Cause-effect relationships and partially defined Boolean functions
Annals of Operations Research
Computational learning theory: an introduction
Computational learning theory: an introduction
Decomposability of partially defined Boolean functions
Discrete Applied Mathematics - Special volume on partitioning and decomposition in combinatorial optimization
Advances in knowledge discovery and data mining
Advances in knowledge discovery and data mining
Positive and Horn decomposability of partially defined Boolean functions
Discrete Applied Mathematics
Error-free and best-fit extensions of partially defined Boolean functions
Information and Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
An Implementation of Logical Analysis of Data
IEEE Transactions on Knowledge and Data Engineering
Multiway Cuts in Directed and Node Weighted Graphs
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
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In such areas as knowledge discovery, data mining and logical analysis of data, methodologies to find relations among attributes are considered important. In this paper, given a data set (T, F) of a phenomenon, 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. Such information will reveal hierarchical structure of the phenomenon under consideration. We first study computational complexity of the problem of finding 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-fit decomposable extensions as a guiding measure, and then finds structural relations among the attributes in the obtained partition. The results of numerical experiment on synthetically generated data sets are also reported.