  Non-negative Matrix Factorization (NMF) is an intensively used technique for
obtaining parts-based, lower dimensional and non-negative representation of
non-negative data. It is a popular method in different research fields.
Scientists performing research in the fields of biology, medicine and pharmacy
often prefer NMF over other dimensionality reduction approaches (such as PCA)
because the non-negativity of the approach naturally fits the characteristics
of the domain problem and its result is easier to analyze and understand.
Despite these advantages, it still can be hard to get exact characterization
and interpretation of the NMF's resulting latent factors due to their numerical
nature. On the other hand, rule-based approaches are often considered more
interpretable but lack the parts-based interpretation. In this work, we present
a version of the NMF approach that merges rule-based descriptions with
advantages of part-based representation offered by the NMF approach. Given the
numerical input data with non-negative entries and a set of rules with high
entity coverage, the approach creates the lower-dimensional non-negative
representation of the input data in such a way that its factors are described
by the appropriate subset of the input rules. In addition to revealing
important attributes for latent factors, it allows analyzing relations between
these attributes and provides the exact numerical intervals or categorical
values they take. The proposed approach provides numerous advantages in tasks
such as focused embedding or performing supervised multi-label NMF.
