Regional co-location patterns represent subsets of feature types that are frequently located together in sub-regions in a study area. These sub-regions are unknown a priori, and instances of these co-location patterns are usually unevenly distributed across a study area. Regional co-location patterns remain challenging to discover. This study developed a multi-level method to identify regional co-location patterns in two steps. First, global co-location patterns were detected, and other non-prevalent co-location patterns were identified as candidates for regional co-location patterns. Second, an adaptive spatial clustering method was applied to detect the sub-regions where regional co-location patterns are prevalent. To improve computational efficiency, an overlap method was developed to deduce the sub-regions of (k + 1)-size co-location patterns from the sub-regions of k-size co-location patterns. Experiments based on both synthetic and ecological data sets showed that the proposed method is effective in the detection of regional co-location patterns.

Recognition of building groups is a critical step in building generalization. To find building groups, various approaches have been developed based on the principles of grouping (or the Gestalt laws of grouping), and the effectiveness of these approaches needs to be evaluated. This study presents a comparative analysis of nine typical such approaches, including three approaches that only consider proximity principle and six approaches that consider multiple grouping principles. Real-life dataset at 1:5000, 1:10,000, and 1:50,000 scales provided by National Geomatics Center of China is used to evaluate the performance of these approaches. Buildings at smaller scales are used to construct the benchmarks to test the grouping results at larger scales, and the adjusted Rand index is adopted to indicate the accuracy of the detected groups. Significant tests (Friedman test and Wilcoxon signed-rank test) are also performed to provide both the overall and pairwise comparisons of these approaches. The results show that (1) the average accuracy of most existing approaches is between 0.3 and 0.5, and the performances of these approaches are significantly different; (2) when only proximity is considered, the buffer analysis approach performs significantly better than other approaches; (3) when multiple grouping principles are considered, the local constraint-based approach usually performs better than other approaches; (4) existing approaches that consider similarity and/or continuity seldom improve the performance of building grouping.

Detecting regional co-location patterns on urban road networks is challenging because it is computationally prohibitive to search all potential co-location patterns and their localities, and effective statistical methods for evaluating the prevalence of regional co-location patterns are lacking. To overcome these challenges, this study developed an adaptive method for detecting network-constrained regional co-location patterns. Specifically, an alternate prevalence measure of regional co-location patterns was defined based on the likelihood ratio statistic. A network-constrained k-nearest neighbor method was used to construct instances of candidate co-location patterns, and a heuristic two-phase expansion method was proposed to identify candidate localities of regional co-location patterns. The statistical significance of regional co-location patterns was evaluated using a Monte Carlo simulation. Experiments using extensive simulated datasets showed that our method was superior to three state-of-the-art methods. The proposed method was also applied to a Beijing points of interest (POI) dataset. The identified regional POI co-location patterns could support a better understanding of the spatial organization of urban functions and may be useful for facilitating urban planning.

Space-time interpolation is widely used to estimate missing or unobserved values in a dataset integrating both spatial and temporal records. Although space-time interpolation plays a key role in space-time modeling, existing methods were mainly developed for space-time processes that exhibit stationarity in space and time. It is still challenging to model heterogeneity of space-time data in the interpolation model. To overcome this limitation, in this study, a novel space-time interpolation method considering both spatial and temporal heterogeneity is developed for estimating missing data in space-time datasets. The interpolation operation is first implemented in spatial and temporal dimensions. Heterogeneous covariance functions are constructed to obtain the best linear unbiased estimates in spatial and temporal dimensions. Spatial and temporal correlations are then considered to combine the interpolation results in spatial and temporal dimensions to estimate the missing data. The proposed method is tested on annual average temperature and precipitation data in China (1984–2009). Experimental results show that, for these datasets, the proposed method outperforms three state-of-the-art methods—e.g., spatio-temporal kriging, spatio-temporal inverse distance weighting, and point estimation model of biased hospitals-based area disease estimation methods.