Systems and Computers in Japan, Vol. 27, zyxwvu No. 7, 1996 zyxwvu Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J78-D-11, No. 10, October 1995, pp. 169-1478 Simplification of Majority-Voting Classifiers Using Binary Decision Diagrams Megumi Ishii, Yasuhiro Akiba and Shigeo Kaneda zyx "IT Communication Science Laboratories, Yokosuka, Japan 238 Hussein Almuallim King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia 31261 SUMMARY Various versions of the majority-voting class- ification method have been proposed in recent years as a strategy for improving classification performance. This method generates multiple decision trees from training examples and performs majority voting of classification results from these decision trees in order to classify test examples. In this method, however, since the target concept is represented in multiple decision trees, its readability is poor. This property makes it ineffective in knowledge-base construction. To enable the majority-voting classification method to be applied to knowledge-base construction, this paper proposes a simplificationmethod that con- verts the entire majority-voting classifier into compact disjunctive normal form (DNF) formulas. zyxwvu A significant feature of this method is the use of binary decision diagrams (BDDs) as internal expressionsin the conver- sion process to achieve high-speed simplification. A problem that must be addressed here is the BDD input variable ordering scheme. This paper proposes an ordering scheme based on the order of variables in the decision trees. The simplification method has been applied to several real-world data sets of the Irvine Database and to data from medical diagnosis domain. It was found that the description size of the majority-voting class- ifier after simplificationwas on the average from 1.2 to 25 2.7 times that of a single decision tree and was less than one-third the size of a majority-voting classifier before simplification. Therefore, the method is ef- fective in reducing the description size and should be applicable to the knowledge acquisition process. Using the input variable ordering scheme proposed here, high-speed simplification of several seconds to several tens of seconds is achieved on a Sun SPARC-sewer 10 workstation. Key words: Machine learning; knowledge acquisi- tion; ID3. 1. Introduction In recent years, majority-voting classification methods have been proposed for improving classifi- cation performance. In these methods, multiple deci- sion trees are generated from training examples through the use of the ID3 inductive learning algo- rithm, and a test example is classified by performing majority-voting over the classes indicated by these decision trees. The pattern classifierwhich is predicted as the target concept* by the majority-voting classifica- tion method is expressed by multiple decision trees *The target concept is a function which correctly classifies every example. ISSN0882- 1666/96/0007-0025 z 0 1996 Scripta Technica, Inc.