标题： PARAFAC2$\times$N: 多模式数据在N个模式中漂移的耦合分解 显示英文标题

标题： PARAFAC2$\times$N: Coupled Decomposition of Multi-modal Data with Drift in N Modes

摘要： 可靠分析综合二维气相色谱-飞行时间质谱（GC$\times$GC-TOFMS）数据被认为是其广泛应用的主要瓶颈。 对于多个样本， GC$\times$GC-TOFMS 数据在特定色谱区域表现为一个四阶张量，包含 I 次质量谱采集、J 个质量通道、K 次调制和 L 个样本。 色谱漂移在第一维（调制）和第二维（质量谱采集）都很常见，而在质量通道和样本维度上的漂移实际上不存在。 已经提出了多种处理 GC$\times$GC-TOFMS 数据的解决方案：这些方案包括重塑数据以适应基于多元曲线分辨（MCR）的二阶分解技术，或三阶分解技术，如平行因子分析 2（PARAFAC2）。 PARAFAC2 已被用于建模沿某一模式的色谱漂移，这使其能够用于稳健分解多个 GC-MS 实验。 尽管可以扩展，但实现一个考虑多模式漂移的 PARAFAC2 模型并不简单。 在这份提交的文章中，我们展示了一种新的方法和一种通用理论，用于建模多模式漂移的数据，应用于具有多变量检测的多维色谱领域。 显示英文摘要

摘要： Reliable analysis of comprehensive two-dimensional gas chromatography - time-of-flight mass spectrometry (GC$\times$GC-TOFMS) data is considered to be a major bottleneck for its widespread application. For multiple samples, GC$\times$GC-TOFMS data for specific chromatographic regions manifests as a 4th order tensor of I mass spectral acquisitions, J mass channels, K modulations, and L samples. Chromatographic drift is common along both the first-dimension (modulations), and along the second-dimension (mass spectral acquisitions), while drift along the mass channel and sample dimensions is for all practical purposes nonexistent. A number of solutions to handling GC$\times$GC-TOFMS data have been proposed: these involve reshaping the data to make it amenable to either 2nd order decomposition techniques based on Multivariate Curve Resolution (MCR), or 3rd order decomposition techniques such as Parallel Factor Analysis 2 (PARAFAC2). PARAFAC2 has been utilised to model chromatographic drift along one mode, which has enabled its use for robust decomposition of multiple GC-MS experiments. Although extensible, it is not straightforward to implement a PARAFAC2 model that accounts for drift along multiple modes. In this submission, we demonstrate a new approach and a general theory for modelling data with drift along multiple modes, for applications in multidimensional chromatography with multivariate detection.