自适应空间聚类方法研究
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摘要
空间聚类分析是地理空间数据挖掘与知识发现的主要研究内容之一,旨在发现潜在的空间实体分布模式以及探测空间异常。空间聚类分析在天文学、地理学、地质学、气象学、地图学及公共卫生等众多领域具有广泛的应用。伴随着实际应用的深入,迫切需要发展具有良好自适应性的空间聚类方法,一方面可以自动适应空间数据的复杂分布,如不同形态、不同密度的空间分布等；另一方面能够便捷用户操作,如需要设置较少的参数。为此,本文较为系统地研究了白适应的空间聚类分析方法,主要包括：
(1)从空间数据的基本特征与性质出发,分析了空间聚类分析的研究特点；进而,对空间聚类问题进行了明确的定义,建立了空间数据清理、空间聚类趋势分析、空间聚类特征提取、空间聚类算法设计及空间聚类有效性评价等五个部分为核心的空间聚类分析理论框架；最后对现有的空间聚类算法进行了较为系统的总结与分析,对其适用范围与性能进行了归纳。
(2)提出了基于场论的自适应空间聚类算法。本文从空间数据场的角度出发,提出了一种适用于空间聚类的凝聚场,并给出了一种新的空间聚类相似性度量指标,即凝聚力。进而,提出了一种基于场论的自适应空间聚类算法(简称FTASC)。该算法根据凝聚力的矢量计算获取每个实体的邻近实体,并通过递归搜索的策略,生成一系列不同的空间簇。通过模拟实验验证、经典算法比较和实际应用分析得出,本文提出的算法能够发现任意形状、密度变化的空间簇,且可以实现无参数聚类。
(3)提出了基于Delaunay三角网的自适应空间聚类算法。借助Delaunay三角网描述空间实体间邻近关系,并采取由整体到局部的策略,构造针对性的Delaunay.边长约束准则来发现空间聚集结构,提出了一种自适应的空间聚类算法(简称ASCDT)。通过实验分析与比较发现,ASCDT算法可以自动地发现复杂的空间簇,且对噪声点稳健。在ASCDT的基础上,顾及了空间聚类过程中可能存在的空间障碍(如河流,山脉),并进一步发展了一种顾及空间障碍的空间聚类方法(简称ASCDT+)。
(4)提出了基于图论与密度的混合空间聚类算法。结合基于图论与基于密度的空间聚类算法的优势,提出了一种顾及专题属性的空间聚类算法(简称HGDSC)。其主要思想为：首先借助基于图论的空间聚类方法思想针对复杂分布的空间数据集构建实体间邻近关系,进一步借助改进的基于密度的空间聚类方法顾及专题属性进行聚类。通过实验分析与比较证明,HGDSC算法不仅能够适应复杂的空间分布,而且可以同时顾及实体间专题属性的相似性,需要人为的干预较少。
(5)提出了基于力学思想的空间聚类有效性评价方法。首先,对较有代表性的空间聚类有效性评价方法进行总结。进而,借助于物理学中的力学思想,结合地理学基本规律,提出了一种基于力学思想的空间聚类有效性评价指标(简称SCV)。通过实验比较分析发现,该指标能够更准确、高效地对二维地理空间数据的聚类结果进行评价。
(6)开发了具有自主知识产权的可视化空间聚类分析软件原型-EasyC luster V1.0。包括：空间数据清理,空间聚类先验信息获取,21种经典及改进的空间聚类算法以及3种空间聚类有效性方法(可选35种空间聚类有效性函数)等主要功能模块。
Spatial clustering has played an important role in spatial data mining and knowledge discovery. It aims to classify a spatial database into several clusters without any prior knowledge (e.g., probability distribution and the number of clusters). Spatial clustering has a wide range of applications, such as astronomy, geography, geology, meteorology, cartography and public health. Currently, the applications on complicated spatial database bring new demand for spatial clustering algorithms-adaptiveness. First, spatial clustering algorithms should be adaptive to complicated spatial database, such as clusters adjacent to each other, with arbitrary geometrical shapes and/or different densities and a large amount of noise possibly exists. Second, spatial clustering algorithms should be adaptive to the requirements of users, such as different kinds of applications, minimal requirements of prior knowledge to determine the input parameters. On that account, a methodology of adaptive spatial clustering analysis is developed in this thesis. The primary contents of the thesis can be summarized as follows:
(1) The special characteristics of spatial clustering are firstly analyzed based on the feathers and characteristics of spatial data. Then, a detailed definition of spatial clustering is given, and a framework for spatial clustering including spatial data cleaning, spatial clustering trend analysis, spatial clustering feature extraction, spatial clustering algorithm and spatial clustering validity assessment is also proposed. Finally, an overview and comparison of current spatial clustering algorithms are made.
