发表机构
University of Pennsylvania; ShanghaiTech University（宾夕法尼亚大学; 上海科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对函数型数据中的幅度与相位变化，提出AP-FAE框架，将潜在空间分解为幅度和相位嵌入，通过平滑解码器和保端点扭曲实现解纠缠，并在合成及真实数据上优于现有方法。
AI 中文摘要
函数型数据本质上是无限维的，并且常常表现出相位变化，即不同观测中对应事件发生的时间不同。现有的线性降维方法难以处理非线性幅度变化，而缺乏显式扭曲的函数自编码器会将时间错位与形状纠缠在一起。我们提出了幅度-相位函数自编码器（AP-FAE），这是一个用于函数型数据的无监督框架，涵盖单变量和多变量情形，重点是多变量设置，并将潜在空间分解为从所有通道导出的分离的幅度和相位嵌入。一个平滑的函数解码器在规范时间上重建特定通道的幅度函数，而一个共享的单调、保持端点的扭曲捕捉相位变化。我们证明了一个将幅度恢复与配准、重建和噪声误差联系起来的界限，并对其进行了数值验证。在合成数据和六个真实世界基准上，AP-FAE在大多数聚类和配准指标以及所有重建指标上优于最先进的基线。仅使用幅度嵌入进行聚类始终优于联合幅度-相位聚类，证实了显式解纠缠的益处。代码可在以下网址获取：https://this https URL }{ this https URL。
英文摘要
Functional data are intrinsically infinite-dimensional, and often exhibit phase variation, where corresponding events occur at different times across observations. Existing linear dimension reduction methods struggle with nonlinear amplitude variation, while functional autoencoders without an explicit warp entangle temporal misalignment with shape. We propose the Amplitude--Phase Functional Autoencoders (AP-FAE), an unsupervised framework for functional data that spans both univariate and multivariate cases, with emphasis on the multivariate setting, and factorizes the latent space into separate amplitude and phase embeddings derived from all channels. A smooth functional decoder reconstructs channel-specific amplitude functions in canonical time, and a shared monotone, endpoint-preserving warp captures phase variation. We prove a bound linking amplitude recovery to registration, reconstruction, and noise errors, and validate it numerically. Across synthetic data and six real-world benchmarks, AP-FAE outperforms state-of-the-art baselines on most clustering and alignment metrics and on all reconstruction metrics. Clustering with amplitude embeddings alone consistently surpasses joint amplitude--phase clustering, confirming the benefit of explicit disentanglement. Code is available at https://anonymous.4open.science/r/APFAE-418C/}{https://anonymous.4open.science/r/APFAE-418C/.
Comments26 pages, 13 figures
