Transfer learning usually utilizes the knowledge learned from the relative labeled source domain to promote the model performance in the unlabeled or few labeled target domain with different distribution. Most of the existing transfer learning methods aim to reduce the discrepancy of distributions between the source and target domains, but ignore the discriminative category information involved in the data from both domains in the process of knowledge transfer. To learn more discriminative feature representation in knowledge transfer, this paper integrates the transfer learning and metric learning into a unified framework and proposes a novel robust transfer learning based on geometric mean metric learning, namely Geometric Mean Transfer Learning (GMTL). GMTL uses weighted geometric mean metric learning to model the intra-class distance and the inter-class similarity. In the meantime, the marginal distributions and conditional distributions of the source and target domains are jointly adapted. Moreover, according to the natures of the datasets in different tasks, we dynamically combine the discriminative modeling and domain adaption to make the proposed model more robust. We assign different weights to the intra-class distance and the inter-class similarity in metric learning and different weights to marginal distribution adaption and conditional distribution adaption, respectively. Finally, the solution to the objective function is converted to the problem of finding a point on the geodesic joining two points on the Riemannian manifold, which is very simple and direct. Extensive experiments are conducted on six datasets widely adopted in transfer learning to verify the superiority of our proposed GMTL over existing state-of-the-art transfer learning methods.

迁移学习通常利用从相对标记的源域中学到的知识来提升模型在不同分布的未标记或很少标记的目标域中的性能。现有的迁移学习方法大多旨在减少源域和目标域之间分布的差异，而忽略了知识迁移过程中来自两个域的数据所涉及的判别类别信息。为了在知识迁移中学习更具判别性的特征表示，本文将迁移学习和度量学习集成到一个统一的框架中，并提出了一种基于几何平均度量学习的新型鲁棒迁移学习，即几何平均迁移学习（GMTL）。GMTL 使用加权几何平均度量学习来建模类内距离和类间相似度。同时，源域和目标域的边缘分布和条件分布被联合调整。此外，根据不同任务中数据集的性质，我们动态地结合了判别建模和领域自适应，使所提出的模型更加健壮。我们为度量学习中的类内距离和类间相似度分配不同的权重，分别为边缘分布适应和条件分布适应分配不同的权重。最后将目标函数的解转化为在黎曼流形上连接两点的测地线上找一个点的问题，非常简单直接。