Message Passing Least Squares: A Unified Framework for Fast and Robust Group Synchronization

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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Yunpeng Shi, Gilad Lerman


We propose an efficient algorithm for solving robust group synchronization given adversarially corrupted group ratios. We first present a theoretically guaranteed message passing algorithm that estimates the corruption levels of the group ratios. We then propose a novel weighted least squares method to estimate the group elements, where the weights are initialized using the estimated corruption levels and are iteratively updated by incorporating cycle consistency information. We demonstrate the superior performance of our algorithm over state-of-the-art methods for $SO(3)$ synchronization using both synthetic and real data.