Geometry Flow-Based Deep Riemannian Metric Learning

Deep metric learning (DML) has achieved great results on visual understanding tasks by seamlessly integrating conventional metric learning with deep neural networks. Existing deep metric learning methods focus on designing pair-based distance loss to decrease intra-class distance while increasing interclass distance. However, these methods fail to preserve the geometric structure of data in the embedding space, which leads to the spatial structure shift across mini-batches and may slow down the convergence of embedding learning. To alleviate these issues, by assuming that the input data is embedded in a lower-dimensional sub-manifold, we propose a novel deep Riemannian metric learning (DRML) framework that exploits the non-Euclidean geometric structural information. Considering that the curvature information of data measures how much the Riemannian (non-Euclidean) metric deviates from the Euclidean metric, we leverage geometry flow, which is called a geometric evolution equation, to characterize the relation between the Riemannian metric and its curvature. Our DRML not only regularizes the local neigh-borhoods connection of the embeddings at the hidden layer but also adapts the embeddings to preserve the geometric structure of the data. On several benchmark datasets, the proposed DRML outperforms all existing methods and these results demonstrate its effectiveness.