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.
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Question: 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.

Answer: Supervised LogEuclidean Metric Learning for Symmetric Positive Definite Matrices

Question: It has been a long time, since data mining technologies have made their ways to the field of data management. Classification is one of the most important data mining tasks for label prediction, categorization of objects into groups, advertisement and data management. In this paper, we focus on the standard classification problem which is predicting unknown labels in Euclidean space. Most efforts in Machine Learning communities are devoted to methods that use probabilistic algorithms which are heavy on Calculus and Linear Algebra. Most of these techniques have scalability issues for big data, and are hardly parallelizable if they are to maintain their high accuracies in their standard form. Sampling is a new direction for improving scalability, using many small parallel classifiers. In this paper, rather than conventional sampling methods, we focus on a discrete classification algorithm with O(n) expected running time. Our approach performs a similar task as sampling methods. However, we use column-wise sampling of data, rather than the row-wise sampling used in the literature. In either case, our algorithm is completely deterministic. Our algorithm, proposes a way of combining 2D convex hulls in order to achieve high classification accuracy as well as scalability in the same time. First, we thoroughly describe and prove our O(n) algorithm for finding the convex hull of a point set in 2D. Then, we show with experiments our classifier model built based on this idea is very competitive compared with existing sophisticated classification algorithms included in commercial statistical applications such as MATLAB.

Answer: DataGrinder: Fast, Accurate, Fully non-Parametric Classification Approach Using 2D Convex Hulls

Question: The Teacher Forcing algorithm trains recurrent networks by supplying observed sequence values as inputs during training and using the network's own one-stepahead predictions to do multi-step sampling. We introduce the Professor Forcing algorithm, which uses adversarial domain adaptation to encourage the dynamics of the recurrent network to be the same when training the network and when sampling from the network over multiple time steps. We apply Professor Forcing to language modeling, vocal synthesis on raw waveforms, handwriting generation, and image generation. Empirically we find that Professor Forcing acts as a regularizer, improving test likelihood on character level Penn Treebank and sequential MNIST. We also find that the model qualitatively improves samples, especially when sampling for a large number of time steps. This is supported by human evaluation of sample quality. Trade-offs between Professor Forcing and Scheduled Sampling are discussed. We produce T-SNEs showing that Professor Forcing successfully makes the dynamics of the network during training and sampling more similar.

Answer:
Professor Forcing: A New Algorithm for Training Recurrent Networks