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Numerous algorithms are used for nonnegative matrix factorization under theassumption that the matrix is nearly separable. In this paper, we show how tomake these algorithms efficient for data matrices that have many more rows thancolumns, so-called "tall-and-skinny matrices". One key component to theseimproved methods is an orthogonal matrix transformation that preserves theseparability of the NMF problem. Our final methods need a single pass over thedata matrix and are suitable for streaming, multi-core, and MapReducearchitectures. We demonstrate the efficacy of these algorithms onterabyte-sized synthetic matrices and real-world matrices from scientificcomputing and bioinformatics.

Scalable methods for nonnegative matrix factorizations of near-separable tall-and-skinny matrices