  Origin-destination (OD) matrices are often used in urban planning, where a
city is partitioned into regions and an element (i, j) in an OD matrix records
the cost (e.g., travel time, fuel consumption, or travel speed) from region i
to region j. In this paper, we partition a day into multiple intervals, e.g.,
96 15-min intervals and each interval is associated with an OD matrix which
represents the costs in the interval; and we consider sparse and stochastic OD
matrices, where the elements represent stochastic but not deterministic costs
and some elements are missing due to lack of data between two regions. We solve
the sparse, stochastic OD matrix forecasting problem. Given a sequence of
historical OD matrices that are sparse, we aim at predicting future OD matrices
with no empty elements. We propose a generic learning framework to solve the
problem by dealing with sparse matrices via matrix factorization and two graph
convolutional neural networks and capturing temporal dynamics via recurrent
neural network. Empirical studies using two taxi datasets from different
countries verify the effectiveness of the proposed framework.
