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- W4301490846 abstract "Motivated by an application in computational biology, we consider low-rank matrix factorization with ${0,1}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared with other matrix factorization schemes, our problem is further complicated by a combinatorial constraint set of size $2^{m cdot r}$, where $m$ is the dimension of the data points and $r$ the rank of the factorization. Despite apparent intractability, we provide - in the line of recent work on non-negative matrix factorization by Arora et al. (2012) - an algorithm that provably recovers the underlying factorization in the exact case with $O(m r 2^r + mnr + r^2 n)$ operations for $n$ datapoints. To obtain this result, we use theory around the Littlewood-Offord lemma from combinatorics." @default.
- W4301490846 created "2022-10-05" @default.
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- W4301490846 date "2014-01-23" @default.
- W4301490846 modified "2023-10-16" @default.
- W4301490846 title "Matrix factorization with Binary Components" @default.
- W4301490846 doi "https://doi.org/10.48550/arxiv.1401.6024" @default.
- W4301490846 hasPublicationYear "2014" @default.
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