You will be given a definition of a task first, then some input of the task.
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.

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 2mr, 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(mr2r +mnr + rn) operations for n datapoints. To obtain this result, we use theory around the Littlewood-Offord lemma from combinatorics.
Output:
Matrix factorization with Binary Components