Spatially orthogonal factor models for spatial transcriptomics and remote sensing data
面向空间转录组与遥感数据的空间正交因子模型AI 解读 ↓
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面向空间转录组与遥感数据的空间正交因子模型
- 研究问题
- 空间数据的概率主成分分析如何同时保留载荷正交性、允许非平稳空间先验，并使计算复杂度随空间位置数量线性增长？
- 方法与思路
- 作者直接参数化正交载荷，推导特殊奇异值结构下的变换分布及最大后验解，并设计 MM-EM 算法、留出位置处理与先验验证策略。
- 材料陈述的贡献
- 摘要称，该方法同时处理正交性、非平稳先验与线性计算问题，并在人脑空间转录组和撒哈拉以南非洲物候案例中应用。
- 阅读关注点
- 核对正交载荷先验的构造、最大后验特征分解公式的条件、线性复杂度所固定的维度，以及非平稳协方差的验证和选择方法。
- 阅读边界
- 这是 arXiv 预印本，同行评审及接收未核实；摘要未提供完整计算规模、误差比较与适用条件，应用对象也不是宏观或金融因子。
原文摘要
Principal component analyses are often applied to spatial data towards inference on latent modes of spatial variation. These analyses are widespread across domains including spatial transcriptomics and environmental sciences, where the modes of spatial variation are represented by corresponding factors of gene expression or remotely sensed time series measurements. Many methods have been proposed for incorporating spatial information into a probabilistic PCA framework; however, there are three main drawbacks to currently available approaches. First, the loadings matrices are not orthogonal, and subsequent orthogonalization of those loadings corrupts the original prior spatial information. Furthermore, currently proposed methods assume stationarity in their spatial prior. Finally, current methods typically do not achieve linear-time computational complexity with respect to the number of spatial locations. To resolve these problems, we first parameterize the model directly with orthogonal loadings. For the prior distribution, we derive the sampling distribution of an SVD transformation with $k$ unique and $m-k$ repeated singular values. We then show under this model that the maximum a posteriori estimator for the orthogonal loadings is the eigendecomposition of $S + \frac{1}{n}Σ$, where $S$ is the empirical covariance matrix and $Σ$ is the prior spatial covariance. We develop a minorization-maximization-within-EM algorithm that is linear in computational complexity with respect to the number of spatial locations. We further extend our MM-EM algorithm to handle held-out locations and develop a validation strategy for optimizing the nonstationary prior covariance. Our methodology is used to infer the spatial distribution of direction-specific length scales in a human brain spatial transcriptomics case study, as well as a continental-scale phenology case study in sub-Saharan Africa.