Scholarlink

<p>We introduce the monoidal Rips filtration, a filtered simplicial set for weighted directed graphs and other lattice-valued networks. Our construction generalizes the Vietoris-Rips filtration for metric spaces by replacing the maximum operator, determining the filtration values, with a more general monoidal product. We establish interleaving guarantees for the monoidal Rips persistent homology, capturing existing stability results for real-valued networks. When the lattice is a product of totally ordered sets, we are in the setting of multiparameter persistence. Here, the interleaving distance is bounded in terms of a generalized network distance. We use this to prove a novel stability result for the sublevel Rips bifiltration. Our experimental results show that our method performs better than Flagser in a graph regression task, and that combining different monoidal products in point cloud classification can improve performance.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Monoidal Rips: stable multiparameter filtrations of directed networks

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月31日

查看全文
  • Nello Blaser,
  • Morten Brun,
  • Odin Hoff Gardaa,
  • Lars M. Salbu

摘要

We introduce the monoidal Rips filtration, a filtered simplicial set for weighted directed graphs and other lattice-valued networks. Our construction generalizes the Vietoris-Rips filtration for metric spaces by replacing the maximum operator, determining the filtration values, with a more general monoidal product. We establish interleaving guarantees for the monoidal Rips persistent homology, capturing existing stability results for real-valued networks. When the lattice is a product of totally ordered sets, we are in the setting of multiparameter persistence. Here, the interleaving distance is bounded in terms of a generalized network distance. We use this to prove a novel stability result for the sublevel Rips bifiltration. Our experimental results show that our method performs better than Flagser in a graph regression task, and that combining different monoidal products in point cloud classification can improve performance.