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Semi-supervised learning aims to learn prediction models from both labeled and unlabeled samples. There has been extensive research in this area. Among existing work, generative mixture models with Expectation-Maximization (EM) is a popular method due to clear statistical properties. However, existing literature on EM-based semi-supervised learning largely focuses on unstructured prediction, assuming that samples are independent and identically distributed. Studies on EM-based semi-supervised approach in structured prediction is limited. This paper aims to fill the gap through a comparative study between unstructured and structured methods in EM-based semi-supervised learning. Specifically, we compare their theoretical properties and find that both methods can be considered as a generalization of self-training with soft class assignment of unlabeled samples, but the structured method additionally considers structural constraint in soft class assignment. We conducted a case study on real-world flood mapping datasets to compare the two methods. Results show that structured EM is more robust to class confusion caused by noise and obstacles in features in the context of the flood mapping application.

Given earth imagery with spectral features on a terrain surface, this paper studies surface segmentation based on both explanatory features and surface topology. The problem is important in many spatial and spatiotemporal applications such as flood extent mapping in hydrology. The problem is uniquely challenging for several reasons: first, the size of earth imagery on a terrain surface is often much larger than the input of popular deep convolutional neural networks; second, there exists topological structure dependency between pixel classes on the surface, and such dependency can follow an unknown and non-linear distribution; third, there are often limited training labels. Existing methods for earth imagery segmentation often divide the imagery into patches and consider the elevation as an additional feature channel. These methods do not fully incorporate the spatial topological structural constraint within and across surface patches and thus often show poor results, especially when training labels are limited. Existing methods on semi-supervised and unsupervised learning for earth imagery often focus on learning representation without explicitly incorporating surface topology. In contrast, we propose a novel framework that explicitly models the topological skeleton of a terrain surface with a contour tree from computational topology, which is guided by the physical constraint (e.g., water flow direction on terrains). Our framework consists of two neural networks: a convolutional neural network (CNN) to learn spatial contextual features on a 2D image grid, and a graph neural network (GNN) to learn the statistical distribution of physics-guided spatial topological dependency on the contour tree. The two models are co-trained via variational EM. Evaluations on the real-world flood mapping datasets show that the proposed models outperform baseline methods in classification accuracy, especially when training labels are limited.

Spatial classification with limited feature observations has been a challenging problem in machine learning. The problem exists in applications where only a subset of sensors are deployed at certain regions or partial responses are collected in field surveys. Existing research mostly focuses on addressing incomplete or missing data, e.g., data cleaning and imputation, classification models that allow for missing feature values, or modeling missing features as hidden variables and applying the EM algorithm. These methods, however, assume that incomplete feature observations only happen on a small subset of samples, and thus cannot solve problems where the vast majority of samples have missing feature observations. To address this issue, we propose a new approach that incorporates physics-aware structural constraints into the model representation. Our approach assumes that a spatial contextual feature is observed for all sample locations and establishes spatial structural constraint from the spatial contextual feature map. We design efficient algorithms for model parameter learning and class inference. Evaluations on real-world hydrological applications show that our approach significantly outperforms several baseline methods in classification accuracy, and the proposed solution is computationally efficient on a large data volume.

This paper studies weakly supervised learning on spatial raster data based on imperfect vector training labels. Given raster feature imagery and imperfect (weak) vector labels with location registration errors, our goal is to learn a deep learning model for pixel classification and refine vector labels simultaneously. The problem is important in many geoscience applications such as streamline delineation and road mapping from earth imagery, where annotating imperfect coarse vector labels is far more efficient than drawing precise labels. But the problem is challenging due to the misalignment of vector labels with raster feature pixels and the need to infer true vector label location while learning neural network parameters. Existing works on weakly supervised learning often focus on noise and errors in label semantics, assuming label locations to be either correct or irrelevant (e.g., identical and independently distributed). A few works exist on label registration errors, but these methods often focus on label misalignment on object segment boundaries at the pixel level without guaranteeing vector continuity. To fill the gap, this paper proposes a spatial learning framework based on Expectation-Maximization that iteratively updates deep neural network parameters while inferring true vector label locations. Specifically, inference of true vector locations is based on both the current pixel class predictions and the geometric properties of vectors. Evaluations on real-world high-resolution remote sensing datasets in National Hydrography Dataset (NHD) refinement show that the proposed framework outperforms baseline methods in classification accuracy and refined vector quality.

