论文标题
通过置换测试了解持久性配对的力量
Understanding the Power of Persistence Pairing via Permutation Test
论文作者
论文摘要
最近，已经做出了许多努力，将持久图（拓扑数据分析中的主要工具之一）纳入机器学习管道中。为了更好地了解持续图的功率和局限性，我们对图数据和形状数据进行了一系列实验，旨在将涉及不同因素的影响解除和检查。为此，我们还提出了所谓的\ emph {置换测试}，以描绘临界值和临界值配对的持续图图。对于图形分类任务，我们注意到，虽然持续配对对各种基准数据集产生一致的改进，但似乎对于测试的各种过滤功能，大多数歧视功率都来自关键值。但是，对于形状分割和分类，我们注意到，持久性配对在大多数基准数据集上都显示出重要的功能，并且基于临界值以及基于置换测试的摘要对两个摘要进行了改进。 Our results help provide insights on when persistence diagram based summaries could be more suitable.
Recently many efforts have been made to incorporate persistence diagrams, one of the major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we carry out a range of experiments on both graph data and shape data, aiming to decouple and inspect the effects of different factors involved. To this end, we also propose the so-called \emph{permutation test} for persistence diagrams to delineate critical values and pairings of critical values. For graph classification tasks, we note that while persistence pairing yields consistent improvement over various benchmark datasets, it appears that for various filtration functions tested, most discriminative power comes from critical values. For shape segmentation and classification, however, we note that persistence pairing shows significant power on most of the benchmark datasets, and improves over both summaries based on merely critical values, and those based on permutation tests. Our results help provide insights on when persistence diagram based summaries could be more suitable.
