Towards a Persistence Diagram that is Robust to Noise and Varied Densities

Hang Zhang, Kaifeng Zhang, Kai Ming Ting, Ye Zhu

Abstract: Recent works have identified that existing methods, which construct persistence diagrams in Topological Data Analysis (TDA), are not robust to noise and varied densities in a point cloud. We analyze the necessary properties of an approach that can address these two issues, and propose a new filter function for TDA based on a new data-dependent kernel which possesses these properties. Our empirical evaluation reveals that the proposed filter function provides a better means for t-SNE visualization and SVM classification than three existing methods of TDA.

Submission Number: 3582