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On Piecewise-Linear Classification
July 1992 (vol. 14 no. 7)
pp. 782-786

The authors make use of a real data set containing 9-D measurements of fine needle aspirates of a patient's breast for the purpose of classifying a tumor's malignancy for which early stopping in the generation of the separating hyperplanes is not appropriate. They compare a piecewise-linear classification method with classification based on a single linear separator. A precise methodology for comparing the relative efficacy of two classification methods for a particular task is described and is applied to the comparison on the breast cancer data of the relative performances of the two versions of the piecewise-linear classifier and the classification based on an optimal linear separator. It is found that for this data set, the piecewise-linear classifier that uses all the hyperplanes needed to separate the training set outperforms the other two methods and that these differences in performance are significant at the 0.001 level. There is no statistically significant difference between the performance of the other two methods. The authors discuss the relevance of these results for this and other applications.

[1] R. O. Duda and P. E. Hart,Pattern Classification and Scene Analysis. New York: Wiley, 1973.
[2] K. Fukunaga,Introduction to Statistical Pattern Recognition. New York: Academic, 1972.
[3] O. L. Mangasarian, R. Setiono, and W. H. Wolberg, "Pattern recognition via linear programming: Theory and applications to medical diagnosis," inLarge-Scale Numerical Optimization(T. F. Coleman and Y. Li, Eds.). Philadelphia: SIAM, 1990, pp. 22-31.
[4] I. Foroutan and J. Sklansky, "Feature selection for piecewise linear classifiers," inIEEE Proc. Comput. Vision Pattern Recog.(San Francisco), 1985, pp. 149-154.
[5] E. Harth, T. Kalogeropoulos, and A. S. Pandya, "A universal optimization network," inProc. Spec. Symp. Maturing Technol. Emerging Horizons Biomed. Eng.(New Orleans), 1988, pp. 97-107.
[6] S. M. Weiss and I. Kapouleas, "An empirical comparison of pattern recognition, neural nets, and machine learning classification methods," inProc. 11th Int. Joint Conf. Artificial Intell.(Detroit, MI), 1989, pp. 781-787.
[7] R. F. Mould,Introduction to Medical Statistics. Bristol, England: Adam Hilger, 1989, 2nd ed.
[8] J. W. Shavlik, R. J. Mooney, and G. G. Towell, "Symbolic and neural learning algorithms: An experimental comparison," to be published inMachine Learning.
[9] G. T. Herman and K. T. D. Yeung, "Evaluators of image reconstruction algorithms,"Int. J. Imag. Syst. Techn., vol. 1, pp. 187-195, 1989.
[10] B. V. Basarathy and B. V. Sheela, "A composite classifier system design: Concept and methodology,"Proc. IEEE, vol. 67, pp. 708-713, 1979.

Index Terms:
tumor malignancy classification; patient diagnosis; pattern recognition; piecewise-linear classification; hyperplanes; breast cancer data; computerised pattern recognition; medical computing; patient diagnosis
G.T. Herman, K.T.D. Yeung, "On Piecewise-Linear Classification," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 7, pp. 782-786, July 1992, doi:10.1109/34.142914
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