Geospatial pattern recognition: Geographical pattern knowledge discovered from surface water data

Analysis and modeling of spatial data based on chemical measurements are of considerable interest in many applications. Traditional cluster analysis, sometimes coupled with feature selection, is often employed to discover geographic patterns based on chemical measurements. A novel cluster analysis method based on a multivariate mixture model, known as model-based clustering is presented for overcoming the limitations of hierarchical clustering and relocation clustering. Markov Chain Monte Carlo simulation, as implemented via Gibbs sampling coupled with model-based clustering is developed and used to assess uncertainty of group memberships during clustering. A successful application of discovering the spatial pattern of multivariate surface water data using model-based clustering is presented. The study is carried out using long-term river water data collected at different broad watersheds of United Stated. In the study, the proper chemical variable selection combined with spatial variation isolation is combined with model-based clustering for separating sample sites into specific patterns. It is found that model-based clustering based on certain chemical variables can produce reasonable and stable sites patterns. Some other application about modeling spatial data based on chemical measurements includes using different classification algorithms to authenticate and identify the geographic origin of chemical samples collected at different locations, known as geographical classification. It is also possible to predict general location or to identify a set of target variables that are location-relevant from chemical measurements or spectral information using regression analysis by partial least squares (PLS), by a spatial regression analysis such as Kriging, a geographically weighted regression, or by Bayesian inference using Gibbs sampling (BUGS). Although there have been numerous explorations of geographical pattern identification and location modeling of regions, the prediction of geographical features from a set of chemical measurements on a set of geographically distinct samples has never been explored. A new, tree-structured hierarchical model for the estimation of geographical location of spatially distributed samples from their chemical measurements is developed. The tree-structured hierarchical modeling used in our study involves a set of geographic regions stored in a hierarchical tree structure, with each non-terminal node representing a classifier and each terminal node representing a regression model. Once the tree-structured model is constructed, given a sample with only chemical measurements available, the predicted regional location of the sample is gradually restricted as it is passed through the series of classification steps. The geographic location can be predicted using a regression model within the terminal sub-region. It is shown that the tree-structured modeling approach provides reasonable estimates of geographical region and geographic location for surface water samples taken across the entire United States. Further, the location uncertainty, an estimate of a probability that a test sample could be located within a pre-estimated, joint prediction interval that is much smaller than the terminal sub-region, can also be assessed.