While large volumes of unlabeled data are usually available, associated labels are often scarce. The unsupervised domain adaptation problem aims at exploiting labels from a source domain to classify data from a related, yet different, target domain. When time series are at stake, new difficulties arise as temporal shifts may appear in addition to the standard feature distribution shift. In this paper, we introduce the Match-And-Deform (MAD) approach that aims at finding correspondences between the source and target time series while allowing temporal distortions. The associated optimization problem simultaneously aligns the series thanks to an optimal transport loss and the time stamps through dynamic time warping. When embedded into a deep neural network, MAD helps learning new representations of time series that both align the domains and maximize the discriminative power of the network. Empirical studies on benchmark datasets and remote sensing data demonstrate that MAD makes meaningful sample-to-sample pairing and time shift estimation, reaching similar or better classification performance than state-of-the-art deep time series domain adaptation strategies.

翻译：尽管通常可以获得大量未标注数据，但相关标签往往稀缺。无监督域自适应问题旨在利用源域的标签对相关但不同的目标域数据进行分类。当涉及时间序列时，除标准特征分布偏移外，还可能出现时间偏移这一新挑战。本文提出"匹配与变形"（MAD）方法，该方法旨在允许时间变形的同时，找到源域与目标域时间序列之间的对应关系。相关优化问题通过最优传输损失与动态时间规整分别实现序列对齐和时间戳对齐。嵌入深度神经网络后，MAD有助于学习既能对齐域又能最大化网络判别能力的时间序列新表示。在基准数据集和遥感数据上的实证研究表明，MAD能够实现有意义的样本配对和时间偏移估计，达到与最先进的深度时间序列域自适应策略相似或更优的分类性能。