Many studies collect data that can be considered as a realization of a point process. Included are medical imaging data where photon counts are recorded by a gamma camera from patients being injected with a gamma emitting tracer. It is of interest to develop analytic methods that can help with diagnosis as well as in the training of inexpert radiologists. Partial least squares (PLS) is a popular analytic approach that combines features from linear modeling as well as dimension reduction to provide parsimonious prediction and classification. However, existing PLS methodologies do not include the analysis of point process predictors. In this article, we introduce point process PLS (P3LS) for analyzing latent time-varying intensity functions from collections of inhomogeneous point processes. A novel estimation procedure for $P^3LS$ is developed that utilizes the properties of log-Gaussian Cox processes, and its empirical properties are examined in simulation studies. The method is used to analyze kidney functionality in patients with renal disease in order to aid in the diagnosis of kidney obstruction.

翻译：许多研究收集的数据可被视为点过程的实现。其中包括医学影像数据，即通过伽马相机记录注射伽马发射示踪剂患者的光子计数。开发有助于诊断及培训非专业放射科医师的分析方法具有重要意义。偏最小二乘法是一种流行的分析方法，它结合了线性建模和降维的特点，以提供简洁的预测和分类。然而，现有的PLS方法未涵盖点过程预测变量的分析。本文针对非齐次点过程集合中潜在时变强度函数的分析，提出了点过程偏最小二乘法。我们基于对数高斯柯西过程的性质，开发了一种新颖的$P^3LS$估计方法，并通过模拟研究检验了其经验特性。该方法被用于分析肾病患者的肾功能，以辅助肾梗阻的诊断。