(2) A field theory based adaptive spatial clustering algorithm-FTASC is proposed. A novel data field for spatial clustering, called aggregation field, is first of all developed. Then a novel concept of aggregation force is utilized to measure the degree of aggregation among the entities. The FTASC algorithm does not involve the setting of input parameters, and a series of iterative strategies are implemented to obtain different clusters according to various spatial distributions. Two experiments are designed to illustrate the advantages of the FTASC algorithm. The practical experiment indicates that FTASC algorithm can effectively discover local aggregation patterns. The comparative experiment is made to further demonstrate the FTASC algorithm superior than classic DBSCAN algorithm.
(3) An adaptive spatial clustering algorithm based on Delaunay triangulation-ASCDT 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 are utilized to demonstrate the effectiveness and advantages of the ASCDT algorithm. Based on the ASCDT algorithm, a novel adaptive spatial clustering algorithm considering spatial obstacles-ASCDT+is further developed.
(4) A graph and density based hybrid spatial clustering algorithm-HGDSC is proposed. First, Delaunay triangulation with edge length constraints is used for the modeling of the spatial proximity relationships among spatial entities. Then, a modified density-based clustering strategy is used to identify the spatial clusters. The algorithm mainly has two desirable properties. First, both spatial and non-spatial attributes are taken into account. Entities in same cluster are similar in both spatial and non-spatial domain. Second, the algorithm can adapt to a complex spatial database which may contain the clusters of arbitrary shapes and/or non-homogeneous densities and/or large amount of noise. Experiments on both synthetic and real-world spatial datasets are utilized to demonstrate the effectiveness and practicability of the HGDSC algorithm.
(5) A spatial clustering validity index based on gravitational theory-SCV is proposed. The construction principle of the spatial clustering validity function is first investigated. Then, the aggregation force is utilized to describe the issue of spatial clustering similar to the FTASC algorithm and a novel spatial clustering validity index for two dimension spatial hard clustering is developed. Through the experiments on both simulated data set and real-world data set, it can be found that the index developed in this thesis can well evaluate the spatial hard clustering scheme including both arbitrary shape clusters and outliers.
(6) A spatial clustering software named as EasyCluster is developed. There are mainly four aspects of functions, including spatial data cleaning, spatial clustering information extraction,21 spatial clustering algorithms and 3 spatial clustering validity index (35 spatial clustering validity functions).
(1)从空间数据的基本特征与性质出发,分析了空间聚类分析的研究特点；进而,对空间聚类问题进行了明确的定义,建立了空间数据清理、空间聚类趋势分析、空间聚类特征提取、空间聚类算法设计及空间聚类有效性评价等五个部分为核心的空间聚类分析理论框架；最后对现有的空间聚类算法进行了较为系统的总结与分析,对其适用范围与性能进行了归纳。
(2)提出了基于场论的自适应空间聚类算法。本文从空间数据场的角度出发,提出了一种适用于空间聚类的凝聚场,并给出了一种新的空间聚类相似性度量指标,即凝聚力。进而,提出了一种基于场论的自适应空间聚类算法(简称FTASC)。该算法根据凝聚力的矢量计算获取每个实体的邻近实体,并通过递归搜索的策略,生成一系列不同的空间簇。通过模拟实验验证、经典算法比较和实际应用分析得出,本文提出的算法能够发现任意形状、密度变化的空间簇,且可以实现无参数聚类。
(3)提出了基于Delaunay三角网的自适应空间聚类算法。借助Delaunay三角网描述空间实体间邻近关系,并采取由整体到局部的策略,构造针对性的Delaunay.边长约束准则来发现空间聚集结构,提出了一种自适应的空间聚类算法(简称ASCDT)。通过实验分析与比较发现,ASCDT算法可以自动地发现复杂的空间簇,且对噪声点稳健。在ASCDT的基础上,顾及了空间聚类过程中可能存在的空间障碍(如河流,山脉),并进一步发展了一种顾及空间障碍的空间聚类方法(简称ASCDT+)。
(4)提出了基于图论与密度的混合空间聚类算法。结合基于图论与基于密度的空间聚类算法的优势,提出了一种顾及专题属性的空间聚类算法(简称HGDSC)。其主要思想为：首先借助基于图论的空间聚类方法思想针对复杂分布的空间数据集构建实体间邻近关系,进一步借助改进的基于密度的空间聚类方法顾及专题属性进行聚类。通过实验分析与比较证明,HGDSC算法不仅能够适应复杂的空间分布,而且可以同时顾及实体间专题属性的相似性,需要人为的干预较少。
(5)提出了基于力学思想的空间聚类有效性评价方法。首先,对较有代表性的空间聚类有效性评价方法进行总结。进而,借助于物理学中的力学思想,结合地理学基本规律,提出了一种基于力学思想的空间聚类有效性评价指标(简称SCV)。通过实验比较分析发现,该指标能够更准确、高效地对二维地理空间数据的聚类结果进行评价。
(6)开发了具有自主知识产权的可视化空间聚类分析软件原型-EasyC luster V1.0。包括：空间数据清理,空间聚类先验信息获取,21种经典及改进的空间聚类算法以及3种空间聚类有效性方法(可选35种空间聚类有效性函数)等主要功能模块。
