# HEAD-DT: Automatic Design of Decision-Tree Algorithms

## Abstract

As presented in Chap. 2, for the past 40 years researchers have attempted to improve decision-tree induction algorithms, either by proposing new splitting criteria for internal nodes, by investigating pruning strategies for avoiding overfitting, by testing new approaches for dealing with missing values, or even by searching for alternatives to the top-down greedy induction. Each new decision-tree induction algorithm presents some (or many) of these strategies, which are chosen in order to maximize performance in empirical analyses. Nevertheless, the number of different strategies for the several components of a decision-tree algorithm is so vast after these 40 years of research that it would be impracticable for a human being to test all possibilities with the purpose of achieving the best performance in a given data set (or in a set of data sets). Hence, we pose two questions for researchers in the area: “is it possible to automate the design of decision-tree induction algorithms?”, and, if so, “how can we automate the design of a decision-tree induction algorithm?” The answer for these questions arose with the pioneering work of Pappa and Freitas [30], which proposed the automatic design of rule induction algorithms through an evolutionary algorithm. The authors proposed the use of a grammar-based GP algorithm for building and evolving individuals which are, in fact, rule induction algorithms. That approach successfully employs EAs to evolve a generic rule induction algorithm, which can then be applied to solve many different classification problems, instead of evolving a specific set of rules tailored to a particular data set. As presented in Chap. 3, in the area of optimisation this type of approach is named hyper-heuristics (HHs) [5, 6]. HHs are search methods for automatically selecting and combining simpler heuristics, resulting in a generic heuristic that is used to solve any instance of a given optimisation problem. For instance, a HH can generate a generic heuristic for solving any instance of the timetabling problem (i.e., allocation of any number of resources subject to any set of constraints in any schedule configuration) whilst a conventional EA would just evolve a solution to one particular instance of the timetabling problem (i.e., a predefined set of resources and constraints in a given schedule configuration). In this chapter, we present a hyper-heuristic strategy for automatically designing decision-tree induction algorithms, namely HEAD-DT (Hyper-Heuristic Evolutionary Algorithm for Automatically Designing Decision-Tree Algorithms). Section 4.1 introduces HEAD-DT and its evolutionary scheme. Section 4.2 presents the individual representation adopted by HEAD-DT to evolve decision-tree algorithms, as well as information regarding each individual’s gene. Section 4.3 shows the evolutionary cycle of HEAD-DT, detailing its genetic operators. Section 4.4 depicts the fitness evaluation process in HEAD-DT, and introduces two possible frameworks for executing HEAD-DT. Section 4.5 computes the total size of the search space that HEAD-DT is capable of traversing, whereas Sect. 4.6 discusses related work.

