE KERNELS; PROBABILITY MEASURES; Q-CONVEXITY; SHANNON'S ENTROPY; STRUCTURED DATA; TSALLIS ENTROPY;

INFORMATION THEORY;

EID: 51849138332     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ITW.2008.4578673     Document Type: Conference Paper

References (27)

1. B. Schölkopf and A. J. Smola, Learning with Kernels, MIT Press, 2002.
2. M. Hein and O. Bousquet, "Hilbertian metrics and positive definite kernels on probability measures," in Proc. 10th Intern. Workshop on Artificial Intelligence and Stats., 2005.
3. M. Cuturi, K. Fukumizu, and J.-P. Vert, "Semigroup kernels on measures," J. Mach. Learn. Res., vol. 6, pp. 1169-1198, 2005.
4. J. Lafferty and G. Lebanon, "Diffusion kernels on statistical manifolds," J. Mach. Learn. Res., vol. 6, pp. 129-163, 2005.
5. J. Lin, "Divergence measures based on the Shannon entropy," IEEE Trans. Inf. Th., vol. 37, pp. 145-151, 1991.
6. A. Rényi, "On measures of entropy and information," in Proc. 4th Berkeley Symp. Math. Statist. and Prob., vol. 1. Berkely: Univ. Calif. Press, 1961, pp. 547-561.
7. M. E. Havrda and F. Charvát, "Quantification method of classification processes: concept of structural α-entropy," Kybernetika, vol. 3, pp. 30-35, 1967.
8. Z. Daróczy, "Generalized information functions," Information and Control, vol. 16, pp. 36-51, Mar. 1970.
9. J. Costa and A. O. Hero, "Geodesic entropic graphs for dimension and entropy estimation in manifold learning," IEEE Trans. Signal Proc., vol. 52, pp. 2210-2221, 2004.
10. Neemuchwala, A. O. Hero, and P. Carson, "Image matching using α-entropy measures and entropic graphs," Signal Processing, vol. 85, pp. 277-296, 2005.
11. C. Tsallis, "Possible generalization of Boltzmann-Gibbs statistics," J. Stat. Physics, vol. 52, pp. 479-487, 1988.
12. S. Abe, "Foundations of nonextensive statistical mechanics," in Chaos, Nonlinearity, Complexity, Springer, 2006.
13. S. Abe and Y. Okamoto, Nonextensive Statistical Mechanics and Its Applications, Springer, 2001.
14. J. Hu, W. Tung, and J. Gao, "Modeling sea clutter as a nonstationary and nonextensive random process," in IEEE Int. Conf. Radar, Gainesville, FL, 2006.
15. Y. Li, X. Fan, and G. Li, "Image segmentation based on Tsallis-entropy and Renyi-entropy and their comparison," in IEEE Int. Conf. Indust. Informatics, 2006.
16. S. Martin, G. Morison, W. Nailon, and T. Durrani, "Fast and accurate image registration using Tsallis entropy and simultaneous perturbation stochastic approximation," Electronics Letters, vol. 40, pp. 595-597, 2004.
17. J. Jensen, "Sur les fonctions convexes et les iné galités entre les valeurs moyennes," Acta Mathematica, vol. 30, pp. 175-193, 1906.
18. T. Cover and J. Thomas, Elements of Information Theory, Wiley, 1991.
19. J. Burbea and C. R. Rao, "On the convexity of some divergence measures based on entropy functions," IEEE Trans. Inf. Th., vol. 28, pp. 489-495, 1982.
20. A. Martins, M. Figueiredo, and P. Aguiar, "On nonextensive entropies and divergences and their application to kernels on measures," 2008, to be submitted.
21. H. Suyari, "Generalization of Shannon-Khinchin axioms to nonextensive systems and the uniqueness theorem for the nonextensive entropy," IEEE Trans. Inf. Th., vol. 50, pp. 1783-1787, 2004.
22. S. Furuichi, "Information theoretical properties of Tsallis entropies," J. Math. Phy., vol. 47, 2006.
23. M. Cuturi and J.-P. Vert, "Semigroup kernels on finite sets," in Advances in Neural Information Processing Systems 17, pp. 329-336, MIT Press, 2005.
24. D. M. Endres and J. E. Schindelin, "A new metric for probability distributions," IEEE Trans. Inf. Th., vol. 49, pp. 1858-1860, 2003.
25. F. Topsøe, "Some inequalities for information divergence and related measures of discrimination," IEEE Trans. Inf. Th., vol. 46, pp. 1602-1609, 2000.
26. A. B. Hamza, "A nonextensive information-theoretic measure for image edge detection," Journal of Electronic Imaging, vol. 15-1, pp. 13011.1-13011.8, 2006.
27. C. Berg, J. Christensen, and P. Ressel, Harmonic Analysis on Semi-groups, Springer, 1984.