When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods
that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete structure. Alternatively, we can first compute a continuous factorization and subsequently apply a rounding procedure to obtain a discrete representation. But what will we gain by rounding? Will this yield lower reconstruction errors? Is it easy
to find a low-rank matrix that rounds to a given binary matrix? Does it matter which threshold we use for rounding? Does it
matter if we allow for only non-negative factorizations? In this paper, we approach these and further questions by presenting
and studying the concept of rounding rank. We show that rounding rank is related to linear classification, dimensionality
reduction, and nested matrices. We also report on an extensive experimental study that compares different algorithms for finding good factorizations under the rounding rank model.
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