Distance metric learning has been widely used to obtain the optimal distance function based on the given training data. We focus on a triplet-based loss function, which imposes a penalty such that a pair of instances in the same class is closer than a pair in different classes. However, the number of possible triplets can be quite large even for a small data set, and this considerably increases the computational cost for metric optimization. In this letter, we propose safe triplet screening that identifies triplets that can be safely removed from the optimization problem without losing the optimality. In comparison with existing safe screening studies, triplet screening is particularly significant because of the huge number of possible triplets and the semidefinite constraint in the optimization problem. We demonstrate and verify the effectiveness of our screening rules by using several benchmark data sets.

中文翻译：

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用于远程度量学习的安全三重筛查

距离度量学习已被广​​泛用于根据给定的训练数据获得最佳距离函数。我们专注于基于三元组的损失函数，它施加惩罚，使得同一类中的一对实例比不同类中的一对更接近。然而，即使对于小数据集，可能的三元组的数量也可能非常大，这大大增加了度量优化的计算成本。在这封信中，我们提出了安全三元组筛选，以识别可以安全地从优化问题中移除而不会失去最优性的三元组。与现有的安全筛选研究相比，三重筛选尤其重要，因为可能的三重筛选数量庞大，优化问题中存在半定约束。