1. Introduction
Based on a point cloud sampled from the surface of an object (or a scene), humans are able to perceive its underlying shape. Via properly capturing the topology behind the point set, human understanding is robust to variations in scales and viewpoints. Intuitively, topology reflects how the points are put together to form an object. Moreover, topology is an intrinsic property of Riemannian manifolds that are usually used to model 3D shapes in geometric learning [2], [23]. Hence, it is important to seek topology-aware representations for point clouds in machine learning.