Abstract
In the previous chapter, it was shown how Cartesian granule feature models exploit a divide-and-conquer strategy to representation, capturing knowledge in terms of a network of low-order semantically related features. Both classification and prediction problems can be modelled quite naturally in terms of these models. This chapter describes a constructive induction algorithm, G_DACG (Genetic Discovery of Additive Cartesian Granule feature models), which facilitates the learning of such models from example data [Shanahan 1998; Shanahan, Baldwin and Martin 1999]. This involves two main steps: language identification (identification of the low-order semantically related features in terms of Cartesian granule features); and parameter identification of class fuzzy sets and rules. The C_DACG algorithm achieves this by embracing the synergistic spirit of soft computing, using genetic programming to discover the language (structure) of the model fuzzy sets and evidential rules for knowledge representation, while relying on the well-developed probability theory for learning the parameters of the model.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Almuallim, H., and Dietterich, T. G. (1991). “Learning with irrelevant features.” In the proceedings of AAAI-91, Anaheim, CA, 547–552.
Baldwin, J. F. (1991). “Combining evidences for evidential reasoning”, International Journal of Intelligent Systems, 6(6):569–616.
Baldwin, J. F. (1993). “Evidential Support logic, FRIL and Cased Base Reasoning”, Int. J. of Intelligent Systems, 8(9):939–961.
Baldwin, J. F., Martin, T. P., and Pilsworth, B. W. (1995). FRIL — Fuzzy and Evidential Reasoning in A.I. Research Studies Press (Wiley Inc.), ISBN 086380159 5.
Baldwin, J. F., Martin, T. P., and Shanahan, J. G. (1997a). “Fuzzy logic methods in vision recognition.” In the proceedings of Fuzzy Logic: Applications and Future Directions Workshop, London, UK, 300–316.
Baldwin, J. F., Martin, T. P., and Shanahan, J. G. (1997b). “Modelling with words using Cartesian granule features.” In the proceedings of FUZZ-IEEE, Barcelona, Spain, 1295–1300.
Baldwin, J. F., Martin, T. P., and Shanahan, J. G. (1997c). “Structure identification of fuzzy Cartesian granule feature models using genetic programming.” In the proceedings of IJCAI Workshop on Fuzzy Logic in Artificial Intelligence, Nagoya, Japan, 1–11.
Baldwin, J. F., Martin, T. P., and Shanahan, J. G. (1998). “System Identification of Fuzzy Cartesian Granule Feature Models using Genetic Programming”, In IJCAI Workshop on Fuzzy Logic in Artificial Intelligence, Lecture notes in Artificial Intelligence (LNAI 1566) — Fuzzy Logic in Artificial Intelligence, A. L. Ralescu and J. G. Shanahan, eds., Springer, Berlin, 91–116.
Baldwin, J. F., and Pilsworth, B. W. (1997). “Genetic Programming for Knowledge Extraction of Fuzzy Rules.” In the proceedings of Fuzzy Logic: Applications and Future Directions Workshop, London, UK, 238–251.
Bastian, A. (1995). “Modelling and Identifying Fuzzy Systems under varying User Knowledge”, PhD Thesis, Meiji University, Tokyo.
Bezdek, J. C. (1976). “A Physical Interpretation of Fuzzy ISODATA”, IEEE Trans. on System, Man, and Cybernetics, 6(5):387–390.
Bezdek, J. C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York.
Bishop, C. M. (1995). Neural Networks for Pattern Recognition. Clarendon Press, Oxford.
Blum, A. L., and Langley, P. (1997). “Selection of relevant features and examples in machine learning”, Artificial Intelligence, 97:245–271.
Bossley, K. M. (1997). “Neurofuzzy Modelling Approaches in System Identification”, PhD Thesis, Department of Electrical and Computer Science, Southampton University, Southampton, UK.
Bouchon-Meunier, B., Marsala, C., and Ramdani, M. (1997). “Learning from Imperfect Data”, In Fuzzy Information Engineering, H. P. D. Dubois, R. R. Yager, ed., Wiley &Sons, Inc., New York.
Devijver, P. A., and Kittler, J. (1982). Pattern Recognition: A Statistical Approach. Prentice-Hall, Englewood Cliffs, NJ.
Dietterich, T. G., and Michalski, R. S. (1983). “A comparative review of selected methods for learning from examples”, In Machine Learning: An Artificial Intelligence Approach, R. S. Michalski, J. G. Carbonell, and T. M. Mitchell, eds., Springer-Verlag, Berlin, 41–81.
