A new filter for deformation-invariant persistence diagram

Kaifeng Zhang, Hang Zhang, Kai Ming Ting, Tianrun Liang

Abstract: Recent studies of Topological Data Analysis have focused on producing isotropic stretching-invariant Persistence Diagram (PD). We show that current methods to generate PDs are sensitive to a general form of deformation of a point cloud, where all the deformed versions share the same topology. We analyze the effect of this deformation on the generated PD, and propose a new filter to produce a deformation-invariant PD. In addition, we provide a theoretical result on our proposed filter’s robustness against outliers in the point cloud. Our empirical evaluation shows that, in the presence of the deformation in a point cloud, our proposed filter outperforms existing filters in clustering tasks at point cloud level. As for point level clustering, our proposed filter produces better outcome when clustering points according to what topological features they contribute to.

External IDs:dblp:journals/ml/ZhangZTL25