Recognizing images with long-tailed distributions remains a challenging problem while there lacks an interpretable mechanism to solve this problem. In this study, we formulate Long-tailed recognition as Domain Adaption (LDA), by modeling the long-tailed distribution as an unbalanced domain and the general distribution as a balanced domain. Within the balanced domain, we propose to slack the generalization error bound, which is defined upon the empirical risks of unbalanced and balanced domains and the divergence between them. We propose to jointly optimize empirical risks of the unbalanced and balanced domains and approximate their domain divergence by intra-class and inter-class distances, with the aim to adapt models trained on the long-tailed distribution to general distributions in an interpretable way. Experiments on benchmark datasets for image recognition, object detection, and instance segmentation validate that our LDA approach, beyond its interpretability, achieves state-of-the-art performance. Code is available at https://github.com/pengzhiliang/LDA.
This paper presents a new online multi-agent trajectory planning algorithm that guarantees to generate safe, dynamically feasible trajectories in a cluttered environment. The proposed algorithm utilizes a linear safe corridor (LSC) to formulate the distributed trajectory optimization problem with only feasible constraints, so it does not resort to slack variables or soft constraints to avoid optimization failure. We adopt a priority-based goal planning method to prevent the deadlock without an additional procedure to decide which robot to yield. The proposed algorithm can compute the trajectories for 60 agents on average 15.5 ms per agent with an Intel i7 laptop and shows a similar flight distance and distance compared to the baselines based on soft constraints. We verified that the proposed method can reach the goal without deadlock in both the random forest and the indoor space, and we validated the safety and operability of the proposed algorithm through a real flight test with ten quadrotors in a maze-like environment.