Logical Analysis of Data with Decomposable Structures

In such areas as knowledge discovery, data mining and logical analysis of data, methodologies to 0nd relations among attributes are considered important. In this paper, given a data set (T; F) where T ⊆ {0; 1}n denotes a set of positive examples and F ⊆ {0; 1}n denotes a set of negative examples, we propose a method to identify decomposable structures among the attributes of the data. We 0rst study computational complexity of the problem of 0nding decomposable Boolean extensions. Since the problem turns out to be intractable (i.e., NP-complete), we propose a heuristic algorithm in the second half of the paper. Our method searches a decomposable partition of the set of all attributes by using the error sizes of almost-0t decomposable extensions as a guiding measure, and then 0nds structural relations among the attributes in the obtained partition. Some results of numerical experiment on randomly generated data sets are also reported. c © 2002 Elsevier Science B.V. All rights reserved.