  Point cloud analysis is still a challenging task due to the disorder and
sparsity of samplings of their geometric structures from 3D sensors. In this
paper, we introduce the homotopy equivalence relation (HER) to make the neural
networks learn the data distribution from a high-dimension manifold. A shuffle
operation is adopted to construct HER for its randomness and zero-parameter. In
addition, inspired by prior works, we propose a local mutual information
regularizer (LMIR) to cut off the trivial path that leads to a classification
error from HER. LMIR utilizes mutual information to measure the distance
between the original feature and HER transformed feature and learns common
features in a contrastive learning scheme. Thus, we combine HER and LMIR to
give our model the ability to learn non-Euclidean features from a
high-dimension manifold. This is named the non-Euclidean feature learner.
Furthermore, we propose a new heuristics and efficiency point sampling
algorithm named ClusterFPS to obtain approximate uniform sampling but at faster
speed. ClusterFPS uses a cluster algorithm to divide a point cloud into several
clusters and deploy the farthest point sampling algorithm on each cluster in
parallel. By combining the above methods, we propose a novel point cloud
analysis neural network called PointShuffleNet (PSN), which shows great promise
in point cloud classification and segmentation. Extensive experiments show that
our PSN achieves state-of-the-art results on ModelNet40, ShapeNet and S3DIS
with high efficiency. Theoretically, we provide mathematical analysis toward
understanding of what the data distribution HER has developed and why LMIR can
drop the trivial path by maximizing mutual information implicitly.
