  Crowd flow forecasting, which aims to predict the crowds entering or leaving
certain regions, is a fundamental task in smart cities. One of the key
properties of crowd flow data is periodicity: a pattern that occurs at regular
time intervals, such as a weekly pattern. To capture such periodicity, existing
studies either fuse the periodic hidden states into channels for networks to
learn or apply extra periodic strategies to the network architecture. In this
paper, we devise a novel periodic residual learning network (PRNet) for a
better modeling of periodicity in crowd flow data. Unlike existing methods,
PRNet frames the crowd flow forecasting as a periodic residual learning problem
by modeling the variation between the inputs (the previous time period) and the
outputs (the future time period). Compared to directly predicting crowd flows
that are highly dynamic, learning more stationary deviation is much easier,
which thus facilitates the model training. Besides, the learned variation
enables the network to produce the residual between future conditions and its
corresponding weekly observations at each time interval, and therefore
contributes to substantially more accurate multi-step ahead predictions.
Extensive experiments show that PRNet can be easily integrated into existing
models to enhance their predictive performance.
