EigenTrajectory: Low-Rank Descriptors for Multi-Modal Trajectory
  Forecasting
Inhwan Bae Jean Oh Hae-Gon Jeon
Capturing high-dimensional social interactions and feasible futures is
essential for predicting trajectories. To address this complex nature, several
attempts have been devoted to reducing the dimensionality of the output
variables via parametric curve fitting such as the B\'ezier curve and B-spline
function. However, these functions, which originate in computer graphics
fields, are not suitable to account for socially acceptable human dynamics. In
this paper, we present EigenTrajectory ($\mathbb{ET}$), a trajectory prediction
approach that uses a novel trajectory descriptor to form a compact space, known
here as $\mathbb{ET}$ space, in place of Euclidean space, for representing
pedestrian movements. We first reduce the complexity of the trajectory
descriptor via a low-rank approximation. We transform the pedestrians' history
paths into our $\mathbb{ET}$ space represented by spatio-temporal principle
components, and feed them into off-the-shelf trajectory forecasting models. The
inputs and outputs of the models as well as social interactions are all
gathered and aggregated in the corresponding $\mathbb{ET}$ space. Lastly, we
propose a trajectory anchor-based refinement method to cover all possible
futures in the proposed $\mathbb{ET}$ space. Extensive experiments demonstrate
that our EigenTrajectory predictor can significantly improve both the
prediction accuracy and reliability of existing trajectory forecasting models
on public benchmarks, indicating that the proposed descriptor is suited to
represent pedestrian behaviors. Code is publicly available at
https://github.com/inhwanbae/EigenTrajectory .