  Modern navigation services often provide multiple paths connecting the same
source and destination for users to select. Hence, ranking such paths becomes
increasingly important, which directly affects the service quality. We present
PathRank, a data-driven framework for ranking paths based on historical
trajectories using multi-task learning. If a trajectory used path P from source
s to destination d, PathRank considers this as an evidence that P is preferred
over all other paths from s to d. Thus, a path that is similar to P should have
a larger ranking score than a path that is dissimilar to P. Based on this
intuition, PathRank models path ranking as a regression problem, where each
path is associated with a ranking score.
  To enable PathRank, we first propose an effective method to generate a
compact set of training data: for each trajectory, we generate a small set of
diversified paths. Next, we propose a multi-task learning framework to solve
the regression problem. In particular, a spatial network embedding is proposed
to embed each vertex to a feature vector by considering both road network
topology and spatial properties, such as distances and travel times. Since a
path is represented by a sequence of vertices, which is now a sequence of
feature vectors after embedding, recurrent neural network is applied to model
the sequence. The objective function is designed to consider errors on both
ranking scores and spatial properties, making the framework a multi-task
learning framework. Empirical studies on a substantial trajectory data set
offer insight into the designed properties of the proposed framework and
indicating that it is effective and practical.
