面向无监督域适应的稀疏正则最优传输模型

A Sparsity-Regularized Optimal Transport Model for Unsupervised Domain Adaptation

摘要: 无监督域适应旨在利用有标签的源域知识提升模型在无标签目标域上的性能。然而，现有方法大多依赖全局分布对齐来学习域不变特征，普遍面临以下挑战：相似性度量未能充分考虑数据内在的流形结构、域分布不平衡易导致对齐偏差，以及结果可解释性不强等。针对上述问题，本文提出一种基于扩散成本的稀疏正则最优传输模型。首先，基于扩散过程度量跨域样本在流形结构上的相似性，并结合源域标签信息构建成本矩阵，从而实现对非欧空间中跨分布样本相似性的准确刻画。其次，在目标函数中引入边际约束惩罚项，以增强模型对数据不平衡场景的适用性。此外，引入稀疏正则项来增强对齐样本间的可解释性，缓解由稠密传输计划引起的噪声误匹配问题。针对模型的非连续性特点，本文采用简化的SPG算法进行高效求解。最后，利用模型求解结果训练分类器，并在三组公开域适应数据集上进行实验评估，从准确率、精确率、召回率和F1分数四个指标对分类结果进行量化比较，实验结果表明，本文所提模型能够有效提升跨域分类精度，并缓解因域偏移与类别不平衡导致的分类偏差。

Abstract: Unsupervised domain adaptation aims to leverage labeled knowledge from a source domain to improve model performance on an unlabeled target domain. However, most existing methods rely on global distribution alignment to learn domain-invariant features, commonly facing the following challenges: similarity measures fail to adequately account for the intrinsic manifold structure of data; they are sensitive to domain distribution imbalance, which leads to biased alignment; and the interpretability of the alignment results remains limited. To address these issues, this paper proposes a diffusion sparse-regularization optimal transport. Specifically, a diffusion process is employed to measure cross-domain sample similarity on the underlying data manifold firstly. And then source domain label information is incorporated to construct the cost matrix, enabling accurate characterization of cross-distribution similarities in non-Euclidean spaces. Furthermore, a marginal constraint penalty term is introduced into the objective function to enhance robustness under imbalanced data scenarios. In addition, a sparsity regularization term is imposed to improve the interpretability of sample alignment and to mitigate noisy mismatches caused by dense transport plans. To efficiently solve the proposed non-smooth optimization problem, a simplified spectral projected gradient (SPG) algorithm is adopted. Finally, a classifier is trained based on the obtained transport plan, and extensive experiments are conducted on three public domain adaptation datasets. Quantitative evaluations in terms of accuracy, precision, recall, and F1-score demonstrate that the proposed method consistently improves cross-domain classification performance and effectively alleviates classification bias induced by domain shift and class imbalance.