当前位置: X-MOL 学术Spat. Stat. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Blind source separation for non-stationary random fields
Spatial Statistics ( IF 2.3 ) Pub Date : 2021-12-21 , DOI: 10.1016/j.spasta.2021.100574
Christoph Muehlmann 1 , François Bachoc 2 , Klaus Nordhausen 3
Affiliation  

Regional data analysis is concerned with the analysis and modeling of measurements that are spatially separated by specifically accounting for typical features of such data. Namely, measurements in close proximity tend to be more similar than the ones further separated. This might hold also true for cross-dependencies when multivariate spatial data is considered. Often, scientists are interested in linear transformations of such data which are easy to interpret and might be used as dimension reduction. Recently, for that purpose spatial blind source separation (SBSS) was introduced which assumes that the observed data are formed by a linear mixture of uncorrelated, weakly stationary random fields. However, in practical applications, it is well-known that when the spatial domain increases in size the weak stationarity assumptions can be violated in the sense that the second order dependency is varying over the domain which leads to non-stationary analysis. In our work we extend the SBSS model to adjust for these stationarity violations, present three novel estimators and establish the identifiability and affine equivariance property of the unmixing matrix functionals defining these estimators. In an extensive simulation study, we investigate the performance of our estimators and also show their use in the analysis of a geochemical dataset which is derived from the GEMAS geochemical mapping project.



中文翻译:

非平稳随机场的盲源分离

区域数据分析涉及通过专门考虑此类数据的典型特征而在空间上分离的测量值的分析和建模。也就是说,靠近的测量值往往比距离更远的测量值更相似。当考虑多元空间数据时,这也可能适用于交叉依赖关系。通常,科学家们对此类数据的线性变换感兴趣,这种变换易于解释并可用作降维。最近,为此目的引入了空间盲源分离 (SBSS),它假设观测数据是由不相关、弱平稳随机场的线性混合形成的。但在实际应用中,众所周知,当空间域的大小增加时,弱平稳性假设可能会被违反,因为二阶依赖性在域上发生变化,从而导致非平稳分析。在我们的工作中,我们扩展了 SBSS 模型以调整这些违反平稳性的行为,提出了三个新的估计量,并建立了定义这些估计量的分解矩阵泛函的可识别性和仿射等方差性质。在一项广泛的模拟研究中,我们调查了估算器的性能,并展示了它们在分析源自 GEMAS 地球化学绘图项目的地球化学数据集中的用途。在我们的工作中,我们扩展了 SBSS 模型以调整这些违反平稳性的行为,提出了三个新的估计量,并建立了定义这些估计量的分解矩阵泛函的可识别性和仿射等方差性质。在一项广泛的模拟研究中,我们调查了估算器的性能,并展示了它们在分析源自 GEMAS 地球化学绘图项目的地球化学数据集中的用途。在我们的工作中,我们扩展了 SBSS 模型以调整这些违反平稳性的行为,提出了三个新的估计量,并建立了定义这些估计量的分解矩阵泛函的可识别性和仿射等方差性质。在一项广泛的模拟研究中,我们调查了估算器的性能,并展示了它们在分析源自 GEMAS 地球化学绘图项目的地球化学数据集中的用途。

更新日期:2022-01-08
down
wechat
bug