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: Consider Input: Metric learning has been shown to be highly effective to improve the performance of nearest neighbor classification. In this paper, we address the problem of metric learning for symmetric positive definite (SPD) matrices such as covariance matrices, which arise in many real-world applications. Naively using standard Mahalanobis metric learning methods under the Euclidean geometry for SPD matrices is not appropriate, because the difference of SPD matrices can be a non-SPD matrix and thus the obtained solution can be uninterpretable. To cope with this problem, we propose to use a properly parameterized LogEuclidean distance and optimize the metric with respect to kernel-target alignment, which is a supervised criterion for kernel learning. Then the resulting non-trivial optimization problem is solved by utilizing the Riemannian geometry. Finally, we experimentally demonstrate the usefulness of our LogEuclidean metric learning algorithm on real-world classification tasks for EEG signals and texture patches.

Output: Supervised LogEuclidean Metric Learning for Symmetric Positive Definite Matrices

Input: Consider Input: Concept maps can be used to concisely represent important information and bring structure into large document collections. Therefore, we study a variant of multidocument summarization that produces summaries in the form of concept maps. However, suitable evaluation datasets for this task are currently missing. To close this gap, we present a newly created corpus of concept maps that summarize heterogeneous collections of web documents on educational topics. It was created using a novel crowdsourcing approach that allows us to efficiently determine important elements in large document collections. We release the corpus along with a baseline system and proposed evaluation protocol to enable further research on this variant of summarization.

Output: Connecting the dots: Summarizing and Structuring Large Document Collections Using Concept Maps

Input: Consider Input: The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification problem using matrix completion on factorized matrix of minimized rank. We formulate relation classification as completing the unknown labels of testing items (entity pairs) in a sparse matrix that concatenates training and testing textual features with training labels. Our algorithmic framework is based on the assumption that the rank of item-by-feature and item-by-label joint matrix is low. We apply two optimization models to recover the underlying low-rank matrix leveraging the sparsity of featurelabel matrix. The matrix completion problem is then solved by the fixed point continuation (FPC) algorithm, which can find the global optimum. Experiments on two widely used datasets with different dimensions of textual features demonstrate that our low-rank matrix completion approach significantly outperforms the baseline and the state-of-the-art methods.
Output: Errata: Distant Supervision for Relation Extraction with Matrix Completion