Identifying correspondences in noisy data is a critically important step in estimation processes. When an informative initial estimation guess is available, the data association challenge is less acute; however, the existence of a high-quality initial guess is rare in most contexts. We explore graph-theoretic formulations for data association, which do not require an initial estimation guess. Existing graph-theoretic approaches optimize over unweighted graphs, discarding important consistency information encoded in weighted edges, and frequently attempt to solve NP-hard problems exactly. In contrast, we formulate a new optimization problem that fully leverages weighted graphs and seeks the densest edge-weighted clique. We introduce two relaxations to this problem: a convex semidefinite relaxation which we find to be empirically tight, and a fast first-order algorithm called CLIPPER which frequently arrives at nearly-optimal solutions in milliseconds. When evaluated on point cloud registration problems, our algorithms remain robust up to at least 95% outliers while existing algorithms begin breaking down at 80% outliers. Code is available at https://mit-acl.github.io/clipper.

翻译：在含噪数据中识别对应关系是估计过程中至关重要的步骤。当存在有信息量的初始猜测时，数据关联的挑战性会降低；然而在大多数场景下，高质量初始猜测很少存在。本文探索了无需初始猜测的图论数据关联方法。现有图论方法优化未加权图，丢弃了加权边中编码的重要一致性信息，且常试图精确求解NP难问题。与之相对，我们提出了一个充分利用加权图并寻求最密边加权团的新优化问题。针对该问题，我们引入了两种松弛方法：经验上严格的凸半定松弛，以及名为CLIPPER的快速一阶算法，该算法通常在毫秒级获得接近最优的解。在点云配准问题的评估中，我们的算法在至少95%外点率下仍保持鲁棒性，而现有算法在80%外点率时即开始失效。代码见https://mit-acl.github.io/clipper。