Recently, deep metric learning techniques received attention, as the learned distance representations are useful to capture the similarity relationship among samples and further improve the performance of various of supervised or unsupervised learning tasks. We propose a novel supervised metric learning method that can learn the distance metrics in both geometric and probabilistic space for image recognition. In contrast to the previous metric learning methods which usually focus on learning the distance metrics in Euclidean space, our proposed method is able to learn better distance representation in a hybrid approach. To achieve this, we proposed a Generalized Hybrid Metric Loss (GHM-Loss) to learn the general hybrid proximity features from the image data by controlling the trade-off between geometric proximity and probabilistic proximity. To evaluate the effectiveness of our method, we first provide theoretical derivations and proofs of the proposed loss function, then we perform extensive experiments on two public datasets to show the advantage of our method compared to other state-of-the-art metric learning methods.

翻译：近年来，深度度量学习技术备受关注，因为其学习到的距离表示能够有效捕捉样本间的相似性关系，从而进一步提升各类监督或无监督学习任务的性能。我们提出一种新颖的监督度量学习方法，能够在几何空间和概率空间中同时学习距离度量，以用于图像识别。与以往通常仅关注在欧几里得空间学习距离度量的方法不同，我们的方法能够以混合方式学习到更优的距离表示。为此，我们提出通用混合度量损失（GHM-Loss），通过控制几何邻近性与概率邻近性之间的权衡，从图像数据中学习通用的混合邻近特征。为了评估本方法的有效性，我们首先对所提出的损失函数进行了理论推导与证明，随后在两个公开数据集上进行了大量实验，展示了本方法相较于其他先进度量学习方法的优势。