Towards Scalable and Robust Filtration Learning for Point Clouds via Principal Persistence Measure

ICLR 2026 Conference Submission18157 Authors

Keywords: Topological Data Analysis

TL;DR: We propose to use Principal Persistence Measure in filtration learning framework to address the robustness and scalability issues in current method based on Persistence Diagram.

Abstract:

Topological features in persistent homology extracted via a filtration process have been shown to enhance the performance of machine learning tasks on point clouds. The performance is highly related to the choice of filtration, thereby underscoring the critical significance of filtration learning. However, current supervised filtration learning method for point clouds can not scale well. We identify that this shortcoming stems from the utilization of Persistence Diagrams (PD) for encoding topological features, such as connected component, ring or void, etc.
To address this issue, we propose to use Principal Persistence Measure (PPM), a statistical approximation of PD, as an alternative representation and adapt existing network for PPM-based filtration learning. Experimental results on point cloud classification task demonstrate the effectiveness, scalability and robustness of our PPM-based framework.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Submission Number: 18157