论文标题
在有限和1个周期序列的等轴测类别上的可计算和连续指标
Exactly computable and continuous metrics on isometry classes of finite and 1-periodic sequences
论文作者
论文摘要
实际测量中的不可避免的噪声激发了问题，以连续量化刚性对象（如定期时间序列）和由有序点给出的蛋白质等刚性对象之间的相似性，并考虑到维持点间距离的等轴测图。过去的工作产生了许多类似Hausdorff的距离，这些距离由于无限多个异构体的最小化而具有缓慢或近似算法。对于在任何高维欧几里得空间中等轴测图下的有限和1个周期序列，我们引入具有更快算法的连续指标。在周期性情况下，关键的新颖性是在扰动下的新指标的连续性改变了最低时期。
The inevitable noise in real measurements motivates the problem to continuously quantify the similarity between rigid objects such as periodic time series and proteins given by ordered points and considered up to isometry maintaining inter-point distances. The past work produced many Hausdorff-like distances that have slow or approximate algorithms due to minimizations over infinitely many isometries. For finite and 1-periodic sequences under isometry in any high-dimensional Euclidean space, we introduce continuous metrics with faster algorithms. The key novelty in the periodic case is the continuity of new metrics under perturbations that change the minimum period.
