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Formal concept analysis is a method of exploratory data analysis
that aims at the extraction of natural cluster from object-attribute
data tables. We present a way to add user's background knowledge to
formal concept analysis. The type of background knowledge we deal
with relates to relative importance of attributes in the input data.
We introduce EM operators which constrain in attributes of formal
concept analysis. The main aim is to make extraction of concepts
from the input data more focused by taking into account the
background knowledge. Particularly, only concepts which are
compatible with the constraint are extracted from data. Therefore,
the number of extracted concepts becomes smaller since we leave out
non-interesting concepts. We concentrate on foundational aspects
such as mathematical feasibility and computational tractability.