Spatial clustering has played an important role in spatial data mining and knowledge discovery. It aims to classify a spatial database into several clusters without any prior knowledge (e.g., probability distribution and the number of clusters). Spatial clustering has a wide range of applications, such as astronomy, geography, geology, meteorology, cartography and public health. Currently, the applications on complicated spatial database bring new demand for spatial clustering algorithms-adaptiveness. First, spatial clustering algorithms should be adaptive to complicated spatial database, such as clusters adjacent to each other, with arbitrary geometrical shapes and/or different densities and a large amount of noise possibly exists. Second, spatial clustering algorithms should be adaptive to the requirements of users, such as different kinds of applications, minimal requirements of prior knowledge to determine the input parameters. On that account, a methodology of adaptive spatial clustering analysis is developed in this thesis. The primary contents of the thesis can be summarized as follows:
(1) The special characteristics of spatial clustering are firstly analyzed based on the feathers and characteristics of spatial data. Then, a detailed definition of spatial clustering is given, and a framework for spatial clustering including spatial data cleaning, spatial clustering trend analysis, spatial clustering feature extraction, spatial clustering algorithm and spatial clustering validity assessment is also proposed. Finally, an overview and comparison of current spatial clustering algorithms are made.
(2) A field theory based adaptive spatial clustering algorithm-FTASC is proposed. A novel data field for spatial clustering, called aggregation field, is first of all developed. Then a novel concept of aggregation force is utilized to measure the degree of aggregation among the entities. The FTASC algorithm does not involve the setting of input parameters, and a series of iterative strategies are implemented to obtain different clusters according to various spatial distributions. Two experiments are designed to illustrate the advantages of the FTASC algorithm. The practical experiment indicates that FTASC algorithm can effectively discover local aggregation patterns. The comparative experiment is made to further demonstrate the FTASC algorithm superior than classic DBSCAN algorithm.
(3) An adaptive spatial clustering algorithm based on Delaunay triangulation-ASCDT 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 are utilized to demonstrate the effectiveness and advantages of the ASCDT algorithm. Based on the ASCDT algorithm, a novel adaptive spatial clustering algorithm considering spatial obstacles-ASCDT+is further developed.
(4) A graph and density based hybrid spatial clustering algorithm-HGDSC is proposed. First, Delaunay triangulation with edge length constraints is used for the modeling of the spatial proximity relationships among spatial entities. Then, a modified density-based clustering strategy is used to identify the spatial clusters. The algorithm mainly has two desirable properties. First, both spatial and non-spatial attributes are taken into account. Entities in same cluster are similar in both spatial and non-spatial domain. Second, the algorithm can adapt to a complex spatial database which may contain the clusters of arbitrary shapes and/or non-homogeneous densities and/or large amount of noise. Experiments on both synthetic and real-world spatial datasets are utilized to demonstrate the effectiveness and practicability of the HGDSC algorithm.
(5) A spatial clustering validity index based on gravitational theory-SCV is proposed. The construction principle of the spatial clustering validity function is first investigated. Then, the aggregation force is utilized to describe the issue of spatial clustering similar to the FTASC algorithm and a novel spatial clustering validity index for two dimension spatial hard clustering is developed. Through the experiments on both simulated data set and real-world data set, it can be found that the index developed in this thesis can well evaluate the spatial hard clustering scheme including both arbitrary shape clusters and outliers.
(6) A spatial clustering software named as EasyCluster is developed. There are mainly four aspects of functions, including spatial data cleaning, spatial clustering information extraction,21 spatial clustering algorithms and 3 spatial clustering validity index (35 spatial clustering validity functions).
引文
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