Continuous-valued X-of-N Attributes Versus Nominal X-of-N Attributes for Constructive Induction: A Case Study

: An X-of-N is a set containing one or more attribute-value pairs. For a given instance, its value corresponds to the number of its attribute-value pairs that are true. In this paper, we explore the characteristics and performance of continuousvalued X-of-N attributes versus nominal X-of-N attributes for constructive induction. Nominal X-of-Ns are more representationally powerful than continuous-valued X-of-Ns, but the former suffer the "fragmentation" problem, although some mechanisms such as subsetting can help to solve the problem. Two approaches to constructive induction using continuous-valued X-of-Ns are described. Continuous-valued X-of-Ns perform better than nominal ones on domains that need X-of-Ns with only one cut point. On domains that need X-of-N representations with more than one cut point, nominal X-of-Ns perform better than continuous-valued ones. Experimental results on a set of artificial and real-world domains support these statements. 1. Introduction A wide variet..