  This study proposes a novel Graph Convolutional Neural Network with
Data-driven Graph Filter (GCNN-DDGF) model that can learn hidden heterogeneous
pairwise correlations between stations to predict station-level hourly demand
in a large-scale bike-sharing network. Two architectures of the GCNN-DDGF model
are explored; GCNNreg-DDGF is a regular GCNN-DDGF model which contains the
convolution and feedforward blocks, and GCNNrec-DDGF additionally contains a
recurrent block from the Long Short-term Memory neural network architecture to
capture temporal dependencies in the bike-sharing demand series. Furthermore,
four types of GCNN models are proposed whose adjacency matrices are based on
various bike-sharing system data, including Spatial Distance matrix (SD),
Demand matrix (DE), Average Trip Duration matrix (ATD), and Demand Correlation
matrix (DC). These six types of GCNN models and seven other benchmark models
are built and compared on a Citi Bike dataset from New York City which includes
272 stations and over 28 million transactions from 2013 to 2016. Results show
that the GCNNrec-DDGF performs the best in terms of the Root Mean Square Error,
the Mean Absolute Error and the coefficient of determination (R2), followed by
the GCNNreg-DDGF. They outperform the other models. Through a more detailed
graph network analysis based on the learned DDGF, insights are obtained on the
black box of the GCNN-DDGF model. It is found to capture some information
similar to details embedded in the SD, DE and DC matrices. More importantly, it
also uncovers hidden heterogeneous pairwise correlations between stations that
are not revealed by any of those matrices.

Machine Learning;Machine Learning