Scalable methods for nonnegative matrix factorizations of near-separable tall-and-skinny matrices
This work addresses scalability issues in NMF for large-scale data in fields like scientific computing and bioinformatics, though it is incremental as it builds on existing near-separable NMF algorithms.
The paper tackles the problem of making nonnegative matrix factorization algorithms efficient for tall-and-skinny matrices by introducing an orthogonal transformation that preserves separability, resulting in single-pass methods suitable for streaming and distributed architectures, demonstrated on terabyte-sized synthetic and real-world datasets.
Numerous algorithms are used for nonnegative matrix factorization under the assumption that the matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than columns, so-called "tall-and-skinny matrices". One key component to these improved methods is an orthogonal matrix transformation that preserves the separability of the NMF problem. Our final methods need a single pass over the data matrix and are suitable for streaming, multi-core, and MapReduce architectures. We demonstrate the efficacy of these algorithms on terabyte-sized synthetic matrices and real-world matrices from scientific computing and bioinformatics.