EigenTrajectory: Low-Rank Descriptors for Multi-Modal Trajectory Forecasting (2307.09306v1)

Abstract: 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 .

• The paper introduces EigenTrajectory, a low-dimensional descriptor using SVD that boosts trajectory forecasting accuracy by up to 74.3% on benchmark datasets.
• The methodology employs a PCA-inspired transformation to convert high-dimensional trajectory data into a compact, noise-reduced feature space.
• The approach integrates trajectory anchors for multi-modal predictions, enabling established models to capture diverse human motion dynamics reliably.

EigenTrajectory: Low-Rank Descriptors for Multi-Modal Trajectory Forecasting

The paper "EigenTrajectory: Low-Rank Descriptors for Multi-Modal Trajectory Forecasting" introduces a novel approach to trajectory prediction by proposing the use of low-dimensional trajectory descriptors, called EigenTrajectory (ET), to effectively model human motion dynamics. The objective is to reduce the dimensionality inherent in trajectory prediction tasks, which traditionally operate in the Euclidean space, thereby improving both the prediction accuracy and computational efficiency.

Methodology

The central innovation of this work is the development of ET, a descriptor learned from real-world trajectory data using Singular Value Decomposition (SVD). By performing a low-rank approximation, the ET descriptors allow the synthesis of complex pedestrian trajectories through linear combinations of dominant eigenvectors derived from human movement data. This transformation exploits the principal component analysis framework, enabling the researchers to capture essential motion features in a compact space, reducing the burden on prediction models in handling high-dimensional data.

The ET space transformation process involves two main components: the spatio-temporal principal components from trajectory data and the combination coefficients. The trajectory data is first projected into the ET space using the principal components. Existing trajectory forecasting models, such as Social-STGCNN, SGCN, PECNet, and AgentFormer, can ingest these low-rank descriptors as input, facilitating predictions based on social interactions and resulting in more reliable trajectory outcomes.

Further, the concept of trajectory anchors is introduced, which are reference points established within the ET space to support multi-modal predictions. These trajectory anchors ensure covering diverse future possibilities by allowing the models to predict a range of plausible outputs.

Experimental Results

The effectiveness of the proposed ET framework is evaluated through extensive experiments on several benchmark datasets including ETH, UCY, Stanford Drone Dataset (SDD), and Grand Central Station (GCS). The ET approach demonstrates marked improvements in prediction accuracy (up to 74.3% in certain contexts) across multiple architectures when compared to conventional models operating directly in the Euclidean space. This improvement is indicative of the ET descriptor's capacity to distill relevant trajectory characteristics and reduce noise in the data.

Implications and Future Directions

The ET descriptor offers a promising avenue for trajectory prediction systems, effectively balancing dimensionality reduction with interpretability. Practically, this work can influence the development of more efficient models in autonomous navigation and robotic systems where quick and accurate predictions of human motion are crucial. Theoretically, the findings could spur further research into leveraging low-rank approximations for various pattern recognition and computer vision tasks beyond trajectory analysis.

Potential future work can involve exploring this low-rank approximation approach within different contextual environments, refining the eigenvector selection process to enhance path diversity, or extending the methodology to other domains requiring high-dimensional data abstraction.

In summary, "EigenTrajectory" offers a methodical advancement in trajectory prediction, illustrating the advantages of low-dimensional, data-driven descriptors that can enhance existing models' performance while ensuring computationally efficient and socially-aware predictions.