Spatial variability is a prominent feature of various geographic phenomena such as climatic zones, USDA plant hardiness zones, and terrestrial habitat types (e.g., forest, grasslands, wetlands, and deserts). However, current deep learning methods follow a spatial-one-size-fits-all (OSFA) approach to train single deep neural network models that do not account for spatial variability. Quantification of spatial variability can be challenging due to the influence of many geophysical factors. In preliminary work, we proposed a spatial variability aware neural network (SVANN-I, formerly called SVANN ) approach where weights are a function of location but the neural network architecture is location independent. In this work, we explore a more flexible SVANN-E approach where neural network architecture varies across geographic locations. In addition, we provide a taxonomy of SVANN types and a physics inspired interpretation model. Experiments with aerial imagery based wetland mapping show that SVANN-I outperforms OSFA and SVANN-E performs the best of all.
Given multi-category point sets from different place-types, our goal is to develop a spatially-lucid classifier that can distinguish between two classes based on the arrangements of their points. This problem is important for many applications, such as oncology, for analyzing immune-tumor relationships and designing new immunotherapies. It is challenging due to spatial variability and interpretability needs. Previously proposed techniques require dense training data or have limited ability to handle significant spatial variability within a single place-type. Most importantly, these deep neural network (DNN) approaches are not designed to work in non-Euclidean space, particularly point sets. Existing non-Euclidean DNN methods are limited to one-size-fitsall approaches. We explore a spatial ensemble framework that explicitly uses different training strategies, including weighted-distance learning rate and spatial domain adaptation, on various place-types for spatially-lucid classification. Experimental results on real-world datasets (e.g., MxIF oncology data) show that the proposed framework provides higher prediction accuracy than baseline methods.
Given Spatial Variability Aware Neural Networks (SVANNs), the goal is to investigate mathematical (or computational) models for comparative physical interpretation towards their transparency (e.g., simulatibility, decomposability and algorithmic transparency). This problem is important due to important use-cases such as reusability, debugging, and explainability to a jury in a court of law. Challenges include a large number of model parameters, vacuous bounds on generalization performance of neural networks, risk of overfitting, sensitivity to noise, etc., which all detract from the ability to interpret the models. Related work on either modelspecific or model-agnostic post-hoc interpretation is limited due to a lack of consideration of physical constraints (e.g., mass balance) and properties (e.g., second law of geography). This work investigates physical interpretation of SVANNs using novel comparative approaches based on geographically heterogeneous features. The proposed approach on feature-based physical interpretation is evaluated using a case-study on wetland mapping. The proposed physical interpretation improves the transparency of SVANN models and the analytical results highlight the trade-off between model transparency and model performance (e.g., F1-score). We also describe an interpretation based on geographically heterogeneous processes modeled as partial differential equations (PDEs).
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