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.

The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained much interest in recent years in the context of large scale optimization and machine learning. A key advantage of the method is that it avoids projections the computational bottleneck in many applications replacing it by a linear optimization step. Despite this advantage, the known convergence rates of the FW method fall behind standard first order methods for most settings of interest. It is an active line of research to derive faster linear optimization-based algorithms for various settings of convex optimization. In this paper we consider the special case of optimization over strongly convex sets, for which we prove that the vanila FW method converges at a rate of 1 t2 . This gives a quadratic improvement in convergence rate compared to the general case, in which convergence is of the order 1t , and known to be tight. We show that various balls induced by `p norms, Schatten norms and group norms are strongly convex on one hand and on the other hand, linear optimization over these sets is straightforward and admits a closed-form solution. We further show how several previous fastrate results for the FW method follow easily from our analysis.
Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets

Latent Dirichlet Allocation (LDA) mining thematic structure of documents plays an important role in nature language processing and machine learning areas. However, the probability distribution from LDA only describes the statistical relationship of occurrences in the corpus and usually in practice, probability is not the best choice for feature representations. Recently, embedding methods have been proposed to represent words and documents by learning essential concepts and representations, such as Word2Vec and Doc2Vec. The embedded representations have shown more effectiveness than LDA-style representations in many tasks. In this paper, we propose the Topic2Vec approach which can learn topic representations in the same semantic vector space with words, as an alternative to probability. The experimental results show that Topic2Vec achieves interesting and meaningful results.
Topic2Vec: Learning Distributed Representations of Topics

This study implements a vector space model approach to measure the sentiment orientations of words. Two representative vectors for positive/negative polarity are constructed using high-dimensional vector space in both an unsupervised and a semisupervised manner. A sentiment orientation value per word is determined by taking the difference between the cosine distances against the two reference vectors. These two conditions (unsupervised and semi-supervised) are compared against an existing unsupervised method (Turney, 2002). As a result of our experiment, we demonstrate that this novel approach significantly outperforms the previous unsupervised approach and is more practical and data efficient as well.

A New Approach for Measuring Sentiment Orientation based on Multi-Dimensional Vector Space