Joint Community Detection and Rotational Synchronization via Semidefinite Programming

In the presence of heterogeneous data, where randomly rotated objects fall into multiple underlying categories, it is challenging to simultaneously classify them into clusters and synchronize them based on pairwise relations. This gives rise to the joint problem of community detection and synchronization. We propose a series of semidefinite relaxations, and prove their exact recovery when extending the celebrated stochastic block model to this new setting where both rotations and cluster identities are to be determined. Numerical experiments demonstrate the efficacy of our proposed algorithms and confirm our theoretical result which indicates a sharp phase transition for exact recovery

Conditional Goal-oriented Trajectory Prediction for Interacting Vehicles with Vectorized Representation

This paper aims to tackle the interactive behavior prediction task, and proposes a novel Conditional Goal-oriented Trajectory Prediction (CGTP) framework to jointly generate scene-compliant trajectories of two interacting agents. Our CGTP framework is an end to end and interpretable model, including three main stages: context encoding, goal interactive prediction and trajectory interactive prediction. First, a Goals-of-Interest Network (GoINet) is designed to extract the interactive features between agent-to-agent and agent-to-goals using a graph-based vectorized representation. Further, the Conditional Goal Prediction Network (CGPNet) focuses on goal interactive prediction via a combined form of marginal and conditional goal predictors. Finally, the Goaloriented Trajectory Forecasting Network (GTFNet) is proposed to implement trajectory interactive prediction via the conditional goal-oriented predictors, with the predicted future states of the other interacting agent taken as inputs. In addition, a new goal interactive loss is developed to better learn the joint probability distribution over goal candidates between two interacting agents. In the end, the proposed method is conducted on Argoverse motion forecasting dataset, In-house cut-in dataset, and Waymo open motion dataset. The comparative results demonstrate the superior performance of our proposed CGTP model than the mainstream prediction methods.Comment: 14 pages, 4 figure