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Abstract:
Finding latent factors of the data using matrix factorizations is a
tried-and-tested approach in data mining. But finding shared factors over
multiple matrices is more novel problem. Specifically, given two matrices, we
want to find a set of factors shared by these two matrices and sets of factors
specific for the matrices. Not only does such decomposition reveal what is
common between the two matrices, it also eliminates the need of explaining that
common part twice, thus concentrating the non-shared factors to uniquely
specific parts of the data. This paper studies a problem called Joint Subspace
Boolean Matrix Factorization asking exactly that: a set of shared factors and
sets of specific factors. Furthermore, the matrix factorization is based on the
Boolean arithmetic. This restricts the presented approach suitable to only
binary matrices. The benefits, however, include much sparser factor matrices
and greater interpretability of the results. The paper presents three
algorithms for finding the Joint Subspace Boolean Matrix Factorization, an MDL-
based method for selecting the subspaces’ dimensionality, and throughout
experimental evaluation of the proposed algorithms.