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Volume 11 Issue 7
Jul.  2024

IEEE/CAA Journal of Automatica Sinica

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B. Xu, J. Yin, C. Lian, Y. Su, and  Z. Zeng,  “Low-rank optimal transport for robust domain adaptation,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 7, pp. 1667–1680, Jul. 2024. doi: 10.1109/JAS.2024.124344
Citation: B. Xu, J. Yin, C. Lian, Y. Su, and  Z. Zeng,  “Low-rank optimal transport for robust domain adaptation,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 7, pp. 1667–1680, Jul. 2024. doi: 10.1109/JAS.2024.124344

Low-Rank Optimal Transport for Robust Domain Adaptation

doi: 10.1109/JAS.2024.124344
Funds:  This work was supported by the National Natural Science Foundation of China (62206204, 62176193), the Natural Science Foundation of Hubei Province, China (2023AFB705), and the Natural Science Foundation of Chongqing, China (CSTB2023NSCQ-MSX0932)
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  • When encountering the distribution shift between the source (training) and target (test) domains, domain adaptation attempts to adjust the classifiers to be capable of dealing with different domains. Previous domain adaptation research has achieved a lot of success both in theory and practice under the assumption that all the examples in the source domain are well-labeled and of high quality. However, the methods consistently lose robustness in noisy settings where data from the source domain have corrupted labels or features which is common in reality. Therefore, robust domain adaptation has been introduced to deal with such problems. In this paper, we attempt to solve two interrelated problems with robust domain adaptation: distribution shift across domains and sample noises of the source domain. To disentangle these challenges, an optimal transport approach with low-rank constraints is applied to guide the domain adaptation model training process to avoid noisy information influence. For the domain shift problem, the optimal transport mechanism can learn the joint data representations between the source and target domains using a measurement of discrepancy and preserve the discriminative information. The rank constraint on the transport matrix can help recover the corrupted subspace structures and eliminate the noise to some extent when dealing with corrupted source data. The solution to this relaxed and regularized optimal transport framework is a convex optimization problem that can be solved using the Augmented Lagrange Multiplier method, whose convergence can be mathematically proved. The effectiveness of the proposed method is evaluated through extensive experiments on both synthetic and real-world datasets.

     

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    Highlights

    • A low-rank optimal transport algorithm is presented for the robust domain adaptation problem
    • Discrete formulation of optimal transport with low-rank constraints is solved by the Augmented Lagrange Multiplier method
    • The rank constraint on the transport matrix recovers the corrupted subspace structures and extracts the class structure information
    • The convergence of the low-rank regularized optimal transport algorithm is mathematically proved

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