Class-Selective Rejection Rules Based on the Aggregation of Pattern Soft Labels
Carl Frélicot, Hoel Le · InTech eBooks · 2010
The problem of aggregating collections of numerical data to obtain a typical value is present in many decision systems. Aggregation operators are used to obtain an overall value for each alternative, which is exploited to establish a final decision. In the context of supervised pattern classification, such a decision consists in assigning objects (or patterns) to one class based on the aggregation of soft labels related to the given classes (posterior probabilities, fuzzy membership degrees, typicality degrees). It is well known that overlapping classes and outliers can significantly decrease a classifier performance and it has been proved that the misclassification risk can significantly be reduced by allowing a classifier to reject extraneous and/or ambiguous patterns (Dubuisson & Masson, 1993), (Tax & Duin, 2008). This results in designing classification rules that allow to assign a pattern to zero (distance rejection), one (exclusive classification) or several (ambiguity rejection) classes, in other words to select a number of classes. This chapter addressed the problem of designing such rules that use ambiguity measures to aggregate pattern soft labels. The contribution is two-fold. An unified view of the resulting classifiers which can be either class-selective rules or simply rejection rules, depending on the ambiguity measure. Three families of ambiguity measures, based on combination of basic triangular norms and conorms as well as parametric ones, are presented. They allow to derive as many rules as many triangular norms (an infinite number!) and it is shown that they