论文标题
紧凑的两点均匀空间的分类分析和分类不断发展
Point pattern analysis and classification on compact two-point homogeneous spaces evolving time
论文作者
论文摘要
本文介绍了一个新的建模框架，用于对歧管M_ {D}上点模式的统计分析，该框架由连接和紧凑的两点均匀空间（包括球的特殊情况）定义。提出的方法基于由l^{2}驱动的时间cox进程（\ mathbb {m} _ {d}） - 估值log-intenty。在时空引用数据的流形数据上，根据对数 - 风险过程的时变离散雅各比多项式变换来实施不同的聚集方案。然后从这种转换中表征了不同流线空间尺度上时间的N维显微点模式演变。进行的仿真研究说明了球形点过程模型的构建，该模型显示了低legendre多项式变换频率（大规模），而在高频（小尺度）下观察到规律性。 K功能分析在日志风险过程的时间短，中间和长期依赖性下支持这些结果。
This paper introduces a new modeling framework for the statistical analysis of point patterns on a manifold M_{d}, defined by a connected and compact two-point homogeneous space, including the special case of the sphere. The presented approach is based on temporal Cox processes driven by a L^{2}(\mathbb{M}_{d})-valued log-intensity. Different aggregation schemes on the manifold of the spatiotemporal point-referenced data are implemented in terms of the time-varying discrete Jacobi polynomial transform of the log-risk process. The n-dimensional microscale point pattern evolution in time at different manifold spatial scales is then characterized from such a transform. The simulation study undertaken illustrates the construction of spherical point process models displaying aggregation at low Legendre polynomial transform frequencies (large scale), while regularity is observed at high frequencies (small scale). K-function analysis supports these results under temporal short-, intermediate- and long-range dependence of the log-risk process.
