标题： 基于几何学的源解析识别 显示英文标题

标题： Identification in source apportionment using geometry

摘要： 源解析分析旨在量化多种空气污染物观测浓度对特定来源的归属，可以表述为非负矩阵分解（NMF）问题。 然而，NMF是不唯一的，并且通常依赖于无法验证的假设，如稀疏性和不可解释的缩放。 在本文中，我们在更弱且更现实的条件下建立了源归属百分比矩阵的可识别性。 我们引入了该矩阵的总体估计量，并证明即使NMF因子不可识别，该估计量也是尺度不变且可识别的。 将数据视为圆锥壳中的点云，我们证明了一种源归属百分比矩阵的几何估计量是一致的，而无需任何稀疏性或参数分布假设，并且可以适应时空依赖性。 数值实验验证了这一理论。 显示英文摘要

摘要： Source apportionment analysis, which aims to quantify the attribution of observed concentrations of multiple air pollutants to specific sources, can be formulated as a non-negative matrix factorization (NMF) problem. However, NMF is non-unique and typically relies on unverifiable assumptions such as sparsity and uninterpretable scalings. In this manuscript, we establish identifiability of the source attribution percentage matrix under much weaker and more realistic conditions. We introduce the population-level estimand for this matrix, and show that it is scale-invariant and identifiable even when the NMF factors are not. Viewing the data as a point cloud in a conical hull, we show that a geometric estimator of the source attribution percentage matrix is consistent without any sparsity or parametric distributional assumptions, and while accommodating spatio-temporal dependence. Numerical experiments corroborate the theory.