Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: 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.

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