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.

Q: Multi Sentence Compression (MSC) is of great value to many real world applications, such as guided microblog summarization, opinion summarization and newswire summarization. Recently, word graph-based approaches have been proposed and become popular in MSC. Their key assumption is that redundancy among a set of related sentences provides a reliable way to generate informative and grammatical sentences. In this paper, we propose an effective approach to enhance the word graph-based MSC and tackle the issue that most of the state-of-the-art MSC approaches are confronted with: i.e., improving both informativity and grammaticality at the same time. Our approach consists of three main components: (1) a merging method based on Multiword Expressions (MWE); (2) a mapping strategy based on synonymy between words; (3) a re-ranking step to identify the best compression candidates generated using a POS-based language model (POS-LM). We demonstrate the effectiveness of this novel approach using a dataset made of clusters of English newswire sentences. The observed improvements on informativity and grammaticality of the generated compressions show that our approach is superior to state-of-the-art MSC methods.

A: On Improving Informativity and Grammaticality for Multi-Sentence Compression
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Q: <lb>We consider a situation in which we see samples Xn ∈ R drawn i.i.d. from some<lb>distribution with mean zero and unknown covariance A. We wish to compute the<lb>top eigenvector of A in an incremental fashion with an algorithm that maintains<lb>an estimate of the top eigenvector in O(d) space, and incrementally adjusts the<lb>estimate with each new data point that arrives. Two classical such schemes are<lb>due to Krasulina (1969) and Oja (1983). We give finite-sample convergence rates<lb>for both.

A: The Fast Convergence of Incremental PCA
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Q: Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is little guarantee on how well these methods work. Recently a surge of research have focused on a very restricted class of NMFs, called separable NMF, where provably correct algorithms have been developed. In this paper, we propose the notion of subset-separable NMF, which substantially generalizes the property of separability. We show that subset-separability is a natural necessary condition for the factorization to be unique or to have minimum volume. We developed the Face-Intersect algorithm which provably and efficiently solves subset-separable NMF under natural conditions, and we prove that our algorithm is robust to small noise. We explored the performance of Face-Intersect on simulations and discuss settings where it empirically outperformed the state-of-art methods. Our work is a step towards finding provably correct algorithms that solve large classes of NMF problems.

A:
Intersecting Faces: Non-negative Matrix Factorization With New Guarantees
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