nips nips2002 nips2002-30 nips2002-30-reference knowledge-graph by maker-knowledge-mining
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Author: Albert E. Parker, Tomá\v S. Gedeon, Alexander G. Dimitrov
Abstract: In this paper we introduce methodology to determine the bifurcation structure of optima for a class of similar cost functions from Rate Distortion Theory, Deterministic Annealing, Information Distortion and the Information Bottleneck Method. We also introduce a numerical algorithm which uses the explicit form of the bifurcating branches to find optima at a bifurcation point. 1
[1] Thomas Cover and Jay Thomas. Elements of Information Theory. Wiley Series in Communication, New York, 1991.
[2] Robert M. Gray. Entropy and Information Theory. Springer-Verlag, 1990.
[3] Kenneth Rose. Deteministic annealing for clustering, compression, classification, regerssion, and related optimization problems. Proc. IEEE, 86(11):2210–2239, 1998.
[4] Alexander G. Dimitrov and John P. Miller. Neural coding and decoding: communication channels and quantization. Network: Computation in Neural Systems, 12(4):441– 472, 2001.
[5] Alexander G. Dimitrov and John P. Miller. Analyzing sensory systems with the information distortion function. In Russ B Altman, editor, Pacific Symposium on Biocomputing 2001. World Scientific Publushing Co., 2000.
[6] Tomas Gedeon, Albert E. Parker, and Alexander G. Dimitrov. Information distortion and neural coding. Canadian Applied Mathematics Quarterly, 2002.
[7] Naftali Tishby, Fernando C. Pereira, and William Bialek. The information bottleneck method. The 37th annual Allerton Conference on Communication, Control, and Computing, 1999.
[8] Noam Slonim and Naftali Tishby. Agglomerative information bottleneck. In S. A. Solla, T. K. Leen, and K.-R. M¨ ller, editors, Advances in Neural Information Processu ing Systems, volume 12, pages 617–623. MIT Press, 2000.
[9] Wolf-Jurgen Beyn, Alan Champneys, Eusebius Doedel, Willy Govaerts, Yuri A. Kuznetsov, and Bjorn Sandstede. Handbook of Dynamical Systems III. World Scientific, 1999. Chapter in book: Numerical Continuation and Computation of Normal Forms.
[10] Eusebius Doedel, Herbert B. Keller, and Jean P. Kernevez. Numerical analysis and control of bifurcation problems in finite dimensions. International Journal of Bifurcation and Chaos, 1:493–520, 1991.
[11] M. Golubitsky and D. G. Schaeffer. Singularities and Groups in Bifurcation Theory I. Springer Verlag, New York, 1985.
[12] M. Golubitsky, I. Stewart, and D. G. Schaeffer. Singularities and Groups in Bifurcation Theory II. Springer Verlag, New York, 1988.
[13] J. Smoller and A. G. Wasserman. Bifurcation and symmetry breaking. Inventiones mathematicae, 100:63–95, 1990.
[14] Allen Gersho and Robert M. Gray. Vector Quantization and Signal Compression. Kluwer Academic Publishers, 1992.
[15] E. T. Jaynes. On the rationale of maximum-entropy methods. Proc. IEEE, 70:939–952, 1982.
[16] J. Nocedal and S. J. Wright. Numerical Optimization. Springer, New York, 2000.
[17] Albert E. Parker III. Solving the rate distortion problem. PhD thesis, Montana State University, 2003.
[18] H. Boerner. Representations of Groups. Elsevier, New York, 1970.
[19] D. S. Dummit and R. M. Foote. Abstract Algebra. Prentice Hall, NJ, 1991.
[20] Tomas Gedeon and Bryan Roosien. Phase transitions in information distortion. In preparation, 2003.