Logical Discriminant Models

Discriminant analysis aims to classify multivariate observations into a priori defined classes and explain the differences between them. Logical discriminant type models — trees and rules — emerge in this context and within the data mining framework as powerful predictive tools that generate very easy to interpret results. Moreover, they generally provide means to deal with explantory variables of different measurement levels (quantitative and qualitative), good handling of missing data and robustness. These characteristics are particularly appreciated in management decision support.Discriminant analysis basic concepts and trees and rules algorithms are presented in this chapter. General issues concerning the evaluation of discriminant analysis and the key concept of diversity are outlined first. Tree algorithms, successively dividing a set of observations to conquer less diversity and increase accuracy, are described next. The induction of propositional rules, whether based on trees or yielded by a set covering approach, is also described. An application in retail and specific algorithms (e.g., CART, C5, CN2 and LEM) illusrate the logical discriminant methodologies. Final remarks provide a contextualisation of the diversity of contributions in this domain.