本文系统评述了超越持续同瘤的TDA与TDL最新进展，研究人员聚焦于解决传统PH在几何演化描述、局部拓扑信息捕捉及特定数据结构适应性等方面的局限，通过发展持续拓扑拉普拉斯算子、持续狄拉克算子、层理论及互作拓扑等新型框架，实现了对点云、流形数据 ...

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based ...