Browsing by Author "Wang, Wen-Ting"

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Regularized Principal Component Analysis for Spatial Data
(2017-01-01)
Wang, Wen-Ting
;
Huang, Hsin-Cheng
;
統計學研究所
;
Institute of Statistics
In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples.
Regularized spatial maximum covariance analysis
(2018-03-01)
Wang, Wen-Ting
;
Huang, Hsin-Cheng
;
統計學研究所
;
Institute of Statistics
In climate and atmospheric research, many phenomena involve more than one spatial processes covarying in space. To understand how one process is affected by another, maximum covariance analysis is commonly applied. However, the patterns obtained from maximum covariance analysis may sometimes be difficult to interpret. In this paper, we propose a regularization approach to promote spatial features in dominant coupled patterns by introducing smoothness and sparseness penalties while accounting for their orthogonalities. We develop an efficient algorithm to solve the resulting optimization problem by using the alternating direction method of multipliers. The effectiveness of the proposed method is illustrated by several numerical examples, including an application to study how precipitation in East Africa is affected by sea surface temperatures in the Indian Ocean.