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Volume 10 Issue 9
Sep.  2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2023  >  10(9): 1882-1892
Y. Y. Li, C. Q. Fei, C. Q. Wang, H. M. Shan, and R. Q. Lu, “Geometry flow-based deep riemannian metric learning,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 9, pp. 1882–1892, Sept. 2023. doi: 10.1109/JAS.2023.123399
Citation: Y. Y. Li, C. Q. Fei, C. Q. Wang, H. M. Shan, and R. Q. Lu, “Geometry flow-based deep riemannian metric learning,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 9, pp. 1882–1892, Sept. 2023. doi: 10.1109/JAS.2023.123399
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Geometry Flow-Based Deep Riemannian Metric Learning

doi: 10.1109/JAS.2023.123399
Funds:  This work was 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) and ZJLab, and Shanghai Municipal of Science and Technology Project (20JC1419500)
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    Abstract
  • 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 inter-class 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 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.

     

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    Highlights

    • A new deep Riemannian metric learning (DRML) is proposed via the geometry flow with adding the geometric structure as a regularization term to the hidden layer
    • DRML firstly uses the curvature information of feature distributions for the regularization of the deep metric learning
    • The effectiveness of DRML has been evaluated on the convergence of the embedding learning as well as the performance of the image clustering

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