PCA for Point Processes

A new statistical framework has been introduced for analyzing replicated point processes, emphasizing the variability of point patterns at the population level. This approach employs functional Principal Component Analysis (fPCA) to treat point process realizations as random measures, which represents a novel methodological perspective. By focusing on the cumulative mass function, the framework offers fresh insights into the underlying structure of point processes. This development advances the understanding of point pattern variability by capturing key modes of variation across multiple realizations. The use of fPCA in this context allows for a more nuanced analysis compared to traditional methods. The framework was detailed in a recent publication on arXiv under the stat.ML category, highlighting its relevance to statistical machine learning. Overall, this innovative method provides a promising tool for researchers studying complex point process data.