Min Deng

An adaptive spatial clustering algorithm based on delaunay triangulation

In this paper, an adaptive spatial clustering algorithm based on Delaunay triangulation (ASCDT for short) is proposed. The ASCDT algorithm employs both statistical features of the edges of Delaunay triangulation and a novel spatial proximity definition based upon Delaunay triangulation to detect spatial clusters. Normally, this algorithm can automatically discover clusters of complicated shapes, and non-homogeneous densities in a spatial database, without the need to set parameters or prior knowledge. The user can also modify the parameter to fit with special applications. In addition, the algorithm is robust to noise. Experiments on both simulated and real-world spatial databases (i.e. an earthquake dataset in China) are utilized to demonstrate the effectiveness and advantages of the ASCDT algorithm.

A density-based spatial clustering algorithm considering both spatial proximity and attribute similarity

Geometrical properties and attributes are two important characteristics of a spatial object. In previous spatial clustering studies, these two characteristics were often neglected. This paper addresses the problem of how to accommodate geometrical properties and attributes in spatial clustering. A new density-based spatial clustering algorithm (DBSC) is developed by considering both spatial proximity and attribute similarity. Delaunay triangulation with edge length constraints is first employed for modeling the spatial proximity relationships among spatial objects. A modified density-based clustering strategy is then designed and used to identify spatial clusters. Objects in the same cluster detected by the DBSC algorithm are proximal in a spatial domain and similar in an attribute domain. In addition, the algorithm is able to detect clusters of arbitrary shapes and non-homogeneous densities in the presence of noise. The effectiveness and practicability of the DBSC algorithm are validated using both simulated and real spatial datasets.

A general method of spatio-temporal clustering analysis

Spatio-temporal clustering has been a hot topic in the field of spatio-temporal data mining and knowledge discovery. It can be employed to uncover and interpret developmental trends of geographic phenomenon in the real world. However, existing spatio-temporal clustering methods seldom consider both spatiotemporal autocorrelations and heterogeneities among spatio-temporal entities, and the coupling in space and time has not been well highlighted. In this paper, a unified framework for the clustering analysis of spatio-temporal data is proposed, and a novel spatio-temporal clustering algorithm is developed by means of a spatio-temporal statistics methodology and intelligence computation technology. Our method is applied successfully to finding spatio-temporal cluster in China’s annual temperature database for the period 1951–1992.

Multi-level Topological Relations Between Spatial Regions Based Upon Topological Invariants

Topological relations have played important roles in spatial query, analysis and reasoning. In a two-dimensional space (IR2), most existing topological models can distinguish the eight basic topological relations between two spatial regions. Due to the arbitrariness and complexity of topological relations between spatial regions, it is difficult for these models to describe the order property of transformations among the topological relations, which is important for detailed analysis of spatial relations. In order to overcome the insufficiency in existing models, a multi-level modeling approach is employed to describe all the necessary details of region–region relations based upon topological invariants. In this approach, a set of hierarchically topological invariants is defined based upon the boundary–boundary intersection set (BBIS) of two involved regions. These topological invariants are classified into three levels based upon spatial set concept proposed, which include content, dimension and separation number at the set level, the element type at the element level, and the sequence at the integrated level. Corresponding to these hierarchical invariants, multi-level formal models of topological relations between spatial regions are built. A practical example is provided to illustrate the use of the approach presented in this paper.

A Statistical Model for Directional Relations Between Spatial Objects

Directional relation, as a kind of spatial constraints, has been recognized as being an important means for spatial query, analysis and reasoning. Directional relation is conventionally concerned with two point objects. However, in spatial query and analysis, there is also a need of directional relations between point and line, point and area, line and line, line and area, and area and area. Therefore, conventional definition of direction needs to be extended to include line and area objects (i.e. the so-called extended objects). Existing models for directional relation of extended objects make use of approximate representations (e.g. minimum bounding rectangles) of the extended objects so as to produce some results with unrealistic impression. In this paper, a statistical model is presented. In this new model, (1) an extended spatial object is decomposed into small components; (2) the directional relation between extended spatial objects is then determined by the directions between these small components which form a distribution; and (3) two measures (i.e. range and median direction) are utilized to describe the statistical property of the distribution. This statistical model is based upon the (extended) spatial objects themselves, instead of their approximate representations. An experimental test has been carried out and the result indicates that the directional relations computed from this model is very close to those perceived by human beings.

Adaptive spatial clustering in the presence of obstacles and facilitators

An intersection-and-combination strategy for clustering spatial point data in the presence of obstacles (e.g. mountain) and facilitators (e.g. highway) is proposed in this paper, and an adaptive spatial clustering algorithm, called ASCDT+, is also developed. The ASCDT+ algorithm can take both obstacles and facilitators into account without additional preprocessing, and automatically detects spatial clusters adjacent to each other with arbitrary shapes and/or different densities. In addition, the ASCDT+ algorithm has the ability to find clustering patterns at both global and local levels so that users can make a more complete interpretation of the clustering results. Several simulated and real-world datasets are utilized to evaluate the effectiveness of the ASCDT+ algorithm. Comparison with two related algorithms, AUTOCLUST+ and DBRS+, demonstrates the advantages of the ASCDT+ algorithm. The ASCDT+ algorithm can consider both obstacles (e.g. mountain) and facilitators (e.g. highway).The ASCDT+ algorithm can detect clusters with different shapes and densities at both global and local levels.The ASCDT+ algorithm is easy to implement with no need of user-specified parameters.

A Hybrid Method for Interpolating Missing Data in Heterogeneous Spatio-Temporal Datasets

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.

An Iterative Detection and Removal Method for Detecting Spatial Clusters of Different Densities

A fundamental element of exploratory spatial data analysis is the discovery of clusters in a spatial point dataset. When clusters with distinctly different local densities exist, the determination of suitable density level is still an unsolved problem. On that account, an iterative detection and removal method is proposed in this study. In each step of the novel method, there are two stages. In the detection stage, density level is statistically modeled as a significance level controlled by the number and support domain of the points in the dataset, and then a hypothesis test is used to detect the high-density points. In the removal stage, the Delaunay triangulation network is used to construct clusters and support domains for the identified high-density points, and then the high-density points and their support domains are removed from the dataset. The detection and removal operation are iteratively implemented until no high-density points can be detected. Experiments and comparisons show that the proposed method, on the one hand, outperforms four state-of-the-art methods for detecting clusters of complex shapes and diverse densities, and on the other hand, no user-specified parameters are required. In addition, the support domains of clusters are very useful for spatial analysis.

Multi-level method for discovery of regional co-location patterns

ABSTRACT 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.

Adaptive detection of spatial point event outliers using multilevel constrained Delaunay triangulation

Abstract Spatial outlier detection is a research hot spot in the field of spatial data mining. Because of the lack of specific research on spatial point events, this study presents an adaptive approach for s patial p oint e vents o utlier d etection (SPEOD) using multilevel constrained Delaunay triangulation. First, the spatial proximity relationships between spatial point events are roughly captured by Delaunay triangulation. Then, three-level constraints are described and used to refine spatial proximity relationships with the consideration of statistical characteristics. Finally, those spatial point events connected by remaining edges are gathered to form a series of subgraphs. Those subgraphs containing very few point events are regarded as spatial outliers. Experiments on both synthetic and real-world spatial data sets are used to show that the proposed SPEOD algorithm can detect various types of spatial point event outliers with high efficiency. Moreover, there is no need to input any parameter in SPEOD.