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 this https URL

在数据关联中，我们提出了一个新的优化问题，使用图论形式化方法，充分利用加权图并寻求最密集的加权边团，进而引入了两种松弛方法，通过凸半定松弛和名为 CLIPPER 的快速一阶算法，实验结果显示，我们的算法在点云配准问题中表现出鲁棒性，当存在至少 95% 的异常值时，现有算法在 80% 的异常值时开始失效。