This article describes one objective function for learning semantically coherent feature embeddings in multi-output classification problems, i.e., when the response variables have dimension higher than one. Such coherent embeddings can be used simultaneously for different tasks, such as identity retrieval and soft biometrics labelling. We propose a generalization of the triplet loss that: 1) defines a metric that considers the number of agreeing labels between pairs of elements; 2) introduces the concept of similar classes, according to the values provided by the metric; and 3) disregards the notion of anchor, sampling four arbitrary elements at each time, from where two pairs are defined. The distances between elements in each pair are imposed according to their semantic similarity (i.e., the number of agreeing labels). Likewise the triplet loss, our proposal also privileges small distances between positive pairs. However, the key novelty is to additionally enforce that the distance between elements of any other pair corresponds inversely to their semantic similarity. The proposed loss yields embeddings with a strong correspondence between the classes centroids and their semantic descriptions. In practice, it is a natural choice to jointly infer coarse (soft biometrics) + fine (ID) labels, using simple rules such as k-neighbours. Also, in opposition to its triplet counterpart, the proposed loss appears to be agnostic with regard to demanding criteria for mining learning instances (such as the semi-hard pairs). Our experiments were carried out in five different datasets (BIODI, LFW, IJB-A, Megaface and PETA) and validate our assumptions, showing results that are comparable to the state-of-the-art in both the identity retrieval and soft biometrics labelling tasks.

中文翻译：

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用于在多输出分类问题中实施语义一致嵌入的四元组损失


本文描述了一种目标函数，用于在多输出分类问题中学习语义连贯的特征嵌入，即当响应变量的维度大于一时。这种连贯嵌入可以同时用于不同的任务，例如身份检索和软生物识别标记。我们提出了三元组损失的概括：1）定义一个度量，考虑元素对之间一致标签的数量； 2）根据度量提供的值，引入相似类的概念； 3）忽略锚的概念，每次采样四个任意元素，从中定义两对。每对元素之间的距离是根据它们的语义相似性（即一致标签的数量）施加的。与三重态损失类似，我们的建议也优先考虑正对之间的小距离。然而，关键的新颖之处在于额外强制任何其他对的元素之间的距离与其语义相似性成反比。所提出的损失产生的嵌入在类质心与其语义描述之间具有很强的对应性。在实践中，使用 k 邻居等简单规则联合推断粗略（软生物识别）+ 精细（ID）标签是一个自然的选择。此外，与三元组相反，所提出的损失似乎与挖掘学习实例（例如半困难对）的严格标准无关。我们的实验在五个不同的数据集（BIODI、LFW、IJB-A、Megaface 和 PETA）中进行，并验证了我们的假设，显示的结果在身份检索和软生物识别标记方面可与最先进的技术相媲美任务。