With the ever increasing volume of geo-referenced datasets, there is a real need for better statistical estimation and prediction techniques for spatial analysis. Most existing approaches focus on predicting multivariate Gaussian spatial processes, but as the data may consist of non-Gaussian (or mixed type) variables, this creates two challenges: (1) how to accurately capture the dependencies among different data types, both Gaussian and non-Gaussian; and (2) how to efficiently predict multivariate non-Gaussian spatial processes. In this article, we propose a generic approach for predicting multiple response variables of mixed types. The proposed approach accurately captures cross-spatial dependencies among response variables and reduces the computational burden by projecting the spatial process to a lower dimensional space with knot-based techniques. Efficient approximations are provided to estimate posterior marginals of latent variables for the predictive process, and extensive experimental evaluations based on both simulation and real-life datasets are provided to demonstrate the effectiveness and efficiency of this new approach.

Spatial kriging is a widely used predictive model for spatial datasets. In spatial kriging model, the observations are assumed to be Gaussian for computational convenience. However, its predictive accuracy could be significantly compromised if the observations are contaminated by outliers. This deficiency can be systematically addressed by increasing the robustness of spatial kriging model using heavy tailed distributions, such as the Huber, Laplace, and Student's t distributions. This paper presents a novel Robust and Reduced Rank Spatial Kriging Model (R3-SKM), which is resilient to the influences of outliers and allows for fast spatial inference. Furthermore, three effective and efficient algorithms are proposed based on R3-SKM framework that can perform robust parameter estimation, spatial prediction, and spatial outlier detection with a linear-order time complexity. Extensive experiments on both simulated and real data sets demonstrated the robustness and efficiency of our proposed techniques.

Spatial Categorical Outlier Detection (SCOD) has attracted considerable attentions from the areas of spatial data mining and geological analysis. When encountering an SCOD problem, some researchers introduce to utilize Spatial Numerical Outlier Detection measures by mapping categorical attributes to continuous ones. However, such approaches fail to capture the special properties of spatial categorical data, which is prone to incur the masking and swamping issues. In this paper, we model spatial dependencies between spatial categorical observations and propose a Pair Correlation Function(PCF) based method to detect SCOs. First, a new metric, named Pair Correlation Ratio(PCR), is estimated for each pair of categorical combinations based on their co-occurrence frequency at different spatial distances. Then discrete PCRs are fitted in a continuous function of distances. The outlier score is computed using the average PCRs between referenced object and its spatial neighbors. Observations with the lowest PCRs are labeled as potential SCOs. Extensive experiments demonstrated that PCF based method outperformed existing approaches.

This paper proposes a STT(spatio-temporal-textual) search engine for extracting, indexing, querying and visualizing crime information. Until recently, it's a labor-intensive work to identify crime entities, cluster similar suspect activities, and discover patterns from massive online collections. It's a big challenge to reveal inherent ST(spatio-temporal) correlations among mass crime information. It's getting more difficult considering the subjectivity and vagueness of information retrieval from narratives of victims or witness and online documents of social networks. We have developed a crime search engine for Washington DC metropolitan area that includes geo-temporal-tagger, STT indexer, heuristic query and ranker and dynamical ST visualization. It assists crime detection for investigators, identification of crime trends and patterns for decision makers and researchers, and security of city life for residents and journalists.

A spatial outlier is a spatially referenced object whose non-spatial attributes are very different from those of its spatial neighbors. Spatial outlier detection has been an important part of spatial data mining and attracted attention in the past decades. Numerous SOD (Spatial Outlier Detection) approaches have been proposed. However, in these techniques, there exist the problems of masking and swamping. That is, some spatial outliers can escape the identification, and normal objects can be erroneously identified as outliers. In this paper, two Random walk based approaches, RW-BP (Random Walk on Bipartite Graph) and RW-EC (Random Walk on Exhaustive Combination), are proposed to detect spatial outliers. First, two different weighed graphs, a BP (Bipartite graph) and an EC (Exhaustive Combination), are modeled based on the spatial and/or non-spatial attributes of the spatial objects. Then, random walk techniques are utilized on the graphs to compute the relevance scores between the spatial objects. Using the analysis results, the outlier scores are computed for each object and the top k objects are recognized as outliers. Experiments conducted on the synthetic and real datasets demonstrated the effectiveness of the proposed approaches.