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An Unsupervised Bayesian Distance Measure

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Advances in Case-Based Reasoning (EWCBR 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1898))

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Abstract

We introduce a distance measure based on the idea that two vectors are considered similar if they lead to similar predictive probability distributions. The suggested approach avoids the scaling problem inherent to many alternative techniques as the method automatically transforms the original attribute space to a probability space where all the numbers lie between 0 and 1. The method is also flexible in the sense that it allows different attribute types (discrete or continuous) in the same consistent framework. To study the validity of the suggested measure, we ran a series of experiments with publicly available data sets. The empirical results demonstrate that the unsupervised distance measure is sensible in the sense that it can be used for discovering the hidden clustering structure of the data.

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References

  1. D. Aha. A Study of Instance-Based Algorithms for Supervised Learning Tasks: Mathematical, Empirical, an Psychological Observations. PhD thesis, University of California, Irvine, 1990.

    Google Scholar 

  2. D. Aha, (editor). Lazy Learning. Kluwer Academic Publishers, Dordrecht, 1997. Reprinted from Artificial Intelligence Review, 11:1–5.

    MATH  Google Scholar 

  3. C. Atkeson, A. Moore, and S. Schaal. Locally weighted learning. In Aha [2], pages 11–73.

    Google Scholar 

  4. J. O. Berger. Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, New York, 1985.

    MATH  Google Scholar 

  5. C. Blake, E. Keogh, and C. Merz. UCI repository of machine learning databases, 1998. URL: http://www.ics.uci.edu/~nilearn/MLRepository.html.

  6. E. Castillo, J. Gutiérrez, and A. Hadi. Expert Systems and Probabilistic Network Models. Monographs in Computer Science. Springer-Verlag, New York, NY, 1997.

    Google Scholar 

  7. C. Chatfield and A. Collins. Introduction to Multivariate Analysis. Chapman and Hall, New York, 1980.

    MATH  Google Scholar 

  8. G. Cooper and E. Herskovits. A Bayesian method for the induction of probabilistic networks from data. Machine Learning, 9:309–347, 1992.

    MATH  Google Scholar 

  9. N. Friedman, D. Geiger, and M. Goldszmidt. Bayesian network classifiers. Machine Learning, 29:131–163, 1997.

    Article  MATH  Google Scholar 

  10. A. Gelman, J. Carlin, H. Stern, and D. Rubin. Bayesian Data Analysis. Chapman & Hall, 1995.

    Google Scholar 

  11. D. Heckerman, D. Geiger, and D. M. Chickering. Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning, 20(3):197–243, September 1995.

    Google Scholar 

  12. D. Heckerman and C. Meek. Models and selection criteria for regression and classification. In D. Geiger and P. Shenoy, (editors), Uncertainty in Arificial Intelligence 13, pages 223–228. Morgan Kaufmann Publishers, San Mateo, CA, 1997.

    Google Scholar 

  13. F. Jensen. An Introduction to Bayesian Networks. UCL Press, London, 1996.

    Google Scholar 

  14. T. Kohonen. Self-Organizing Maps. Springer-Verlag, Berlin, 1995.

    Google Scholar 

  15. J. Kolodner. Case-Based Reasoning. Morg.an Kaufmann Publishers, San Mateo, 1993.

    Google Scholar 

  16. P. Kontkanen, J. Lahtinen, P. Myllymäki, T. Silander, and H. Tirri. Using Bayesian networks for visualizing high-dimensional data. Intelligent Data Analysis, 2000. To appear.

    Google Scholar 

  17. P. Kontkanen, P. Myllymäki, T. Silander, and H. Tirri. BAYDA: Software for Bayesian classification and feature selection. In R. Agrawal, P. Stolorz, and G. Piatetsky-Shapiro, (editors), Proceedings of the Fourth International Conference on Knowledge Discovery and Data Mining (KDD-98), pages 254–258. AAAI Press, Menlo Park, 1998.

    Google Scholar 

  18. P. Kontkanen, P. Myllymäki, T. Silander, and H. Tirri. Bayes optimal instance-based learning. In C. Nédellec and C. Rouveirol, (editors), Machine Learning: ECML-98, Proceedings of the 10th European Conference, volume 1398 of Lecture Notes in Artificial Intelligence, pages 77–88. Springer-Verlag, 1998.

    Google Scholar 

  19. P. Kontkanen, P. Myllymäki, T. Silander, and H. Tirri. On Bayesian case matching. In B. Smyth and P. Cunningham, (editors), Advances in Case-Based Reasoning, Proceedings of the 4th European Workshop (EWCBR-98), volume 1488 of Lecture Notes in Artificial Intelligence, pages 13–24. Springer-Verlag, 1998.

    Google Scholar 

  20. P. Kontkanen, P. Myllymäki, T. Silander, and H. Tirri. On supervised selection of Bayesian networks. In K. Laskey and H. Prade, (editors), Proceedings of the 15th International Conference on Uncertainty in Artificial Intelligence (UAI’99), pages 334–342. Morgan Kaufmann Publishers, 1999.

    Google Scholar 

  21. P. Kontkanen, P. Myllymäki, T. Silander, H. Tirri, and P. Grünwald. On predictive distributions and Bayesian networks. Statistics and Computing, 10:39–54, 2000.

    Article  Google Scholar 

  22. A. Moore. Acquisition of dynamic control knowledge for a robotic manipulator. In Seventh International Machine Learning Workshop. Morgan Kaufmann, 1990.

    Google Scholar 

  23. R. E. Neapolitan. Probabilistic Reasoning in Expert Systems. John Wiley & Sons, New York, NY, 1990.

    Google Scholar 

  24. J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers, San Mateo, CA, 1988.

    Google Scholar 

  25. C. Stanfill and D. Waltz. Toward memory-based reasoning. Communications of the ACM, 29(12):1213–1228, 1986.

    Article  Google Scholar 

  26. H. Tirri, P. Kontkanen, and P. Myllymäki. Probabilistic instance-based learning. In L. Saitta, (editor), Machine Learning: Proceedings of the Thirteenth International Conference (ICML’96), pages 507–515. Morgan Kaufmann Publishers, 1996.

    Google Scholar 

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Kontkanen, P., Lahtinen, J., Myllymäki, P., Tirri, H. (2000). An Unsupervised Bayesian Distance Measure. In: Blanzieri, E., Portinale, L. (eds) Advances in Case-Based Reasoning. EWCBR 2000. Lecture Notes in Computer Science, vol 1898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44527-7_14

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  • DOI: https://doi.org/10.1007/3-540-44527-7_14

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  • Print ISBN: 978-3-540-67933-2

  • Online ISBN: 978-3-540-44527-2

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