Nonextensive entropic kernels

Proceedings of the 25th International Conference on Machine Learning

Volumn , Issue , 2008, Pages 640-647

  Martins, André F T ^a,b   Figueiredo, Mário A T ^b   Aguiar, Pedro M Q ^b   Smith, Noah A ^a   Xing, Eric P ^a  

^a Carnegie Mellon University   (United States)

^b INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

MACHINE LEARNING; TEXT PROCESSING; LEARNING SYSTEMS; PROGRAMMING THEORY; ROBOT LEARNING;

CLASSIC INFORMATION; JENSEN-SHANNON DIVERGENCE; MUTUAL INFORMATION KERNEL; MUTUAL INFORMATIONS; POSITIVE DEFINITE KERNELS; PROBABILITY MEASURES; SHANNON'S INFORMATION THEORY; TEXT CATEGORIZATION;

INFORMATION THEORY;

CLASSIC INFORMATIONS; JENSEN-SHANNON DIVERGENCES; LINEAR KERNELS; MUTUAL INFORMATION KERNELS; MUTUAL INFORMATIONS; POSITIVE DEFINITE KERNELS; PROBABILITY MEASURES; STRUCTURED DATUM; TEXT CATEGORIZATIONS; TSALLIS STATISTICS;

EID: 56449122467     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1390156.1390237     Document Type: Conference Paper

References (28)

1. Abe, S. (2006). Foundations of nonextensive statistical mechanics. Chaos, Nonlinearity, Complexity. Springer.
2. Banerjee, A., Merugu., S., Dhillon, I. S. & Ghosh, J. (2005). Clustering with Bregman divergences. JMLR, 6, 1705-1749.
3. Berg, C., Christensen, J., & Ressel, P. (1984). Harmonic analysis on semigroups. Springer.
4. Burbea, J., & Rao, C. (1982). On the convexity of some divergence measures based on entropy functions. IEEE Trans. Inf. Theory, 28, 489-495.
5. Cover, T., & Thomas, J. (1991). Elements of information theory. Wiley.
6. Cuturi, M., Fukumizu, K., & Vert, J.-P. (2005). Semigroup kernels on measures. JMLR, 6, 1169-1198.
7. Endres, D., & Schindelin, J. (2003). A new metric for probability distributions. IEEE Trans. Inf. Theory, 49, 1858-1860.
8. Fuglede, B. (2005). Spirals in Hilbert space. Expositiones Mathematicae, 25, 23-46.
9. Furuichi, S. (2006). Information theoretical properties of Tsallis entropies. J. Math. Physics, 47, no. 2.
10. Gell-Mann, M., & Tsallis, C. (2004). Nonextensive entropy: interdisciplinary applications. Oxford University Press.
11. Hamza, A. (2006). A nonextensive information-theoretic measure for image edge detection. Journal of Electronic Imaging, 15-1, 13011.1-13011.8.
12. Havrda, M., & Charvát, F. (1967). Quantification method of classification processes: concept of structural α-entropy. Kybernetika, 3, 30-35.
13. Hein, M., α Bousquet, O. (2005). Hilbertian metrics and positive definite kernels on probability measures. Proc. 10th AISTATS.
14. Hein, M., Lal, T., α Bousquet, O. (2004). Hilbertian metrics on probability measures and their application in SVMs. DAGM-Symposium, 270-277.
15. Jebara, T., Kondor, R., & Howard, A. (2004). Probability product kernels. JMLR, 5, 819-844.
16. Joachims, T. (1997). Text categorization with support vector machines: Learning with many relevant features (T.R.). Universität Dortmund.
17. Karakos, D., Khudanpur, S., Eisner, J., & Priebe, C. (2007). Iterative denoising using Jensen-Rényi divergences with an application to unsupervised document categorization. Proc. IEEE ICASSP.
18. Khinchin, A. (1957). Mathematical foundations of information theory. Dover.
19. Lafferty, J., & Lebanon, G. (2005). Diffusion kernels on statistical manifolds. JMLR, 6, 129-163.
20. Li, Y., Fan, X., & Li, G. (2006). Image segmentation based on Tsallis-entropy and Rényi-eutropy and their comparison. IEEE Intern. Conf. on Industrial Informatics (pp. 943-948).
21. Lin, J. (1991). Divergence measures based on Shannon entropy. IEEE Trans. Inf. Theory, 37, 145-151.
22. Martins, A.F.T., Figueiredo, M.A.T., Aguiar, P.M.Q., Smith, N.A., Xing, E.P. (2008). Nonextensive entropic kernels. T.R. CMU-ML-08-106.
23. Moreno, P., Ho, P., & Vasconcelos, N. (2003). A Kullback-Leibler divergence based kernel for SVM classification in multimedia applications. NIPS.
24. Rényi, A. (1961). On measures of entropy and information. Proc. 4th Berkeley Symp. Math. Statist. and Prob. (pp. 547-561). Univ. Calif. Press.
25. Schölkopf, B., & Smola, A. (2002). Learning with kernels. MIT Press.
26. Topsøe, F. (2000). Some inequalities for information divergence and related measures of discrimination. IEEE Trans. Inf. Theory, 46, 1602-1609.
27. Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. J. Stats. Physics, 52, 479-487.
28. Zhang, D., Chen, X., & Lee, W. (2005). Text classification with kernels on the multinomial manifold. Proc. ACM SIGIR.