Geographical Hidden Markov Tree

Zhe Jiang, Miao Xie, Arpan Man Sainju

Abstract: Given a spatial raster framework with explanatory feature layers, a spatial contextual layer (e.g., a potential field), as well as a set of training samples with class labels, the spatial prediction problem aims to learn a model that can predict a class layer. The problem is important in societal applications such as flood extent mapping for disaster response and national water forecasting, but is challenging due to the noise, obstacles, and heterogeneity in feature maps, implicit spatial dependency between locations based on the contextual layer (e.g., gradient directions on a potential field), and the large number of sample locations. Existing work often assumes undirected spatial dependency, or directed dependency with a total order, and thus cannot reflect complex directed dependency with a partial order. In contrast, we recently proposed geographical hidden Markov tree, a probabilistic graphical model that generalizes the common hidden Markov model from a one-dimensional sequence to a two-dimensional map. Partial order class dependency is incorporated in the hidden class layer with a reverse tree structure. We also investigated computational algorithms for reverse tree construction, model parameter learning and class inference. This paper extends our recent model with overlaying class nodes between observation nodes and underlying hidden class nodes. The additional overlaying class layer makes the model more robust to large scale feature obstacles. We also proposed corresponding learning and inference methods. Extensive evaluations on real world datasets show that our models outperform multiple baselines in flood mapping applications, our algorithms are scalable on large data sizes, and the proposed extension enhances classification performance.