A Comparison of Three Approximation Strategies for Incomplete Data Sets

In this paper we consider incomplete data sets, i.e., data sets with missing attribute values. Two different types of missing attribute values are studied: lost and "do not care". Furthermore, three definitions of approximations are discussed: singleton, subset, and concept. Theoretically, singleton approximations should not be used in data mining since concepts approximated by singleton approximations are not definable. However, we conducted a number of experiments on 44 different incomplete data sets using all three approximation definitions and our results show that none of these approximations is superior to the other.