Geospatial data have a wide range of applicability in many disciplines, including environmental science, urban planning, healthcare, and public administration. The proliferation of such data in recent years have presented opportunities to develop novel data mining algorithms for modeling and extracting useful patterns from the data. However, there are many practical issues remain that must be addressed before the algorithms can be successfully applied to real-world problems. First, the algorithms must be able to incorporate spatial relationships and other domain constraints defined by the problem. Second, the algorithms must be able to handle missing values, which are common in many geospatial data sets. In particular, the models constructed by the algorithms may need to be extrapolated to locations with no observation data. Another challenge is to adequately capture the nonlinear relationship between the predictor and response variables of the geospatial data. Accurate modeling of such relationship is not only a challenge, it is also computationally expensive. Finally, the variables may interact at different spatial scales, making it necessary to develop models that can handle multi-scale relationships present in the geospatial data. This thesis presents the novel algorithms I have developed to overcome the practical challenges of applying data mining to geospatial datasets. Specifically, the algorithms will be applied to both supervised and unsupervised learning problems such as cluster analysis and spatial prediction. While the algorithms are mostly evaluated on datasets from the ecology domain, they are generally applicable to other geospatial datasets with similar characteristics. First, a spatially constrained spectral clustering algorithm is developed for geospatial data. The algorithm provides a flexible way to incorporate spatial constraints into the spectral clustering formulation in order to create regions that are spatially contiguous and homogeneous. It can also be extended to a hierarchical clustering setting, enabling the creation of fine-scale regions that are nested wholly within broader-scale regions. Experimental results suggest that the nested regions created using the proposed approach are more balanced in terms of their sizes compared to the regions found using traditional hierarchical clustering methods. Second, a supervised hash-based feature learning algorithm is proposed for modeling nonlinear relationships in incomplete geospatial data. The proposed algorithm can simultaneously infer missing values while learning a small set of discriminative, nonlinear features of the geospatial data. The efficacy of the algorithm is demonstrated using synthetic and real-world datasets. Empirical results show that the algorithm is more effective than the standard approach of imputing the missing values before applying nonlinear feature learning in more than 75% of the datasets evaluated in the study. Third, a multi-task learning framework is developed for modeling multiple response variables in geospatial data. Instead of training the local models independently for each response variable at each location, the framework simultaneously fits the local models for all response variables by optimizing a joint objective function with trace-norm regularization. The framework also leverages the spatial autocorrelation between locations as well as the inherent correlation between response variables to improve prediction accuracy. Finally, a multi-level, multi-task learning framework is proposed to effectively train predictive models from nested geospatial data containing predictor variables measured at multiple spatial scales. The framework enables distinct models to be developed for each coarse- scale region using both its fine-level and coarse-level features. It also allows information to be shared among the models through a common set of latent features. Empirical results show that such information sharing helps to create more robust models especially for regions with limited or no training data. Another advantage of using the multi-level, multi-task learning framework is that it can automatically identify potential cross-scale interactions between the regional and local variables.
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