The effects of air pollution on adolescents need further consideration. Although there is evidence that maternal exposure to air pollution may affect the cognitive function of offspring, relevant studies remain limited and inconsistent, with a lack of studies assessing the causal effects and evidence from developing countries. Using data from Chinese Family Panel Studies, a representative Chinese nationwide cohort study, OLS combined with instrumental variable + two-stage least square (IV+2SLS) was used to explore the causal effects of exposure to PM

Spatial classification with limited observations is important in geographical applications where only a subset of sensors are deployed at certain spots or partial responses are collected in field surveys. For example, in observation-based flood inundation mapping, there is a need to map the full flood extent on geographic terrains based on earth imagery that partially covers a region. Existing research mostly focuses on addressing incomplete or missing data through data cleaning and imputation or modeling missing values as hidden variables in the EM algorithm. These methods, however, assume that missing feature observations are rare and thus are ineffective in problems whereby the vast majority of feature observations are missing. To address this issue, we recently proposed a new approach that incorporates physics-aware structural constraint into the model representation. We design efficient learning and inference algorithms. This paper extends our recent approach by allowing feature values of samples in each class to follow a multi-modal distribution. Evaluations on real-world flood mapping applications show that our approach significantly outperforms baseline methods in classification accuracy, and the multi-modal extension is more robust than our early single-modal version. Computational experiments show that the proposed solution is computationally efficient on large datasets.

Given a 3D surface defined by an elevation function on a 2D grid as well as non-spatial features observed at each pixel, the problem of surface segmentation aims to classify pixels into contiguous classes based on both non-spatial features and surface topology. The problem has important applications in hydrology, planetary science, and biochemistry but is uniquely challenging for several reasons. First, the spatial extent of class segments follows surface contours in the topological space, regardless of their spatial shapes and directions. Second, the topological structure exists in multiple spatial scales based on different surface resolutions. Existing widely successful deep learning models for image segmentation are often not applicable due to their reliance on convolution and pooling operations to learn regular structural patterns on a grid. In contrast, we propose to represent surface topological structure by a contour tree skeleton, which is a polytree capturing the evolution of surface contours at different elevation levels. We further design a graph neural network based on the contour tree hierarchy to model surface topological structure at different spatial scales. Experimental evaluations based on real-world hydrological datasets show that our model outperforms several baseline methods in classification accuracy.

Over the last decade, deep learning research has achieved tremendous success in computer vision and natural language processing. The current widely successful deep learning models are largely based on convolution and pooling operations on a Euclidean plane with a regular grid (e.g., image and video data) and thus cannot be directly applied to the non-Euclidean surface. Geometric deep learning aims to fill the gap by generalizing deep learning models from a 2D Euclidean plane to a 3D geometric surface. The problem has important applications in human-computer interaction, biochemistry, and mechanical engineering, but is uniquely challenging due to the lack of a regular grid framework and the difficulties in learning geometric features on a non-Euclidean manifold. Existing works focus on generalizing deep learning models from 2D image to graphs (e.g., graph neural networks) or 3D mesh surfaces but without fully learning geometric features from a differential geometry perspective. In contrast, this paper proposes a novel geometric deep learning model called CurvaNet that integrates differential geometry with graph neural networks. The key idea is to learn direction sensitive 3D shape features through directional curvature filters. We design a U-Net like architecture with downsampling and upsampling paths based on mesh pooling and unpooling operations. Evaluation on real-world datasets shows that the proposed model outperforms several baseline methods in classification accuracy.