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Advances in Numerical Analysis
Volume 2012 (2012), Article ID 579050, 15 pages
Interpreting the Phase Spectrum in Fourier Analysis of Partial Ranking Data
School of Computer Engineering, Nanyang Technological University, Singapore 637665
Received 28 September 2011; Revised 14 February 2012; Accepted 23 February 2012
Academic Editor: Mustapha Ait Rami
Copyright © 2012 Ramakrishna Kakarala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- P. Diaconis, “A generalization of spectral analysis with application to ranked data,” The Annals of Statistics, vol. 17, no. 3, pp. 949–979, 1989.
- G. Lebanon and Y. Mao, “Non-parametric modeling of partially ranked data,” Journal of Machine Learning Research, vol. 9, pp. 2401–2429, 2008.
- P. Hall and H. Miller, “Modeling the variability of rankings,” The Annals of Statistics, vol. 38, no. 5, pp. 2652–2677, 2010.
- P. Diaconis, Group Representations in Probability and Statistics, Institute of Mathematical Statistics, Hayward, Calif, USA, 1988.
- P. Diaconis and B. Sturmfels, “Algebraic algorithms for sampling from conditional distributions,” The Annals of Statistics, vol. 26, no. 1, pp. 363–397, 1998.
- J. Huang, C. Guestrin, and L. Guibas, “Fourier theoretic probabilistic inference over permutations,” Journal of Machine Learning Research, vol. 10, pp. 997–1070, 2009.
- R. Kondor and K. Borgwardt, “The skew spectrum of graphs,” in Proceedings of the International Conference on Machine Learning (ICML), A. McCallum and S. Roweis, Eds., pp. 496–503, Omnipress, 2008.
- R. Kakarala, “A signal processing approach to Fourier analysis of ranking data: the importance of phase,” IEEE Transactions on Signal Processing, vol. 59, no. 4, pp. 1518–1527, 2011.
- A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Sigals and Systems, Prentice-Hall, 2nd edition, 1996.
- R. Kondor, “ob: a C++ library for fast Fourier transforms on the symmetric group,” 2006, http://www.its.caltech.edu/~risi/index.html.
- P. Lancaster and M. Tismenetsky, The Theory of Matrices, Computer Science and Applied Mathematics, Academic Press, Orlando, Fla, USA, 2nd edition, 1985.
- E. Hewitt and K. A. Ross, Abstract Harmonic Analysis. Vol. II: Structure and Analysis for Compact Groups. Analysis on Locally Compact Abelian Groups, Springer, New York, NY, USA, 1970.
- R. Kondor, “The skew spectrum of functions on finite groups and their homogeneous spaces,” Representation Theory. In press, http://arxiv.org/abs/0712.4259.
- M. Croon, “Latent class models for the analysis of rankings,” in New Developments in Psychological Choice Modeling, G. D. Solte, H. Feger, and K. C. Klauer, Eds., pp. 99–121, North-Holland, 1989.
- D. K. Maslen, “The efficient computation of Fourier transforms on the symmetric group,” Mathematics of Computation, vol. 67, no. 223, pp. 1121–1147, 1998.
- M. Clausen and R. Kakarala, “Computing Fourier transforms and convolutions of -invariant signals on in time linear in n,” Applied Mathematics Letters, vol. 23, no. 2, pp. 183–187, 2010.