Multi-scale decomposition of point process data
Multi-scale decomposition of point process data
复制标题
点过程数据的多尺度分解
DOI：
10.1007/s10707-012-0165-8
复制
发表时间：
2012-10-01
期刊：
影响因子：
2
通讯作者：
Zhou, Chenghu
中科院分区：
文献类型：
--
作者：
Pei, Tao;Gao, Jianhuan;Zhou, Chenghu
为了自动识别点数据中的任意形状聚类，提出了基于第k个最近邻距离的点过程分解理论。我们假设一组给定的点数据是可以根据其密度分离的均匀过程的混合物。理论上，一个点的局部密度是用它的第skth最近距离来测量的。理论分为三个部分。首先，构建第k个最近距离的目标函数，其中将点数据集建模为不同齐次过程的概率密度函数（pdf）的混合物。其次，我们使用两种不同的方法将混合物分离成不同的不同的pdf，代表不同的同质过程。一种是可逆跳跃马尔可夫链蒙特卡罗策略，它同时将数据分离成不同的分量。另一种是逐步期望最大化算法，它将数据逐步划分为不同的组件。聚类结果是一个二叉树，其中每个叶子代表一个同质过程。第三，根据点的密度连通性，在每个同质点过程中生成不同的聚类。我们使用窗口近邻期望最大化（window Nearest Neighbour Expectation-Maximization， WNNEM）方法来扩展该理论并识别时空聚类。我们处理点过程的方法类似于小波变换，其中任何函数都可以看作是基小波函数的和。在我们的理论中，任何点过程数据集都可以看作是有限个齐次点过程的混合。小波变换可以将一个函数分解成不同频率的分量，而我们的理论可以将点过程数据分离成不同密度的齐次过程。用两个综合数据的实验来说明这一理论。最后以水库诱发地震为例对理论进行了验证。结果表明，该理论清晰地揭示了库区地震的空间点型。揭示了主震与群集地震（即前震和余震）的时空关系。
To automatically identify arbitrarily-shaped clusters in point data, a theory of point process decomposition based onkth Nearest Neighbour distance is proposed. We assume that a given set of point data is a mixture of homogeneous processes which can be separated according to their densities. Theoretically, the local density of a point is measured by itskth nearest distance. The theory is divided into three parts. First, an objective function of thekth nearest distance is constructed, where a point data set is modelled as a mixture of probability density functions (pdf) of different homogeneous processes. Second, we use two different methods to separate the mixture into different distinct pdfs, representing different homogeneous processes. One is the reversible jump Markov Chain Monte Carlo strategy, which simultaneously separates the data into distinct components. The other is the stepwise Expectation-Maximization algorithm, which divides the data progressively into distinct components. The clustering result is a binary tree in which each leaf represents a homogeneous process. Third, distinct clusters are generated from each homogeneous point process according to the density connectivity of the points. We use the Windowed Nearest Neighbour Expectation-Maximization (WNNEM) method to extend the theory and identify the spatiotemporal clusters. Our approach to point processes is similar to wavelet transformation in which any function can be seen as the summation of base wavelet functions. In our theory, any point process data set can be viewed as a mixture of a finite number of homogeneous point processes. The wavelet transform can decompose a function into components of different frequencies while our theory can separate point process data into homogeneous processes of different densities. Two experiments on synthetic data are provided to illustrate the theory. A case study on reservoir-induced earthquakes is also given to evaluate the theory. The results show the theory clearly reveals spatial point patterns of earthquakes in a reservoir area. The spatiotemporal relationship between the main earthquake and the clustered earthquake (namely, foreshocks and aftershocks) was also revealed.