用几何方法统一对齐源域和目标域的均值与协方差，提升无监督领域适应性能。
Geometric Moment Alignment for Domain Adaptation via Siegel Embeddings
- 将一阶和二阶矩融合为对称正定矩阵，利用黎曼流形距离统一对齐
- 在图像去噪和分类任务上显著降低目标域误差，优于现有方法
- 适合关注领域自适应中分布对齐机制的研究者与工程师
针对无监督领域适应中的分布偏移问题，我们提出一种基于矩匹配的方法。现有方法通常在嵌入空间中通过随意相似性度量对齐源域和目标域的低阶统计矩。本文提出一种更严谨的方案，利用分布的内在几何结构，采用黎曼距离进行对齐。核心创新在于通过塞格尔嵌入将一阶与二阶矩表示为单一对称正定（SPD）矩阵，从而在共享的SPD矩阵流形上使用自然几何距离同时适应两个矩，保持源域与目标域的均值和协方差结构，实现更准确的跨域比较。我们建立了黎曼流形距离与目标域误差界之间的联系，并在图像去噪与图像分类基准上验证了方法的有效性。代码已公开于 https://github.com/shayangharib/GeoAdapt。
原文摘要 · Abstract (English)
We address the problem of distribution shift in unsupervised domain adaptation with a moment-matching approach. Existing methods typically align low-order statistical moments of the source and target distributions in an embedding space using ad-hoc similarity measures. We propose a principled alternative that instead leverages the intrinsic geometry of these distributions by adopting a Riemannian distance for this alignment. Our key novelty lies in expressing the first- and second-order moments as a single symmetric positive definite (SPD) matrix through Siegel embeddings. This enables simultaneous adaptation of both moments using the natural geometric distance on the shared manifold of SPD matrices, preserving the mean and covariance structure of the source and target distributions and yielding a more faithful metric for cross-domain comparison. We connect the Riemannian manifold distance to the target-domain error bound, and validate the method on image denoising and image classification benchmarks. Our code is publicly available at https://github.com/shayangharib/GeoAdapt.
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