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.

Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.
Top-N Recommendation on Graphs

Résumé. Le crowdsourcing, un enjeu économique majeur, est le fait d’externaliser une tâche interne d’une entreprise vers le grand-public, la foule. C’est ainsi une forme de sous-traitance digitale destinée à toute personne susceptible de pouvoir réaliser la tâche demandée généralement rapide et non automatisable. L’évaluation de la qualité du travail des participants est cependant un problème majeur en crowdsourcing. En effet, les contributions doivent être contrôlées pour assurer l’efficacité et la pertinence d’une campagne. Plusieurs méthodes ont été proposées pour évaluer le niveau d’expertise des participants. Ce travail a la particularité de proposer une méthode de calcul de degrés d’expertise en présence de données dont l’ordre de classement est connu. Les degrés d’expertise sont ensuite considérés sur des données sans ordre pré-établi. Cette méthode fondée sur la théorie des fonctions de croyance tient compte des incertitudes des réponses et est évaluée sur des données réelles d’une campagne réalisée en 2016.
Une mesure d’expertise pour le crowdsourcing

Aiming to unify known results about clustering mixtures of distributions under separation conditions, Kumar and Kannan [KK10] introduced a deterministic condition for clustering datasets. They showed that this single deterministic condition encompasses many previously studied clustering assumptions. More specifically, their proximity condition requires that in the target k-clustering, the projection of a point x onto the line joining its cluster center μ and some other center μ, is a large additive factor closer to μ than to μ. This additive factor can be roughly described as k times the spectral norm of the matrix representing the differences between the given (known) dataset and the means of the (unknown) target clustering. Clearly, the proximity condition implies center separation – the distance between any two centers must be as large as the above mentioned bound. In this paper we improve upon the work of Kumar and Kannan [KK10] along several axes. First, we weaken the center separation bound by a factor of √ k, and secondly we weaken the proximity condition by a factor of k (in other words, the revised separation condition is independent of k). Using these weaker bounds we still achieve the same guarantees when all points satisfy the proximity condition. Under the same weaker bounds, we achieve even better guarantees when only (1−ǫ)-fraction of the points satisfy the condition. Specifically, we correctly cluster all but a (ǫ + O(1/c))-fraction of the points, compared to O(kǫ)-fraction of [KK10], which is meaningful even in the particular setting when ǫ is a constant and k = ω(1). Most importantly, we greatly simplify the analysis of Kumar and Kannan. In fact, in the bulk of our analysis we ignore the proximity condition and use only center separation, along with the simple triangle and Markov inequalities. Yet these basic tools suffice to produce a clustering which (i) is correct on all but a constant fraction of the points, (ii) has k-means cost comparable to the k-means cost of the target clustering, and (iii) has centers very close to the target centers. Our improved separation condition allows us to match the results of the Planted Partition Model of McSherry [McS01], improve upon the results of Ostrovsky et al [ORSS06], and improve separation results for mixture of Gaussian models in a particular setting.

Improved Spectral-Norm Bounds for Clustering

