Formal Concept Analysis With Background Knowledge: Attribute Priorities

This paper deals with background knowledge in knowledge extraction from binary data. A background knowledge represents an additional piece of information a user may have along with the input data. Such information can be considered as specifying the type of knowledge a user is looking for in the data. In particular, we emphasize the need for taking into account background knowledge in formal concept analysis. We present an approach to modeling background knowledge that represents user's priorities regarding attributes and their relative importance. Such priorities serve as a constraint-only those formal concepts that are compatible with user's priorities are considered relevant, extracted from data, and presented to the user. Our approach has two main practical features. First, the number of formal concepts presented to the user may get significantly reduced. As a result, the user is supplied with relevant formal concepts only and is not overloaded by a large number of possibly nonrelevant formal concepts. Second, different priorities lead to different pieces of knowledge extracted from data. This way, the input data may be repeatedly used in knowledge extraction for different purposes corresponding to different priorities. We concentrate on foundational aspects such as mathematical feasibility, reasoning with background knowledge, removing redundancy from background knowledge, and computational tractability, and present several illustrative examples. In addition, we discuss directions for future research.