  Traffic speed is a key indicator for the efficiency of an urban
transportation system. Accurate modeling of the spatiotemporally varying
traffic speed thus plays a crucial role in urban planning and development. This
paper addresses the problem of efficient fine-grained traffic speed prediction
using big traffic data obtained from static sensors. Gaussian processes (GPs)
have been previously used to model various traffic phenomena, including flow
and speed. However, GPs do not scale with big traffic data due to their cubic
time complexity. In this work, we address their efficiency issues by proposing
local GPs to learn from and make predictions for correlated subsets of data.
The main idea is to quickly group speed variables in both spatial and temporal
dimensions into a finite number of clusters, so that future and unobserved
traffic speed queries can be heuristically mapped to one of such clusters. A
local GP corresponding to that cluster can then be trained on the fly to make
predictions in real-time. We call this method localization. We use non-negative
matrix factorization for localization and propose simple heuristics for cluster
mapping. We additionally leverage on the expressiveness of GP kernel functions
to model road network topology and incorporate side information. Extensive
experiments using real-world traffic data collected in the two U.S. cities of
Pittsburgh and Washington, D.C., show that our proposed local GPs significantly
improve both runtime performances and prediction accuracies compared to the
baseline global and local GPs.
