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：近来，深度度量学习技术备受关注，因为学习到的距离表示能够有效捕捉样本间的相似关系，并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。与以往通常专注于在欧几里得空间中学习距离度量的度量学习方法不同，我们的方法能够以混合方式学习更优的距离表示。为实现这一目标，我们提出一种广义混合度量损失（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。为评估我们方法的有效性，我们首先对所提出的损失函数进行了理论推导和证明，接着在两个公开数据集上开展了大量实验，以展示我们的方法相较于其他最先进的度量学习方法的优势。