  In this paper, we consider the detection of a decrease of engagement by users
spontaneously interacting with a socially assistive robot in a public space. We
first describe the UE-HRI dataset that collects spontaneous Human-Robot
Interactions following the guidelines provided by the Affective Computing
research community to collect data "in-the-wild". We then analyze the users'
behaviors, focusing on proxemics, gaze, head motion, facial expressions and
speech during interactions with the robot. Finally, we investigate the use of
deep learning techniques (Recurrent and Deep Neural Networks) to detect user
engagement decrease in realtime. The results of this work highlight, in
particular, the relevance of taking into account the temporal dynamics of a
user's behavior. Allowing 1 to 2 seconds as buffer delay improves the
performance of taking a decision on user engagement.
