将时间序列异常检测建模为球面表示学习，提升分布外识别能力。
Learning Hyperspherical Time-Frequency Representations for Time-Series Out-of-Distribution Detection
- 在单位球面上用vMF分布建模类别条件结构，融合时频域编码器
- 在UCR/UEA全数据集上，k-NN与马氏距离评分均优于对比学习基线
- 适合需要高可靠性异常检测的时间序列场景，如工业监控
时间序列的分布外（OOD）检测相较于视觉和自然语言任务仍研究不足，且对如何利用监督式时间序列表示应对分布偏移缺乏系统理解。本文将时间序列OOD检测建模为超球面嵌入的表示学习，通过单位球面上的冯·米塞斯-费舍尔（vMF）似然函数诱导类别条件结构。所学表示通过领域特定编码器融合时域与频域信息，构建联合嵌入空间以支持检测。检测基于嵌入空间的距离度量，包括k近邻（k-NN）和马氏距离。我们在完整的UCR与UEA时间序列存档上采用跨数据集协议进行了大规模评估。实验结果表明，在相同设置下，该方法在k-NN与马氏评分上均显著优于强对比学习及后处理基线。代码已公开于 https://github.com/tiiuae/hypertf-time-series-ood。
原文摘要 · Abstract (English)
Out-of-distribution (OOD) detection for time-series data remains comparatively underexplored compared to vision and language, with a limited principled understanding of how supervised time-series representations can be leveraged for reliable detection under distributional shifts. This work formulates time-series OOD detection as representation learning with hyperspherical embeddings, where class-conditional structure is induced by a von Mises-Fisher (vMF) likelihood-based objective on the unit sphere. The learned representation combines time- and frequency-domain views of the input signal via domain-specific encoders, integrating them into a joint embedding space for OOD detection. Detection uses distance-based scores over the learned embeddings, including k-nearest neighbors (k-NN) and Mahalanobis scores. We evaluate the approach at scale on the complete UCR and UEA time-series archives under a cross-dataset protocol. Empirical results show consistent improvements under both k-NN and Mahalanobis scoring over strong contrastive learning and post-hoc baselines in the same setting. Code is available at https://github.com/tiiuae/hypertf-time-series-ood.
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