The Choquet-integral as an aggregation operator in case-based learning

Abstract

In case-based learning, various types of aggregation problems have to be solved. In particular, proceeding from an attribute-value representation of cases, a (global) similarity measure for (pairs of) cases is commonly derived from local similarity functions pertaining to individual attributes. Moreover, in connection with the nearest neighbor estimation principle, an aggregation operator is needed in order to combine the votes coming from the query's neighbors. In this paper, we argue that considering potential interdependencies between individual pieces of information (like similarity degrees or votes) is quite important in the context of case-based learning. In this connection, we advocate the Choquet integral as a suitable aggregation operator. In particular, we introduce a method called Cho-κ-NN, which generalizes the weighted nearest neighbor estimation by taking the mutual similarities between the query's neighbors into account. Besides, we suggest using the Choquet integral in order to combine local similarity functions into global measures.