论文标题
涂料距离是SIC：稳定，信息丰富且可计算的时间序列，并有序合并树木
The DOPE Distance is SIC: A Stable, Informative, and Computable Metric on Time Series And Ordered Merge Trees
论文作者
论文摘要
迄今为止，合并的树木合并的树木同时稳定，信息丰富且可有效地计算。我们在这项工作中表明，在将合并的合并限制为订购的域（例如间隔和圆）时，可以设计这样的度量。我们介绍``动态有序的持久性编辑''（DOPE）距离，我们证明，在满足度量属性的同时，我们证明这是稳定且信息丰富的。然后，我们设计了一个简单的$ o（n^2）$动态编程算法，以在间隔上计算它，并为其（n^3）$算法计算以在圆圈上计算它。令人惊讶的是，我们通过忽略合并树的所有层次结构信息来实现这一目标，而只是专注于一系列有序的临界点，可以将其解释为时间序列。因此，我们的算法与字符串编辑距离和动态时间扭曲更相似，而不是传统的合并比较比较算法。在以域间隔为域的时间序列的上下文中，我们在UCR时间序列分类数据集上进行了经验显示，涂料在持久图之间的性能优于瓶颈/Wasserstein距离。
Metrics for merge trees that are simultaneously stable, informative, and efficiently computable have so far eluded researchers. We show in this work that it is possible to devise such a metric when restricting merge trees to ordered domains such as the interval and the circle. We present the ``dynamic ordered persistence editing'' (DOPE) distance, which we prove is stable and informative while satisfying metric properties. We then devise a simple $O(N^2)$ dynamic programming algorithm to compute it on the interval and an $O(N^3)$ algorithm to compute it on the circle. Surprisingly, we accomplish this by ignoring all of the hierarchical information of the merge tree and simply focusing on a sequence of ordered critical points, which can be interpreted as a time series. Thus our algorithm is more similar to string edit distance and dynamic time warping than it is to more conventional merge tree comparison algorithms. In the context of time series with the interval as a domain, we show empirically on the UCR time series classification dataset that DOPE performs better than bottleneck/Wasserstein distances between persistence diagrams.