## Keywords

Automatic design Hyper-heuristic decision-tree induction HEAD-DT## References

- 1.R.C. Barros, D.D. Ruiz, M.P. Basgalupp, Evolutionary model trees for handling continuous classes in machine learning. Inf. Sci.
**181**, 954–971 (2011)CrossRefGoogle Scholar - 2.R.C. Barros et al., Towards the automatic design of decision tree induction algorithm, in
*13th Annual Conference Companion on Genetic and Evolutionary Computation*(GECCO 2011). pp. 567–574 (2011)Google Scholar - 3.R.C. Barros et al., A survey of evolutionary algorithms for decision-tree induction. IEEE Trans. Syst., Man, Cybern., Part C: Appl. Rev.
**42**(3), 291–312 (2012)CrossRefMathSciNetGoogle Scholar - 4.L. Breiman et al.,
*Classification and Regression Trees*(Wadsworth, Belmont, 1984)zbMATHGoogle Scholar - 5.E. Burke, S. Petrovic, Recent research directions in automated timetabling. Eur. J. Oper. Res.
**140**(2), 266–280 (2002)CrossRefzbMATHGoogle Scholar - 6.E.K. Burke, G. Kendall, E. Soubeiga, A tabu-search hyperheuristic for timetabling and rostering. J. Heuristics
**9**(6), 451–470 (2003)CrossRefGoogle Scholar - 7.E.K. Burke et al., A Classification of Hyper-heuristics Approaches, in
*Handbook of Metaheuristics*, 2nd edn., International Series in Operations Research & Management Science, ed. by M. Gendreau, J.-Y. Potvin (Springer, Berlin, 2010), pp. 449–468CrossRefGoogle Scholar - 8.B. Cestnik, I. Bratko,
*On Estimating Probabilities in Tree Pruning*, Machine learning-EWSL-91. Vol. 482. Lecture Notes in Computer Science (Springer, Berlin, 1991)Google Scholar - 9.B. Chandra, P.P. Varghese, Moving towards efficient decision tree construction. Inf. Sci.
**179**(8), 1059–1069 (2009)CrossRefzbMATHGoogle Scholar - 10.B. Chandra, R. Kothari, P. Paul, A new node splitting measure for decision tree construction. Pattern Recognit.
**43**(8), 2725–2731 (2010)CrossRefzbMATHGoogle Scholar - 11.J. Ching, A. Wong, K. Chan, Class-dependent discretization for inductive learning from continuous and mixed-mode data. IEEE Trans. Pattern Anal. Mach. Intell.
**17**(7), 641–651 (1995)CrossRefGoogle Scholar - 12.P. Clark, T. Niblett, The CN2 induction algorithm. Mach. Learn.
**3**(4), 261–283 (1989)Google Scholar - 13.B. Delibasic et al., Component-based decision trees for classification. Intell. Data Anal.
**15**(5), 1–38 (2011)Google Scholar - 14.F. Esposito, D. Malerba, G. Semeraro, A comparative analysis of methods for pruning decision trees. IEEE Trans. Pattern Anal. Mach. Intell.
**19**(5), 476–491 (1997)CrossRefGoogle Scholar - 15.U. Fayyad, K. Irani, The attribute selection problem in decision tree generation, in
*National Conference on Artificial Intelligence*. pp. 104–110 (1992)Google Scholar - 16.A. Frank, A. Asuncion, UCI Machine Learning Repository (2010)Google Scholar
- 17.J.H. Friedman, A recursive partitioning decision rule for nonparametric classification. IEEE Trans. Comput.
**100**(4), 404–408 (1977)CrossRefGoogle Scholar - 18.M. Gleser, M. Collen, Towards automated medical decisions. Comput. Biomed. Res.
**5**(2), 180–189 (1972)CrossRefGoogle Scholar - 19.T. Ho, M. Basu, Complexity measures of supervised classification problems. IEEE Trans. Pattern Anal. Mach. Intell.
**24**(3), 289–300 (2002)CrossRefGoogle Scholar - 20.T. Ho, M. Basu, M. Law,
*Measures of Geometrical Complexity in Classification Problems*, Data Complexity in Pattern Recognition (Springer, London, 2006)Google Scholar - 21.B. Jun et al., A new criterion in selection and discretization of attributes for the generation of decision trees. IEEE Trans. Pattern Anal. Mach. Intell.
**19**(2), 1371–1375 (1997)CrossRefGoogle Scholar - 22.I. Kononenko, I. Bratko, E. Roskar, Experiments in automatic learning of medical diagnostic rules. Tech. rep. Ljubljana, Yugoslavia: Jozef Stefan Institute (1984)Google Scholar
- 23.W. Loh, Y. Shih, Split selection methods for classification trees. Stat. Sinica
**7**, 815–840 (1997)zbMATHMathSciNetGoogle Scholar - 24.R.L. De Mántaras,
*A Distance-Based Attribute Selection Measure for Decision Tree Induction*, Machine learning 6.1 (Kluwer, The Netherland, 1991). ISSN: 0885–6125Google Scholar - 25.J. Martin, An exact probability metric for decision tree splitting and stopping. Mach. Learn.
**28**(2), 257–291 (1997)CrossRefGoogle Scholar - 26.J. Mingers, Expert systems—rule induction with statistical data. J. Oper. Res. Soc.
**38**, 39–47 (1987)Google Scholar - 27.J. Mingers, An empirical comparison of selection measures for decision-tree induction. Mach. Learn.
**3**(4), 319–342 (1989)Google Scholar - 28.T. Niblett, I. Bratko, Learning decision rules in noisy domains, in
*6th Annual Technical Conference on Research and Development in Expert Systems III*. pp. 25–34 (1986)Google Scholar - 29.G.L. Pappa, Automatically Evolving Rule Induction Algorithms with Grammar-Based Genetic Programming. PhD thesis. University of Kent at Canterbury (2007)Google Scholar
- 30.G.L. Pappa, A.A. Freitas,
*Automating the Design of Data Mining Algorithms: An Evolutionary Computation Approach*(Springer Publishing Company, Incorporated, 2009)Google Scholar - 31.J.R. Quinlan, Induction of decision trees. Mach. Learn.
**1**(1), 81–106 (1986)Google Scholar - 32.J.R. Quinlan, Decision trees as probabilistic classifiers, in
*4th International Workshop on Machine Learning*(1987)Google Scholar - 33.J.R. Quinlan, Simplifying decision trees. Int. J. Man-Mach. Stud.
**27**, 221–234 (1987)CrossRefGoogle Scholar - 34.J.R. Quinlan, Unknown attribute values in induction, in
*6th International Workshop on Machine Learning*. pp. 164–168 (1989)Google Scholar - 35.J. R. Quinlan, C4.5: programs for machine learning. San Francisco: Morgan Kaufmann (1993). ISBN: 1-55860-238-0Google Scholar
- 36.C.E. Shannon, A mathematical theory of communication. BELL Syst. Tech. J.
**27**(1), 379–423, 625–56 (1948)Google Scholar - 37.P.C. Taylor, B.W. Silverman, Block diagrams and splitting criteria for classification trees. Stat. Comput.
**3**, 147–161 (1993)CrossRefGoogle Scholar - 38.A. Vella, D. Corne, C. Murphy, Hyper-heuristic decision tree induction, in
*World Congress on Nature and Biologically Inspired Computing*, pp. 409–414 (2010)Google Scholar - 39.I.H. Witten, E. Frank, Data mining: practical machine learning tools and techniques with java implementations. Morgan Kaufmann. ISBN: 1558605525 (1999)Google Scholar