We propose a logic-informed knowledge-driven modeling framework for human movements by analyzing their trajectories. Our approach is inspired by the fact that human actions are usually driven by their intentions or desires, and are influenced by environmental factors such as the spatial relationships with surrounding objects. In this paper, we introduce a set of spatial-temporal logic rules as knowledge to explain human actions. These rules will be automatically discovered from observational data. To learn the model parameters and the rule content, we design an expectation-maximization (EM) algorithm, which treats the rule content as latent variables. The EM algorithm alternates between the E-step and M-step: in the E-step, the posterior distribution over the latent rule content is evaluated; in the M-step, the rule generator and model parameters are jointly optimized by maximizing the current expected log-likelihood. Our model may have a wide range of applications in areas such as sports analytics, robotics, and autonomous cars, where understanding human movements are essential. We demonstrate the model's superior interpretability and prediction performance on pedestrian and NBA basketball player datasets, both achieving promising results.

翻译：我们提出一种基于逻辑、知识驱动的建模框架，通过分析人类运动轨迹来理解其行为。该方法的灵感来源于人类行为通常由意图或欲望驱动，同时受环境因素（如与周围物体的空间关系）影响。本文引入一组时空逻辑规则作为知识，用于解释人类行为。这些规则将从观测数据中自动发现。为学习模型参数与规则内容，我们设计了期望最大化（EM）算法，将规则内容视为潜在变量。EM算法在E步和M步之间交替迭代：E步评估潜在规则内容的后验分布；M步则通过最大化当前期望对数似然，联合优化规则生成器与模型参数。该模型可广泛应用于体育分析、机器人学及自动驾驶等需要理解人类运动行为的领域。我们使用行人及NBA篮球运动员数据集验证了模型的优越可解释性与预测性能，两者均取得了令人满意的结果。