Designing a metric for the difference between Gaussian densities

Advances in Intelligent and Soft Computing

Volumn 83, Issue , 2010, Pages 57-70

  Abou Moustafa, Karim T ^a   De La Torre, Fernando ^b   Ferrie, Frank P ^a  

^a MCGILL UNIVERSITY   (Canada)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BHATTACHARYYA COEFFICIENT; BHATTACHARYYA DISTANCE; GAUSSIAN DENSITY; GAUSSIANS; KULLBACK LEIBLER DIVERGENCE; METRIC PROPERTIES; SPECTRAL CLUSTERING;

GAUSSIAN DISTRIBUTION;

EID: 80052957794     PISSN: 18675662     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-16259-6_5     Document Type: Conference Paper

References (28)

1. Ali, S.M., Silvey, S.D.: A general class of coefficients of divergence of one distribution from another. J. of the Royal Statistical Society. Seris B 28(1), 131-142 (1966)
2. Bar-Hillel, A., Hertz, T., Shental, N.,Weinshall, D.: Learning aMahalanobis metric from equivalence constraints. J. of Machine Learning Research 6, 937-965 (2005)
3. Bhattacharyya, A.: On a measure of divergence between two statistical populations defined by their probability distributions. Bull. Calcutta Math. Soc. 35, 99-109 (1943)
4. Chernoff, H.: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Annals of Mathematical Statistics 22, 493-507 (1952)
5. Christakos, G., Papanicolaou, V.: Norm-dependent covariance permissibility of weakly homogeneous spatial random fields and its consequences in spatial statistics. Stochastic Environmental Research and Risk Management 14, 471-478 (2000)
6. Csiszár, I.: Information-type measures of difference of probability distributions and indirect observations. Studia Scientiarium Mathematicarum Hungarica 2, 299-318 (1967)
7. De La Torre, F., Kanade, T.: Multimodal oriented discriminant analysis. In: ACM Proc. of ICML, pp. 177-184 (2005) (Pubitemid 43183331)
8. Elkan, C.: Using the trinagle inequality to accelerate k-means. In: ACM Proc. of ICML, pp. 147-153 (2003)
9. Förstner,W.,Moonen, B.: A metric for covariance matrices. Tech. rep., Dept. of Geodesy and Geo-Informatics, Stuttgart University (1999)
10. Genton, M.: Classes of kernels for machine learning: A statistics perspective. J. of Machine Learning Research 2, 299-312 (2001)
11. Jaakkola, T., Haussler, D.: Exploiting generative models in discriminative classifiers. In: NIPS 11, pp. 487-493. MIT Press, Cambridge (1999)
12. Jebara, T., Kondor, R., Howard, A.: Probability product kenrels. J. of Machine Learning Research 5, 819-844 (2004)
13. Kailath, T.: The divergence and Bhattacharyya distance measures in signal selection. IEEE Trans. on Communication Technology 15(1), 52-60 (1967)
14. Knuth, D.E. (ed.): The Stanford graphbase. Springer, New York (1988)
15. Kondor, R., Jebara, T.: A kernel between sets of vectors. In: ACM Proc. of ICML 2003 (2003)
16. Kullback, S.: Information Theory and Statistics - Dover Edition. Dover, New York (1997)
17. Lafferty, J., Lebanon, G.: Information diffusion kernels. In: NIPS 14, MIT Press, Cambridge (2002)
18. Luxburg, U.v.: A tutotrial on spectral clustering. Tech. Rep. TR-149, Max Plank Institute for Biological Cybernetics (2006)
19. Martins, A., Smith, N., Xing, E., Aguiar, P., Figueiredo, M.: Nonextensive information theoretic kernels on measures. J. of Machine Learning Research 10, 935-975 (2009)
20. Moreno, P., Ho, P., Vasconcelos, N.: A Kullback-Leibler divergence based kernel for svm classification in multimedia applications. In: NIPS 16 (2003)
21. Rao, C.: Use of Hellinger distance in graphical displays. In: Titt, E., Kollo, T., Niemi, H. (eds.) Multivariate Statistics and Matrices in Statistics, pp. 143-161 (1995)
22. Roth, V., Laub, J., Buhmann, J.: Optimal cluster preserving embedding of nonmetric proximity data. IEEE Trans. PAMI 25(12), 1540-1551 (2003)
23. Schölkopf, B., Smola, A.: Learning with kernels. MIT Press, Cambridge (2002)
24. Shi, J., Malik, J.: Motion segmentation and tracking using normalized cuts. In: IEEE Proc. of ICCV, pp. 1154-1160 (1998)
25. Sriperumbudur, B., Gretton, A., Fukumizu, K., Schölkopf, B., Lanckriet, G.: Hilbert space embeddings and metrics on probability distributions. J. of Machine Learning Research 11, 1517-1561 (2010)
26. Tsuda, K., Kawanabi, M., Ratsch, G., Sonnenburg, S., Muller, K.R.: A new discriminative kernel from probability distributions. Neural Computation 14, 2397-2414 (2002)
27. Young, G., Householder, A.: Discussion of a set of points in temrs of their mutual distances. Psychometrika 3(1), 19-22 (1938)
28. Zha, H., Ding, C., Gu, M., He, X., Simon, H.: Spectral relaxation for k-means clustering. In: NIPS 13, MIT Press, Cambridge (2001)