Structured point process data harvested from various platforms poses new challenges to the machine learning community. By imposing a matrix structure to repeatedly observed marked point processes, we propose a novel mixture model of multi-level marked point processes for identifying potential heterogeneity in the observed data. Specifically, we study a matrix whose entries are marked log-Gaussian Cox processes and cluster rows of such a matrix. An efficient semi-parametric Expectation-Solution (ES) algorithm combined with functional principal component analysis (FPCA) of point processes is proposed for model estimation. The effectiveness of the proposed framework is demonstrated through simulation studies and a real data analysis.

翻译：从各种平台获取的结构性点进程数据给机器学习界带来了新的挑战。我们通过将矩阵结构强加给反复观察到的点点进程,提出了一个新的多级点点进程混合模型,以确定所观测数据中潜在的异质性。具体地说,我们研究一个矩阵,其条目有标记的对数-Gausian Cox进程和这种矩阵的集群行。提出了高效半参数期望算法,加上点进程的主要功能分析。通过模拟研究和真正的数据分析,表明了拟议框架的有效性。