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Accurate and timely large-scale paddy rice maps with remote sensing are essential for crop monitoring and management and are used for assessing its impacts on food security, water resource management, and transmission of zoonotic infectious diseases. Optical image-based paddy rice mapping studies employed the unique spectral feature during the flooding/transplanting period of paddy rice. However, the lack of high-quality observations during the flooding/transplanting stage caused by rain and clouds and spectral similarity between paddy rice and natural wetlands often introduce errors in paddy rice identification, especially in paddy rice and wetland coexistent areas. In this study, we used a knowledge-based algorithm and time series observation from optical images (Sentinel-2 and Landsat 7/8) and microwave images (Sentinel-1) to address these issues. The final 10-m paddy rice map had user’s accuracy, producer’s accuracy, F1-score, and overall accuracy of 0.91 ± 0.004, 0.74 ± 0.010, 0.82, and 0.98 ± 0.001 (± value is the standard error), respectively. Over half (62.0%) of the paddy rice pixels had a confidence level of 1 (detected by both optical images and microwave images), while 38.0% had a confidence level of 0.5 (detected by either optical images or microwave images). The estimated paddy rice area in northeast China for 2020 was 60.83 ± 0.86 × 103 km2. Provincial and municipal rice areas in our data set agreed well with other existing paddy rice data sets and the Agricultural Statistical Yearbooks. These findings indicate that knowledge-based paddy rice mapping algorithms and a combination of optical and microwave images hold great potential for timely and frequently accurate paddy rice mapping in large-scale complex landscapes. 

Summary We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $$n$$, the smoothing spline estimator can be expressed as a linear combination of $$n$$ basis functions, requiring $O(n^3)$ computational time when the number $$d$$ of predictors is two or more. Such a sizeable computational cost hinders the broad applicability of smoothing splines. In practice, the full-sample smoothing spline estimator can be approximated by an estimator based on $$q$$ randomly selected basis functions, resulting in a computational cost of $O(nq^2)$. It is known that these two estimators converge at the same rate when $$q$$ is of order $$O\{n^{2/(pr+1)}\}$$, where $$p\in [1,2]$$ depends on the true function and $r > 1$ depends on the type of spline. Such a $$q$$ is called the essential number of basis functions. In this article, we develop a more efficient basis selection method. By selecting basis functions corresponding to approximately equally spaced observations, the proposed method chooses a set of basis functions with great diversity. The asymptotic analysis shows that the proposed smoothing spline estimator can decrease $$q$$ to around $$O\{n^{1/(pr+1)}\}$$ when $$d\leq pr+1$$. Applications to synthetic and real-world datasets show that the proposed method leads to a smaller prediction error than other basis selection methods. 

Abstract Optimal transport (OT) methods seek a transformation map (or plan) between two probability measures, such that the transformation has the minimum transportation cost. Such a minimum transport cost, with a certain power transform, is called the Wasserstein distance. Recently, OT methods have drawn great attention in statistics, machine learning, and computer science, especially in deep generative neural networks. Despite its broad applications, the estimation of high‐dimensional Wasserstein distances is a well‐known challenging problem owing to the curse‐of‐dimensionality. There are some cutting‐edge projection‐based techniques that tackle high‐dimensional OT problems. Three major approaches of such techniques are introduced, respectively, the slicing approach, the iterative projection approach, and the projection robust OT approach. Open challenges are discussed at the end of the review. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Dimension ReductionStatistical Learning and Exploratory Methods of the Data Sciences > Manifold Learning