基于Schatten p-范数的监督分类度量学习
Supervised Categorical Metric Learning with Schatten p-Norms
摘要：
度量学习在学习适应数值数据集的新度量方面已经取得了成功。然而，它在分类数据上的发展仍需要进一步的探索。在本文中，我们提出了一种方法，称为CPML的\emph{categorical projected metric learning}，试图有效地~（即更少的计算时间和更好的预测精度）解决问题的度量学习分类数据。我们使用值距离度量来表示我们的数据，并基于此表示提出新的距离。然后，我们展示了如何有效地学习新的指标。我们还通过Schatten $p$ -范数推广了几个以前的正则化器，并为其提供了一个泛化界，补充了度量学习的标准泛化界。实验结果表明，我们的方法提供了
英文摘要：
Metric learning has been successful in learning new metrics adapted to numerical datasets. However, its development on categorical data still needs further exploration. In this paper, we propose a method, called CPML for \emph{categorical projected metric learning}, that tries to efficiently~(i.e. less computational time and better prediction accuracy) address the problem of metric learning in categorical data. We make use of the Value Distance Metric to represent our data and propose new distances based on this representation. We then show how to efficiently learn new metrics. We also generalize several previous regularizers through the Schatten $p$-norm and provides a generalization bound for it that complements the standard generalization bound for metric learning. Experimental results show that our method provides
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