Geometry Flow-Based Deep Riemannian Metric Learning  

作　　者：Yangyang Li Chaoqun Fei Chuanqing Wang Hongming Shan Ruqian Lu 

机构地区：[1]Key Lab of MADIS Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]IEEE [3]Institute of Science and Technology for Brain-Inspired Intelligence and Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence(Ministry of Education)and MOE Frontiers Center for Brain Science,Fudan University,Shanghai 200433 [4]Shanghai Center for Brain Science and Brain-Inspired Technology,Shanghai 200031,China

出　　处：《IEEE/CAA Journal of Automatica Sinica》2023年第9期1882-1892,共11页自动化学报（英文版）

基　　金：supported in part by the Young Elite Scientists Sponsorship Program by CAST(2022QNRC001);the National Natural Science Foundation of China(61621003,62101136);Natural Science Foundation of Shanghai(21ZR1403600);Shanghai Municipal Science and Technology Major Project(2018SHZDZX01);ZJLab,and Shanghai Municipal of Science and Technology Project(20JC1419500)。

摘　　要：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(nonEuclidean)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 neighborhoods 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.

关 键 词：Curvature regularization deep metric learning(DML) embedding learning geometry flow riemannian metric 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O186.12[自动化与计算机技术—控制科学与工程]