The multivariate watson distribution: Maximum-likelihood estimation and other aspects

Journal of Multivariate Analysis

Volumn 114, Issue 1, 2013, Pages 256-269

  Sra, Suvrit ^a   Karp, Dmitrii ^b  

^a MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

^b FAR EASTERN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Confluent hypergeometric; Diametrical clustering; Directional statistics; Hypergeometric identities; Kummer function; Special function; Watson distribution

Indexed keywords

EID: 84867742351     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2012.08.010     Document Type: Article

References (21)

1. G.E. Andrews, R. Askey, R. Roy, Special Functions, Cambridge University Press, 1999.
2. A. Banerjee, I.S. Dhillon, J. Ghosh, S. Sra, Generativemodel-based clustering of directional data, in: Proceedings of The Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD-2003. 2003, pp. 19-28.
3. A. Banerjee, I.S. Dhillon, J. Ghosh, S. Sra, Clustering on the unit hypersphere using von Mises-Fisher distributions, Journal of Machine Learning Research 6 (2005) 1345-1382.
4. A. Bijral, M. Breitenbach, G.Z. Grudic, Mixture of watson distributions: a generative model for hyperspherical embeddings, in: Artificial Intelligence and Statistics, AISTATS 2007, 2007, pp. 35-42.
5. A. Cuyt, V.B. Petersen, B. Verdonk, H. Waadeland, W.B. Jones, Handbook of Continued Fractions for Special Functions, Springer, 2008.
6. A. Dempster, N. Laird, D. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society 39 (1977).
7. I.S. Dhillon, E.M. Marcotte, U. Roshan, Diametrical clustering for identifying anti-correlated gene clusters, Bioinformatics 19 (13) (2003) 1612-1619.
8. A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher transcendental functions. Vol. 1, McGraw Hill, 1953.
9. W. Gautschi, Anomalous convergence of a continued fraction for ratios of kummer functions, Mathematics of Computation 31 (140) (1977) 994-999.
10. A. Gil, J. Segura, N.M. Temme, Numerical Methods for Special Functions, Cambridge University Press, 2007.
11. P.D. Hoff, Simulation of the Matrix Bingham-von Mises-Fisher Distribution, with applications to multivariate and relational data, Journal of Computational and Graphical Statistics 18 (2) (2009) 438-456.
12. T.R. Hughes, M.J. Marton, A.R. Jones, C.J. Roberts, R. Stoughton, C.D. Armour, H.A. Bennett, E. Coffey, H. Dai, D.D. Shoemaker, D. Gachotte, K. Chakraburtty, J. Simon, M. Bard, S.H. Friend, Functional discovery via a compendium of expression profiles, Cell 102 (2000) 109-126.
13. V.R. Iyer, M.B. Eisen, D.T. Ross, G. Schuler, T. Moore, J.C.F. Lee, J.M. Trent, L.M. Staudt, J. Hudson, M.S. Boguski, D. Lashkari, D. Shalon, D. Botstein, P.O. Brown, The transcriptional program in the response of human fibroblasts to serum, Science 283 (5398) (1999) 83-87.
14. D. Karp, Turán's inequality for the Kummer function of the phase shift of two parameters, Journal of Mathematical Sciences 178 (2) (2011) 178-186.
15. D. Karp, S.M. Sitnik, Log-convexity and log-concavity of hypergeometric-like functions, Journal of Mathematical Analysis and Applications 364 (2010) 384-394.
16. K.V. Mardia, P. Jupp, Directional Statistics, second ed., John Wiley & Sons, 2000.
17. P.T. Spellman, G. Sherlock, M. Zhang, V.R. Iyer, K. Anders, M. Eisen, P.O. Brown, D. Botstein, B. Futcher, Comprehensive identification of cell cycle regulated gene of the yeast Saccharomyces Cerevisia by microarray hybridization, Molecular Biology of the Cell 9 (1998) 3273-3297.
18. S. Sra, Matrix nearness problems in data mining, Ph.D. Thesis, University of Texas at Austin, 2007.
19. S. Sra, D. Karp, The multivariate Watson distribution: Maximum-likelihood estimation and other aspects, 2011. arXiv:stat.CO-1104.4422.
20. A. Tanabe, K. Fukumizu, S. Oba, T. Takenouchi, S. Ishii, Parameter estimation for von Mises-Fisher distributions, Computational Statistics 22 (1) (2007) 145-157.
21. G.S. Watson, Equatorial distributions on a sphere, Biometrika 52 (1-2) (1965) 193-201.