用拓扑方法分析脑网络，提升癫痫检测准确率
Persistent reachability homology in machine learning applications
- 基于有向图凝聚构造新拓扑特征PRH
- 在癫痫分类中准确率优于传统方法DPH
- 适合神经科学与复杂网络研究者
我们研究了近期提出的有向图数据持久可达同调（PRH）在机器学习中的应用，重点评估其在癫痫检测这一关键神经科学问题中的网络分类性能。PRH是基于有向旗复形的持久同调（DPH）的一种变体，主要优势在于通过考虑持久过滤中出现的有向图凝聚，从而在更小的图上进行计算。我们对比了PRH与DPH在分类任务中的表现，结果表明PRH在该任务中具有更高效果。实验采用贝蒂数曲线及其积分作为拓扑特征，并基于支持向量机实现完整分析流程。
原文摘要 · Abstract (English)
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 filtration and thus is computed from smaller digraphs. We compare the effectiveness of PRH to that of DPH and we show that PRH outperforms DPH in the classification task. We use the Betti curves and their integrals as topological features and implement our pipeline on support vector machine.
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