instruction:
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.
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:
We investigate crowdsourcing algorithms for finding the top-quality item within a large collection of objects with unknown intrinsic quality values. This is an important problem with many relevant applications, for example in networked recommendation systems. The core of the algorithms is that objects are distributed to crowd workers, who return a noisy evaluation. All received evaluations are then combined, to identify the top-quality object. We first present a simple probabilistic model for the system under investigation. Then, we devise and study a class of efficient adaptive algorithms to assign in an effective way objects to workers. We compare the performance of several algorithms, which correspond to different choices of the design parameters/metrics. We finally compare our approach based on scoring object qualities against traditional proposals based on comparisons and tournaments.
answer:
Selecting the top-quality item through crowd scoring

question:
We consider a broad class of first-order optimization algorithms which are oblivious, in the sense that their step sizes are scheduled regardless of the function under consideration, except for limited sideinformation such as smoothness or strong convexity parameters. With the knowledge of these two parameters, we show that any such algorithm attains an iteration complexity lower bound of ( L/o) for L-smooth convex functions, and ( L/ ln(1/o)) for L-smooth -strongly convex functions. These lower bounds are stronger than those in the traditional oracle model, as they hold independently of the dimension. To attain these, we abandon the oracle model in favor of a structure-based approach which builds upon a framework recently proposed in [1]. We further show that without knowing the strong convexity parameter, it is impossible to attain an iteration complexity better than ((L/) ln(1/o)). This result is then used to formalize an observation regarding L-smooth convex functions, namely, that the iteration complexity of algorithms employing time-invariant step sizes must be at least (L/o).
answer:
On the Iteration Complexity of Oblivious First-Order Optimization Algorithms