Effective expression feature representations generated by a triplet-based
deep metric learning are highly advantageous for facial expression recognition
(FER). The performance of triplet-based deep metric learning is contingent upon
identifying the best threshold for triplet loss. Threshold validation, however,
is tough and challenging, as the ideal threshold changes among datasets and
even across classes within the same dataset. In this paper, we present the
multi-threshold deep metric learning technique, which not only avoids the
difficult threshold validation but also vastly increases the capacity of
triplet loss learning to construct expression feature representations. We find
that each threshold of the triplet loss intrinsically determines a distinctive
distribution of inter-class variations and corresponds, thus, to a unique
expression feature representation. Therefore, rather than selecting a single
optimal threshold from a valid threshold range, we thoroughly sample thresholds
across the range, allowing the representation characteristics manifested by
thresholds within the range to be fully extracted and leveraged for FER. To
realize this approach, we partition the embedding layer of the deep metric
learning network into a collection of slices and model training these embedding
slices as an end-to-end multi-threshold deep metric learning problem. Each
embedding slice corresponds to a sample threshold and is learned by enforcing
the corresponding triplet loss, yielding a set of distinct expression features,
one for each embedding slice. It makes the embedding layer, which is composed
of a set of slices, a more informative and discriminative feature, hence
enhancing the FER accuracy. Extensive evaluations demonstrate the superior
performance of the proposed approach on both posed and spontaneous facial
expression datasets.

利用多阈值深度度量学习技术，通过提取不同阈值下的表情特征表示，可以大幅提高面部表情识别准确性。通过将嵌入层划分为一组切片，并采用多阈值深度度量学习算法，每个切片对应一个样本阈值，并通过对应的三元组损失进行学习，从而获得一组独特的表情特征，从而增强面部表情识别的准确性。在多个表情数据集上进行的实验评估显示了该方法的优越性能。