Persistent reachability homology in machine learning applications
Luigi Caputi, Nicholas Meadows, Henri Riihimäki
我们探索了最近引入的digraph数据的持久可访问性同源性(PRH),即以定向图的形式的数据。 特别是,我们研究PRH在一个关键的神经科学问题中的网络分类任务的有效性:癫痫检测。 PRH是digraphs的持久同源的变体,传统上基于定向旗体(DPH)。 PRH的一个主要优点是它考虑了在持久过滤中出现的digraphs的凝结,因此是由较小的digraphs计算的。 我们将PRH的有效性与DPH的有效性进行比较,我们表明PRH在分类任务中优于DPH。 我们使用Betti曲线及其积分作为拓扑特征,并在支持矢量机上实现我们的管道。
We explore the recently introduced persistent reachability homology (PRH) of digraph data, i.e. data in the form of directed graphs. In particular, we study the effectiveness of PRH in network classification task in a key neuroscience problem: epilepsy detection. PRH is a variation of the persistent homology of digraphs, more traditionally based on the directed flag complex (DPH). A main advantage of PRH is that it considers the condensations of the digraphs appearing in the persistent filtratio...