Sesión 3: Cambios y corresponsabilidad en las familias (I)

FUZZYBEXA is the first algorithm that made use of the set covering methodology for the induction of fuzzy classification rules. Set covering has proven to be perfectly suitable for the induction of highly accurate and interpretable fuzzy rule sets. In this chapter we proposed the general fuzzy set covering framework, FCF. FCF consists of two top layers and a bottom layer implementing a specialization model. The top layers implement the fuzzy set covering methodology, and also apply various search heuristics for improving the performance of the framework. FCF is designed to allow the implementa- tion of various specialization models with different description languages and specialization behaviour. Since different covering algorithms (both fuzzy and crisp) all fit within the same framework, they can easily be characterized and compared. In the remainder of the dissertation we use the term FCF to refer to the collection of fuzzy set covering algorithms that fit within the framework.

We also proposed four specializations models for the framework, thereby bringing the total number of fuzzy set covering algorithms proposed in this dissertation to four. FUZZYSEEDSEARCH and FEM both use FuzzyAL as description language, and we have shown that FEM is a more general algorithm per- forming a more thorough search of its description space, while FUZZYSEEDSEARCH incorporates seed instances to guide its search. FUZZYPRISM and FUZZCONRI’s description language is FuzzyCDL. FUZZCONRI performs a more thorough search while FUZZYPRISM employs the fuzzy information gain to decide how to specialize. We compared the different specialization models by tracing the con- junctions generated during specialization in the lattice of concept descriptions of the respective descrip- tion languages. Finally, we presented a comparison of the different specialization models with respect to classification accuracy and search effort which substantiated the expectation that the more general and thorough algorithms would obtain better classification accuracy, require more search.

CHAPTER

10

Simultaneous Concept Learning

10.1

Introduction

Learning multiple concepts generally follows one of two strategies. (1) For a concept (or class) in the data set, a set of disjunctive rules are induced by repeating the learning procedure for each concept in turn. (2) Multiple concepts are learned by finding a good classification rule for any one of the con- cepts, and assigning this class as consequent of the rule. The literature, e.g. [Mitchell, 1997], offers no preference for one strategy over the other. We call the two strategies for this process iterated concept

learning (learning one class at a time, iterated over all classes) and simultaneous concept learning (si-

multaneously considering all classes by learning one rule at a time for any class, repeated until all data are covered), and abbreviate them as ICL and SCL, respectively. Examples of algorithms following the ICL strategy are FUZZYBEXA, BEXA, and Webb’s rule learner, whereas C4.5, CN2, and Neural Net- works all follow the SCL strategy [Cloete and van Zyl, 2006; Webb, 1993; Quinlan, 1996b; Clark and Niblett, 1989]. Fuzzy classification rules can be extracted from fuzzy decision trees and fuzzy neural networks, and although learning is done using SCL, unordered rule sets are obtained [Yuan and Shaw, 1995; Kasabov, 2001b].

FUZZYBEXAis the first algorithm to use set covering for the induction of fuzzy classification rules. The rule sets induced by FUZZYBEXAare unordered, and rules can be evaluated in any order. To the best of our knowledge, no work has been done on the induction of ordered fuzzy rule sets (also called decision lists), using any induction method. Here we mean that the induction method explicitly uses the order of rule induction, and not the ordering or prioritising of an unordered rule set after rule induction. The semantics of an ordered rule set is thus different from that of an unordered rule set. In an ordered rule set, as opposed to an unordered rule set, an instance is only matched against a rule (and the rule can thus only fire) if all previous rules did not fire. Thus, a single rule rule cannot be seen in isolation, and the antecedents of previous rules must also be considered.

In this chapter we introduce FUZZYBEXAII, the first fuzzy rule induction algorithm that induces fuzzy

decision lists. FUZZYBEXAII makes use of SCL for its induction process. This induction process produces an ordered rule set, and we show that in many cases this methodology produces superior results compared to ICL, i.e. on average better classification performance, radically smaller rule sets, and also significantly less search effort. We also introduce the fuzzy Accuracy function for rule evaluation in

Table 10.1:FUZZYBEXAII’s CoverConcepts procedure.

CoverConcepts

Input: Set of training instancesT , Set of concepts to learn C Output: A rule set describing the concepts

Set the current rule set to empty WhileT contains instances

best = FindBestRule(T , C) Addbest to the rule set

Remove the instances covered bybest Return the rule set

SCL, and demonstrate that this function is much better behaved for SCL learning than, for example, the fuzzy Entropy function used during SCL in fuzzy decision trees.

The layout of the chapter is as follows. In Section 10.2 we show how to extend FUZZYBEXA to use the SCL strategy. In the next section we show that the rule evaluation function plays a pivotal role in finding good classification rules, and we introduction the Accuracy function for SCL. In Section 10.4 we provide the results of five different experiments on nine data sets for FUZZYBEXA with ICL and SCL using several different evaluation functions, as well as an empirical comparison between FUZZYBEXAII and other concept learners. The following section contains a discussion of the experimental data, and Section 10.5 concludes the chapter.