Abstract
Cartesian granule features were originally introduced to address some of the shortcomings of existing forms of knowledge representation such as decomposition error and transparency, and also to enable the paradigm modelling with words through related learning algorithms. This chapter presents a detailed analysis of the impact of granularity on Cartesian granule features models that are learned from example data in the context of classification problems. This analysis provides insights on how to effectively model problems using Cartesian granule features using various levels of granulation, granule characterizations, granule dimensionalies and granule generation techniques. Other modelling with words approaches such as the data browser [1, 2] and fuzzy probabilistic decision trees [3] are also examined and compared. In addition, this chapter provides a useful platform for understanding many other learning algorithms that may or may not explicitly manipulate fuzzy events. For example, it is shown how a naive Bayes classifier is equivalent to crisp Cartesian granule feature classifiers under certain conditions.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Part of the work reported here was carried out while at the Advance Computing Research Centre, University of Bristol, Bristol, UK. This part of the work was supported by the European Community Marie Curie Fellowship Program and by DERA (UK) under grant 92W69.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baldwin, J. F., Martin, T. P., and Pilsworth, B. W. (1995). FRIL - Fuzzy and Evidential Reasoning in A.I. Research Studies Press(Wiley Inc.).
Baldwin, J. F., and Martin, T. P. (1995). “Fuzzy Modelling in an Intelligent Data Browser.” In the proceedings of FUZZ-IEEE, Yokohama, Japan, 11711176.
Baldwin, J. F., Lawry, J., and Martin, T. P. (1997). “Mass assignment fuzzy ID3 with applications.” In the proceedings of Fuzzy Logic: Applications and Future Directions Workshop, London, UK, 278–294.
Quinlan, J. R. (1986). “Induction of Decision Trees”, Machine Learning, 1 (1): 86–106.
Quinlan, J. R. (1993). C4. 5: Programs for Machine Learning. Morgan Kaufmann, San Mateo, CA.
Ruspini, E. H. (1969). “A New Approach to Clustering”, Inform. Control, 15 (1): 22–32.
Zadeh, L. A. (1994). “Soft Computing and Fuzzy Logic”, IEEE Software, 11 (6): 48–56.
Zadeh, L. A. (1996). “Fuzzy Logic = Computing with Words”, IEEE Transactions on Fuzzy Systems, 4 (2): 103–111.
Shanahan, J. G. (2000). Soft computing for knowledge discovery: Introducing Cartesian granule features. Kluwer Academic Publishers, Boston.
Baldwin, J. F., Martin, T. P., and Shanahan, J. G. (1998). “Aggregation in Cartesian granule feature models.” In the proceedings of IPMU, Paris, 6.
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.
Baldwin, J. F. (1993). “Evidential Support logic, FRIL and Case Based Reasoning”, Int. J. of Intelligent Systems, 8 (9): 939–961.
Baldwin, J. F., Lawry, J., and Martin, T. P. (1996). “Efficient Algorithms for Semantic Unification.” In the proceedings of IPMU, Granada, Spain, 527532.
Lindley, D. V. (1985). Making decisions. John Wiley, Chichester.
Kohavi, R., and John, G. H. (1997). “Wrappers for feature selection”, Artificial Intelligence, 97: 273–324.
Baldwin, J. F. (1995). “Machine Intelligence using Fuzzy Computing.” In the proceedings of ACRC Seminar (November),University of Bristol.
Miller, G. A. (1956). “The magical number seven, plus or minus two: some limits on our capacity to process information”, Psychological Review, 63: 8197.
Bezdek, J. C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York.
Kohonen, T. (1984). Self-Organisation and Associative Memory. Springer-Verlag, Berlin.
Sugeno, M., and Yasukawa, T. (1993). “A Fuzzy Logic Based Approach to Qualitative Modelling”, IEEE Trans on Fuzzy Systems, 1(1): 7–31.
Zadeh, L. A. (1994). “Soft computing”, LIFE Seminar, LIFE Laboratory, Yokohama, Japan (February, 24), published in SOFT Journal, 6:1–10.
Baldwin, J. F., Martin, T. P., and Shanahan, J. G. (1997). “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.
Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, New York.
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.
Baldwin, J. F., and Martin, T. P. (1999). “Basic concepts of a fuzzy logic data browser with applications”, Report No. ITRC 250, Dept. of Engineering Maths, University of Bristol.
Weiss, S. M., and Indurkhya, N. (1998). Predictive data mining: a practical guide. Morgan Kaufmann.
Zell, A., Mamier, G., Vogt, M., and Mache, N. (1995). SNNS (Stuggart Neural Network Simulator) Version 4.1. Institute for Parallel and Distributed High Performance Systems (NPR), Applied Computer Science, University of Stuggart, Stuggart, Germany.
Moller, M. F. (1993). “A scaled conjugate gradient algorithm for fast supervised learning”, Neural Networks, 6: 525–533.
Shanahan, J. G. (2000). “A comparison between naive Bayes classifiers and product Cartesian granule feature models”,Report No. In preparation, XRCE.
Breiman, L. (1996). “Bagging predictors”, Machine Learning, 66: 34–53.
Baldwin, J. F. (1992). “Fuzzy and Probabilistic Uncertainties”, In Encyclopaedia of AI, 2nd ed., Shapiro, ed., 528–537.
Baldwin, J. F. (1991). “Combining evidences for evidential reasoning”, International Journal of Intelligent Systems, 6 (6): 569–616.
Sudkamp, T. (1992). “On probability-possibility transformation”, Fuzzy Sets and Systems, 51: 73–81.
Zadeh, L. A. (1968). “Probability Measures of Fuzzy Events”, Journal of Mathematical Analysis and Applications, 23: 421–427.
Dubois, D., and Prade, H. (1983). “Unfair coins and necessary measures: towards a possibilistic interpretation of histograms”, Fuzzy sets and systems, 10: 15–20.
Baldwin, J. F. (1991). “A Theory of Mass Assignments for Artificial Intelligence”, In IJCAI ‘81 Workshops on Fuzzy Logic and Fuzzy Control, Sydney, Australia, Lecture Notes in Artificial Intelligence, A. L. Ralescu, ed., 22–34.
Klir, K. (1990). “A principle of uncertainty and information invariance”, International journal of general systems, 17 (2, 3): 249–275.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Shanahan, J.G. (2002). Knowledge Discovery with Words Using Cartesian Granule Features: An Analysis for Classification Problems. In: Lin, T.Y., Yao, Y.Y., Zadeh, L.A. (eds) Data Mining, Rough Sets and Granular Computing. Studies in Fuzziness and Soft Computing, vol 95. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1791-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1791-1_3
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2508-4
Online ISBN: 978-3-7908-1791-1
eBook Packages: Springer Book Archive