Clustering algorithms are attractive for the task of class identification in spatial databases. However, the application to large spatial databases rises the following requirements for clustering algorithms: minimal requirements of domain knowledge to determine the input parameters, discovery of clusters with arbitrary shape and good efficiency on large databases. The well-known clustering algorithms offer no solution to the combination of these requirements. In this paper, we present the new clustering algorithm DBSCAN relying on a density-based notion of clusters which is designed to discover clusters of arbitrary shape. DBSCAN requires only one input parameter and supports the user in determining an appropriate value for it. We performed an experimental evaluation of the effectiveness and efficiency of DBSCAN using synthetic data and real data of the SEQUOIA 2000 benchmark. The results of our experiments demonstrate that (1) DBSCAN is significantly more effective in discovering clusters of arbitrary shape than the well-known algorithm CLAR-ANS, and that (2) DBSCAN outperforms CLARANS by a factor of more than 100 in terms of efficiency.

A density-based algorithm for discovering clusters a density-based algorithm for discovering clusters in large spatial databases with noise

Clustering algorithms are attractive for the task of class identification in spatial databases. However, the application to large spatial databases rises the following requirements for clustering algorithms: minimal requirements of domain knowledge to determine the input parameters, discovery of clusters with arbitrary shape and good efficiency on large databases. The well-known clustering algorithms offer no solution to the combination of these requirements. In this paper, we present the new clustering algorithm DBSCAN relying on a density-based notion of clusters which is designed to discover clusters of arbitrary shape. DBSCAN requires only one input parameter and supports the user in determining an appropriate value for it. We performed an experimental evaluation of the effectiveness and efficiency of DBSCAN using synthetic data and real data of the SEQUOIA 2000 benchmark. The results of our experiments demonstrate that (1) DBSCAN is significantly more effective in discovering clusters of arbitrary shape than the well-known algorithm CLARANS, and that (2) DBSCAN outperforms CLARANS by a factor of more than 100 in terms of efficiency.

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A density-based algorithm for discovering clusters in large spatial Databases with Noise

The R-tree, one of the most popular access methods for rectangles, is based on the heuristic optimization of the area of the enclosing rectangle in each inner node. By running numerous experiments in a standardized testbed under highly varying data, queries and operations, we were able to design the R*-tree which incorporates a combined optimization of area, margin and overlap of each enclosing rectangle in the directory. Using our standardized testbed in an exhaustive performance comparison, it turned out that the R*-tree clearly outperforms the existing R-tree variants. Guttman's linear and quadratic R-tree and Greene's variant of the R-tree. This superiority of the R*-tree holds for different types of queries and operations, such as map overlay, for both rectangles and multidimensional points in all experiments. From a practical point of view the R*-tree is very attractive because of the following two reasons 1 it efficiently supports point and spatial data at the same time and 2 its implementation cost is only slightly higher than that of other R-trees.

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The R*-tree: an efficient and robust access method for points and rectangles

Cluster analysis is a primary method for database mining. It is either used as a stand-alone tool to get insight into the distribution of a data set, e.g. to focus further analysis and data processing, or as a preprocessing step for other algorithms operating on the detected clusters. Almost all of the well-known clustering algorithms require input parameters which are hard to determine but have a significant influence on the clustering result. Furthermore, for many real-data sets there does not even exist a global parameter setting for which the result of the clustering algorithm describes the intrinsic clustering structure accurately. We introduce a new algorithm for the purpose of cluster analysis which does not produce a clustering of a data set explicitly; but instead creates an augmented ordering of the database representing its density-based clustering structure. This cluster-ordering contains information which is equivalent to the density-based clusterings corresponding to a broad range of parameter settings. It is a versatile basis for both automatic and interactive cluster analysis. We show how to automatically and efficiently extract not only 'traditional' clustering information (e.g. representative points, arbitrary shaped clusters), but also the intrinsic clustering structure. For medium sized data sets, the cluster-ordering can be represented graphically and for very large data sets, we introduce an appropriate visualization technique. Both are suitable for interactive exploration of the intrinsic clustering structure offering additional insights into the distribution and correlation of the data.

