Abstract
Predictions computed by a classification tree are usually constant on axis-parallel hyperrectangles corresponding to the leaves and have strict jumps on their boundaries. Frequently a better approximation may be expected, if the prediction function of the original tree is replaced by a continuous approximation. The approximation is constructed using the same training data on which the original tree was grown and the structure of the tree is preserved.
The current paper uses the model of trees with soft splits suggested by Quinlan and implemented in C4.5, however, the training algorithm is substantially different. The method uses simulated annealing, so it is quite computationally expensive. However, numerical test with data derived from an experiment in particle physics shows that besides the expected better approximation of the training data, also smaller generalization error is achieved.
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
Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J.: Classification and Regression Trees. Wadsworth, Belmont (1993)
Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers, San Mateo (1993)
Bock, R.K., Chilingarian, A., Gaug, M., Hakl, F., Hengstebeck, T., Jirina, M., Klaschka, J., Kotrč, E., Savický, P., Towers, S., Vaicilius, A.: Methods for multidimensional event classification: a case study using images from a Cherenkov gamma-ray telescope. Nuclear Instruments and Methods in Physics Research 516(2-3), 511–528 (2004)
Olaru, C., Wehenkel, L.: A complete fuzzy decision tree technique. Fuzzy Sets and Systems 138, 221–254 (2003)
Janikow, C.Z.: Fuzzy Decision Trees: Issues and Methods. IEEE Transactions on Systems, Man, and Cybernetics 28(1), 1–14 (1998)
R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2005), http://www.r-project.org
Heck, D., et al.: CORSIKA, A Monte Carlo code to simulate extensive air showers. Forschungszentrum Karlsruhe FZKA 6019 (1998)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Dvořák, J., Savický, P. (2007). Softening Splits in Decision Trees Using Simulated Annealing. In: Beliczynski, B., Dzielinski, A., Iwanowski, M., Ribeiro, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2007. Lecture Notes in Computer Science, vol 4431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71618-1_80
Download citation
DOI: https://doi.org/10.1007/978-3-540-71618-1_80
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71589-4
Online ISBN: 978-3-540-71618-1
eBook Packages: Computer ScienceComputer Science (R0)