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An Optimal Approach for Random Signals Classification
November 1991 (vol. 13 no. 11)
pp. 1192-1196

A method is proposed which solves the problem of the Bayes classification of ARMA (autoregressive moving average) signals when the models of classes and samples are not exactly known but only estimated from finite-length data sequences. Justified approximations and the hypothesis lead to decision rules including the variances of the estimations. The results obtained on a large set of simulated data show that this approach is superior to the best classical methods (cepstral distance or Kullback divergence), particularly in the common case where the hypothesis of those methods is not verified (short samples. small training sets. random classes).

[1] R.M. Gray, A. Buzo, A.H. Gray, and Y. Matsuyama, "Distortion measures for speech processing,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-28, pp. 367-376, Aug. 1980.
[2] A. H. Gray, Jr. and J. D. Markel, "Distance measures for speech processing,"IEEE Trans Acoust. Speech Signal Processing, vol. ASSP- 24, pp. 380-391, Oct. 1976.
[3] T. L. Grettenberg, "Signal selection in communication and radar systtems,"IEEE Trans. Inform. Theory, vol. IT-9, 1963.
[4] D. Kazakos, "The Battacharrya distance and detection between Markov chains,"IEEE Trans. Inform. Theory, vol. IT-24, no. 6, pp. 747-754, Nov. 1978.
[5] T. Kailath, "The divegence and Bhattacharyya distance measures in signal detection,"IEEE Trans. Comm. Tech., vol. COM-15, pp. 52-60, Feb. 1967.
[6] W. Gersch, "Nearest neighbor rule in classification of stationary and non stationary time series," inApplied Time Series Analysis(D. F. Findley, Ed.), New York: Academic, 1981, pp. 221-270.
[7] T. Itakura, "Minimum prediction residual principle applied to speech recognition,"IEEE Trans. Acous. Speech Signal Processing, vol. ASSP- 23, no. 1, pp. 67-72, Feb. 1975.
[8] F. Itakura and T. Umezaki, "Distance measure for speech recognition based on the smoothed group delay spectrum, inProc. ICASSP, 1987, pp. 1257-1260.
[9] J. Makhoul and A. O. Steinhardt, "On matching correlation sequences by parametric spectral models," inProc. ICASSP, 1987, pp 995-998.
[10] J. E. Shore and R. M. Gray, "Minimum cross-entropy pattern classification and cluster analysis,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-14, no. 1, pp. 11-17, Jan. 1982.
[11] P. V. de Souza, "Statistical results and distance measures for LPC coefficients,"IEEE Trans. Acous. Speech Signal Processing, vol. ASSP- 25, no. 6, pp. 554-559, Dec. 1977.
[12] P. M. Trouborstet al., "New families of probabilistic distance measures," inProc. 2 Int. Joint Conf. Patt. Recogn.(Copenhagen), 1974.
[13] J. M. Tribolet, L. R. Rabiner, and M. M. Sondhi, "Statistical properties of an LPC distance measure," inProc. ICASSP, 1979, pp. 739-743.
[14] M. Basseville, "Distances measures for signal processing and pattern recognition,"Signal Processing, vol. 18, no. 4, Dec. 1989.

Index Terms:
ARMA signals; optimal approach; random signals classification; Bayes classification; finite-length data sequences; decision rules; cepstral distance; Kullback divergence; Bayes methods; decision theory; pattern recognition; signal processing
C. Doncarli, E. LeCarpentier, "An Optimal Approach for Random Signals Classification," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 11, pp. 1192-1196, Nov. 1991, doi:10.1109/34.103278
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