  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.