Fletcher, G. P., and Hinde, C. J. (1995). “Using neural networks for constructing rule based systems”, Knowledge Based Systems, 8(4): 183–189.
Geman, S., Bienenstock, E., and Doursat, R. (1992). “Neural networks and the bias/variance dilemma”, Neural computation, 4:1–58.
Goldberg, D. E., and Deb, K. (1991). “A comparative analysis of selection schemes used in genetic algorithms”, In Foundations of Genetic Algorithms, G. Rawlins, ed., Morgan Kaufmann, San Francisco.
Grabisch, M., and Nicolas, J. (1994). “Classification by fuzzy integral: Performance and tests”, Fuzzy Sets and Systems, 65:255–271.
Hertz, J., Anders, K., and Palmer, R. G. (1991). Introduction to the Theory of Neural Computation. Addison-Wesley, New York.
Hinde, C. J. (1997). “Intelligible interpretation of neural networks.” In the proceedings of Fuzzy Logic: Applications and Future Directions Workshop, London, UK, 95-122.
Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Michigan.
Ivanhnenko, A. G. (1971). “Polynomial theory of complex systems”, IEEE Transactions on Systems, Man and Cybernetics, 1(4):363–378.
Jang, J. S. R. (1994). “Structure Determination in Fuzzy Modelling.” In the proceedings of International Conference on Fuzzy Systems, 480-485.
Jolliffe, I. T. (1986). Principal Component Analysis. Springer, New York.
Kalvi, T. (1993). “ASMOD: an algorithm for Adaptive Spline Modelling of Observation Data”, International Journal of Control, 58(4):947–968.
Kira, K., and Rendell, L. (1992). “A practical approach to feature selection.” In the proceedings of 9th Conference in Machine Learning, Aberdeen, Scotland, 249-256.
Klir, G. J., and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic, Theory and Applications. Prentice Hall, New Jersey.
Kohavi, R., and John, G. H. (1997). “Wrappers for feature selection”, Artificial Intelligence, 97:273–324.
Kohonen, T. (1984). Self-Organisation and Associative Memory. Springer-Verlag, Berlin.
Kononenko, I., and Hong, S. J. (1997). “Attribute selection for modelling”, FGCS Special Issue in Data Mining(Fall):34-55.
Koza, J. R. (1992). Genetic Programming. MIT Press, Massachusetts.
Koza, J. R. (1994). Genetic Programming II. MIT Press, Massachusetts.
Lawrence, S., Burns, I., Back, A., Tsos, A. C., and Giles, C. L. (1999). “Neural network classification and prior probabilities”, In Tricks of the trade, Lecture notes in computer science, G. Orr, K. R. Muller, and R. Caruana, eds., Springer-Verlag, New York, 20–36.
Ljung, L. (1987). System identification: theory for the user. Prentice Hall, Englewood Cliffs, New Jersey, U.S.A.
Minsky, M., and Papert, S. (1969). Perceptrons: An introduction to computational geometry. M.I.T. Press, Cambridge, MA.
Moller, M. F. (1993). “A scaled conjugate gradient algorithm for fast supervised learning”, Neural Networks, 6:525–533.
Powell, M. J. D. (1964). “An efficient method for finding the minimum of a function of several variables without calculating derivatives”, The Computer Journal, 7:155–162.
Quinlan, J. R. (1986). “Induction of Decision Trees”, Machine Learning, 1(1):86–106.
Shanahan, J. G. (1998). “Cartesian Granule Features: Knowledge Discovery of Additive Models for Classification and Prediction”, PhD Thesis, Dept. of Engineering Mathematics, University of Bristol, Bristol, UK.
Shanahan, J. G., Baldwin, J. F., and Martin, T. P. (1999). “Constructive induction of fuzzy Cartesian granule feature models using Genetic Programming with Applications.” In the proceedings of Congress of Evolutionary Computation (CEC), Washington D.C., 218–225.
Syswerda, G. (1989). “Uniform crossover in genetic algorithms”, In Third Int’l Conference on Genetic Algorithms, J. D. Schaffer, ed., Morgan Kaufmann, San Francisco, USA, 989–995.
Tackett, W. A. (1995). “Mining the Genetic Program”, IEEE Expert, 6:28–28.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Kluwer Academic Publishers
About this chapter
Cite this chapter
Shanahan, J.G. (2000). Learning Cartesian Granule Feature Models. In: Soft Computing for Knowledge Discovery. The Springer International Series in Engineering and Computer Science, vol 570. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4335-0_9
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4335-0_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6947-9
Online ISBN: 978-1-4615-4335-0
eBook Packages: Springer Book Archive