OPTICS: ordering points to identify the clustering structure

Clustering is the division of data into groups of similar objects. In clustering, some details are disregarded in exchange for data simplification. Clustering can be viewed as a data modeling technique that provides for concise summaries of the data. Clustering is therefore related to many disciplines and plays an important role in a broad range of applications. The applications of clustering usually deal with large datasets and data with many attributes. Exploration of such data is a subject of data mining. This survey concentrates on clustering algorithms from a data mining perspective.

A Survey of Clustering Data Mining Techniques

In the past few years a large number of multidimensional point access methods, also called multiattribute index structures, has been suggested, all of them claiming good performance. Since no performance comparison of these structures under arbitrary (strongly correlated nonuniform, short "ugly") data distributions and under various types of queries has been performed, database researchers and designers were hesitant to use any of these new point access methods. As shown in a recent paper, such point access methods are not only important in traditional database applications. In new applications such as CAD/CIM and geographic or environmental information systems, access methods for spatial objects are needed. As recently shown such access methods are based on point access methods in terms of functionality and performance. Our performance comparison naturally consists of two parts. In part I we will compare multidimensional point access methods, whereas in part II spatial access methods for rectangles will be compared. In part I we present a survey and classification of existing point access methods. Then we carefully select the following four methods for implementation and performance comparison under seven different data files (distributions) and various types of queries: the 2-level grid file, the BANG file, the hB-tree and a new scheme, called the BUDDY hash tree. We were surprised to see one method to be the clear winner which was the BUDDY hash tree. It exhibits an at least 20 % better average performance than its competitors and is robust under ugly data and queries. In part II we compare spatial access methods for rectangles. After presenting a survey and classification of existing spatial access methods we carefully selected the following four methods for implementation and performance comparison under six different data files (distributions) and various types of queries: the R-tree, the BANG file, PLOP hashing and the BUDDY hash tree. The result presented two winners: the BANG file and the BUDDY hash tree. This comparison is a first step towards a standardized tested or benchmark. We offer our data and query files to each designer of a new point or spatial access method such that he can run his implementation in our testbed.

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Performance comparison of point and spatial access methods

Polygonal objects are characterized by the following well-known parameters: number of vertices, area, perimeter and so on. These parameters describe the data sets that are used in benchmarks and experimental as well as analytical performance comparisons of data structures and algorithms in the area of spatial database systems. Also, a spatial query optimizer should be based on a cost model depending on these parameters. The scope of this paper is to demonstrate the importance and usefulness of parameters describing the complexity of a spatial object. Obviously, complexity is an intuitive term. Therefore, we have to ask: What does " complex " mean? Starting with a basic set of parameters describing a polygon and a set of intuitive lingual properties, we develop a complexity model consisting of three quantitative parameters. In a further step, these parameters are condensed into one measure of complexity. Using real cartographical maps, we document the suitability of our approach by three applications. 1. It distinguishes a wider range of more and less complex objects and is more intuitive than the fractal dimension. 2. The cost for answering the point-in-polygon test depends on the degree of complexity and not on the number of verti-ces of a polygon when the TR*-tree is used as a spatial data structure. 3. Using our complexity parameter, we detected special features in the data sets of the SEQUOIA 2000 storage benchmark.

Measuring the Complexity of Polygonal Objects.

Geographic database systems, known as geographic information systems (GISs) particularly among noncomputer scientists, are one of the most important applications of the very active research area named spatial database systems. Additionally to other spatial database systems where query and manipulation processing are emphasized, the most important purpose of a GIS is to analyze geographical data. The basic building block for analysis operations in GIS is the operation map overlay. However, available map overlay algorithms suffer from poor performance. In this paper, we present an efficient map overlay algorithm using as ingredients spatial access methods and state-of-the-art computational geometry concepts. An experimental performance analysis of our implemented map overlay algorithm demonstrates the fruitfulness of the marriage of spatial access methods with computational geometry methods for improving the efficiency of GISs. The possibility of coupling these two areas is based on the fact that both use spatial order relations in order to increase the performance of query processing.

Ralf Schneider

Papers

The R*-tree: an efficient and robust access method for points and rectangles

Performance comparison of point and spatial access methods

Measuring the Complexity of Polygonal Objects.

An Efficient Map Overlay Algorithm Based on Spatial Access Methods and Computational Geometry

An Access Method Based Query Processor for Spatial Database Systems