From projection pursuit and CART to adaptive discriminant analysis?

IEEE Transactions on Neural Networks

Volumn 16, Issue 3, 2005, Pages 522-532

  Gribonval, Rémi ^a  

^a CAMPUS DE BEAULIEU   (France)

Author keywords

Classification and regression trees (CART); Classification tree; Discriminant analysis; Mutual information; Nonlinear approximation; Projection pursuit; Sequential testing

Indexed keywords

APPROXIMATION THEORY; DECISION THEORY; FEATURE EXTRACTION; MATRIX ALGEBRA; PATTERN MATCHING; REGRESSION ANALYSIS; SIGNAL PROCESSING; THEOREM PROVING; TREES (MATHEMATICS);

ADAPTIVE DISCRIMINANT ANALYSIS; CLASSIFICATION AND REGRESSION TREES (CART); COVARIANCE MATRIX; MUTUAL INFORMATION; NONLINEAR APPROXIMATION; PROJECTION PURSUIT; SEQUENTIAL TESTING;

PATTERN RECOGNITION;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; AUTOMATED PATTERN RECOGNITION; COMPUTER SIMULATION; DISCRIMINANT ANALYSIS; EVALUATION; MATHEMATICAL COMPUTING; METHODOLOGY; NONLINEAR SYSTEM; SIGNAL PROCESSING; STATISTICS;

ALGORITHMS; COMPUTER SIMULATION; DISCRIMINANT ANALYSIS; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; SIGNAL PROCESSING, COMPUTER-ASSISTED; STOCHASTIC PROCESSES;

EID: 19344368768     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2005.844900     Document Type: Article

References (29)

1. S. Mallat, A Wavelet Tour of Signal Processing, CA: Academic, 1998.
2. R. A. DeVore, "Nonlinear approximation, in Acta Numerica. Cambridge, U.K.: Cambridge Univ. Press, 1998, vol. 7, pp. 51-150.
3. R. Coifman and M. V. Wickerhauser, "Entropy-based algorithms for best basis selection," IEEE Trans. Inf. Theory, vol. 38, 2, pp. 713-718, Mar. 1992.
4. J. M. Shapiro, "Embedded image coding using zero trees of wavelet coefficients," IEEE Trans. Acoust., Speech, Signal Process., vol, 41, no. 12, pp. 3445-3462, Dec. 1993,
5. R. A. DeVore, B. Jawerth, and V. Popov, "Compression of wavelet decompositions," Amer. J. Math., vol. 114, no. 4, pp. 737-785, 1992.
6. D. L. Donoho and I. M. Johnstone, "Ideal denoising in an orthonormal basis chosen from a library of bases," C. R. Acad. Sci. Paris Ser. I, vol. 319, pp. 1317-1322, Sep. 1994.
7. J. H. Friedman and J. W. Tukey, "A projection pursuit algorithm for exploratory data analysis," IEEE Trans. Comput., vol. C-23, no. 9, pp. 881-889 Sep. 1974.
8. L. Breiman, J. H. Friedman, R. A. Olshen, and C.J. Stone, Classification and Regression Trees. London, U.K.: Chapman & Hall, 1984.
9. R. A. Fisher, The Design of Experiments, 2nd ed. London U.K.: Oliver & Boyd, 1937.
10. K. S. Fu, Sequential Methods in Pattern Recognition and Machine Learning, Vol. 52 of Mathematics in Science and Engineering. New York: Academic 1968.
11. K. Fukunaga, Introduction to Statistical Pattern Recognition, Electrical Science. New York: Academic, 1972.
12. G. McLachlan, Discriminant Analysis and Statistical Pattern Recognition. New York: Wiley, 1992.
13. R. Duda and P. Hart, Pattern Recognition and Scene Analysis. New York: Wiley, 1973.
14. A. Hyvärinen and E. Oja, "Independent component analysis: Algorithms and applications," Neural Netw., vol. 13, no. 4-5, pp. 411-430, 2000.
15. D. J. Field and B. A. Olshausen, "Emergence of simple-cell receptive field properties by learning a sparse code for natural images," Nature, vol. 381, pp. 607-609, 1996.
16. N. Saito and R. R. Coifman, "Local discriminant bases," J. Math. Imag Vis., vol. 5, no. 4, pp. 337-358, Dec. 1995.
17. N. Saito, "Least statistically-dependent basis and its application to image modeling," in Wavelet Applications in Signal and Image Processing VI, A: F. Laine, M. A. Unser, and A. Aldroubi Eds. San Diego, CA, Jul. 1998 pp. 24-37. vol. 3458 of Proc. SPIE.
18. B. Liu and S.-F. Ling, "On the selection of informative wavelets for machine diagnosis," J. Mech. Syst. Signal Process., vol. 13, no. 1, pp. 145-162, 1999.
19. S. Mallat and Z. Zhang, "Matching pursuit with time-frequency dictionaries," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397-3415, Dec. 1993.
20. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
21. P. J. Phillips, "Matching pursuit filters applied to face identification," IEEE Trans. Image Process., vol. 7, no. 8, pp. 1150-1164, Aug. 1998.
22. Q. Jiang, S. S. Goh, and Z. Lin, "Local discriminant time-frequency atoms for signal classification," Signal Process., vol. 72, pp. 47-52, 1999.
23. A. Wald, "Sequential tests of statistical hypothesis," Ann. Math. Statist., vol. 16, no. 2 pp. 117-186, Jun. 1945.
24. F. Esposito, D. Malerba, and G. Semeraro, "A comparative analysis of methods for pruning decision trees," IEEE Trans. Pattern Anal. Mach. Intell., vol. 19, no. 5, pp. 476-491, May 1997.
25. D. Geman and B. Jedynak, "An active testing model for tracking roads in satellite images," IEEE Trans. Pattern Anal. Mach. Intell., vol. 18, no. 1, pp. 1-14, Jan. 1996.
26. C. Li, "Classification by active testing with applications to imaging and change detection," Ph.D. dissertation, Univ. Massachussets, Amherst, Feb. 1999.
27. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1993.
28. Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, "Orthonormal matching: pursuit: Recursive function approximation with applications to wavelet decomposition," in Proc. 27th Annu. Asilomar Conf. Signals, Systems Computers, Nov. 1993.
29. L. Benaroya and F. Bimbot, "Wiener-based source separation with HMM /GMM using a single sensor," in Proc. 4th Int. Symp. Independent Component Analysis Blind Signal Separation (ICA'03), Nara, Japan, Apr. 2003.