Closure-based constraints in formal concept analysis |
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Authors: | Radim Belohlavek Vilem Vychodil |
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Institution: | Data Analysis and Modeling Laboratory (DAMOL), Department of Computer Science, Palacky University, Olomouc, Czech Republic |
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Abstract: | We present a method of imposing constraints in extracting formal concepts (equivalently, closed itemsets or fixpoints of Galois connections) from a binary relation. The constraints are represented by closure operators and their purpose is to mimic background knowledge a user may have of the data. The idea is to consider and extract only these itemsets that are compatible with the background knowledge. As a result, the method extracts less clusters, those that are interesting from the user point of view, in a shorter time. The method makes it also possible to extract minimal bases of attribute dependencies in the input data that are compatible with the background knowledge. We provide examples of several particular types of constraints including those that appeared in the literature in the past and present algorithms to compute the constrained formal concepts and attribute implications. |
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Keywords: | Closure structure Binary relation Formal concept analysis Attribute implication Background knowledge Algorithms |
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