This Article 
 Bibliographic References 
 Add to: 
Decision Rule for Pattern Classification by Integrating Interval Feature Values
April 1998 (vol. 20 no. 4)
pp. 440-448

Abstract—Pattern classification based on Bayesian statistical decision theory needs a complete knowledge of the probability laws to perform the classification. In the actual pattern classification, however, it is generally impossible to get the complete knowledge as constant feature values by the influence of noise. Therefore, it is necessary to construct more flexible and robust theory for pattern classification. In this paper, a pattern classification theory using feature values defined on closed interval is formalized in the framework of Dempster-Shafer measure. Then, in order to make up lacked information, an integration algorithm is proposed, which integrates information observed by several information sources with considering source values.

[1] K.M. Andress and A.C. Kak, "Evidence Accumulation&Flow of Control in a Hierarchical Spatial Reasoning System," AI Magazine, vol. 9, no. 2, pp. 75-94, 1988.
[2] R.L. Berger, "Gamma Minimax Robustness of Bayes Rules," Comm. Statistics—Theory and Methods, vol. A8, pp. 543-560, 1979.
[3] C.H. Chen, "A Review of Statistical Pattern Recognition," Pattern Recognition and Signal Processing, pp. 117-132.New York: Academic Press, 1978.
[4] C.K. Chow, "An Optimum Character Recognition System Using Decision Functions," Inst. Radio Eng. Trans. Electronic Computers, vol. 6, pp. 247-254, 1957.
[5] C.K. Chow, "On Optimum Recognition Error and Reject TradeOff," IEEE Trans. Information Theory, vol. 16, no. 1, pp. 41-46, 1970.
[6] C.K. Chow, "Recognition Error and Reject Tradeoff," Proc. Third Ann. Symp. Document Analysis and Information Retrieval, pp. 1-8, 1994.
[7] A.P. Dempster, "Upper and Lower Probabilities Induced by a Multivalued Mapping," Annals Math. Statistics, vol. 39, pp. 325-339, 1967.
[8] B. Dubusson and M. Masson, "A Statistical Decision Rule With Incomplete Knowledge About Classes," Pattern Recognition, vol. 26, no. 1, pp. 155-165, 1993.
[9] R.O. Duda and P.E. Hart, Pattern Classification and Scene Analysis.New York: Jon Wiley&Sons, 1973.
[10] K. Fukunaga, Introduction to Statistical Pattern Recognition, second edition. San Diego: Academic Press, 1990.
[11] T.D. Garvey, "Evidential Reasoning for Geographic Evaluation for Helicopter Route Planning," IEEE Trans. Geoscience Electronics, vol. 25, no. 3, pp. 294-304, 1987.
[12] S.D. Gupta, "Theories and Methods in Classification: A Review," Discriminant Analysis and Prediction.New York: Academic Press, 1973.
[13] S.D. Gupta, "Some Problems in Statistical Pattern Recognition," Multivariate Analysis-IV,New York: North-Holland, 1977.
[14] T.M. Ha, "An Optimum Class-Selective Rejection Rule for Pattern Recognition," Proc. ICPR '96, vol. 2, pp. 75-80, 1996.
[15] T.M. Ha, "The Optimum Class-Selective Rejection Rule," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 6, pp. 608-615, 1997.
[16] F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw, and W.A. Stahel, "Robust Statics: The Approach Based on Influence Functions,"New York: John Wiley&Sons, 1986.
[17] T. Horiuchi, K. Yamamoto, H. Yamada, and K. Toraichi, "Relaxation Optimizing Operations in Extended Probabilistic Space," Int'l J. Systems Science, vol. 27, no. 5, pp. 447-452, 1996.
[18] T. Horiuchi, K. Yamamoto, and H. Yamada, "Robust Relaxation Method for Structural Matching Under Uncertainty," Proc. 13th ICPR '96, vol. 2, pp. 176-180, 1996.
[19] T. Horiuchi, "Class-Selective Rejection Rule to Minimize the Maximum Distance Between Selected Classes," Pattern Recognition, (in press).
[20] P.J. Huber, Robust Statistics.New York: John Wiley&Sons, 1981.
[21] J.B. Kadane and D.T. Chuang, "Stable Decision Problems," Annals Statistics, vol. 6, pp. 1,095-1,110, 1978.
[22] Y. Kharin, Robustness in Statistical Pattern Recognition.Dordrecht: Kluwer Academic Publishers, 1996.
[23] P.A. Lachenbruch, Discriminant Analysis.New York: Hafner Press, 1975.
[24] L. Launer and G.N. Wilknton, eds., Robustness in Statics.New York: Academic Press, 1979.
[25] T. Matsuyama and M. Kurita, "Pattern Classification Based on Dempster-Shafer Probability Model-Belief Formation From Observation and Belief Integration Using Virtual Belief Space," IEICE Trans. Japan, vol. J76-D-II, no. 4, pp. 843-853, 1993 [in Japanese].
[26] T. Matsuyama, "Belief Formation From Observation and Belief Integration Using Virtual Belief Space in Dempster-Shafer Probability Model," Proc. MFI '94, pp. 379-386, 1994.
[27] G.J. McLachlan, Discriminant Analysis and Statistical Pattern Recognition.New York: John Wiley&Sons, 1992.
[28] F.A. Patrick, Fundamentals of Pattern Recognition.Englewood Cliffs, N.J.: Prentice-Hall, 1972.
[29] W.J.J. Rey, "Robust Statistical Method," Lecture Notes in Math., vol. 690, pp. 1-129, 1978.
[30] H. Rieder, Robust Asymptotic Statistics.New York: Springer-Verlag, 1994.
[31] B.D. Ripley, Pattern Recognition and Neural Network. Cambridge Univ. Press, 1996.
[32] G. Shafer, A Mathematical Theory of Evidence. Princeton Univ. Press, 1976.
[33] P. Smets, "Constructing the Pignistic Probability Function in a Context of Uncertainty," M. Henrion et al., eds. Uncertainty in Artificial Intelligence, vol. 5, pp. 29-39. North-Holland, 1990.
[34] M.L. Tiku, W.Y. Tan, and M. Balakrishnan, Robust Inference.New York: Marcel Dekker, 1986.
[35] J.W. Tukey, "A Survey of Sampling From Contaminated Distributions," Contributions to Probability and Statistics, pp. 448-485.Stanford, Calif: Stanford Univ. Press, 1960.
[36] C.J.D.M. Verhagen, "Progress Report on Pattern Recognition," Reports on Progress in Physics, vol. 43, no. 6, pp. 785-831, 1980.
[37] R.R. Yager, "On the Dempster-Shafer Framework and New Combination Rules," Information Sciences, vol. 41, pp. 93-137, 1987.
[38] L. Zadeh, "A Mathematical Theory of Evidence (book review)," Artificial Intelligence, vol. 5, no. 3, pp. 81-83, 1984.

Index Terms:
Bayesian classification, Dempster-Shafer theory, integration, pattern classification, probability.
Takahiko Horiuchi, "Decision Rule for Pattern Classification by Integrating Interval Feature Values," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 4, pp. 440-448, April 1998, doi:10.1109/34.677286
Usage of this product signifies your acceptance of the Terms of Use.