# PointShuffleNet: Learning Non-Euclidean Features with Homotopy Equivalence and Mutual Information

arXiv: https://arxiv.org/abs/2104.02611 · HTML: https://mlsanity.com/paper/2104.02611/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 39 references that are in the map.
- First posted on arXiv 31 Mar 2021.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [RandLA-Net: Efficient Semantic Segmentation of Large-Scale Point Clouds](https://mlsanity.com/paper/1911.11236/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Joint 2D-3D-Semantic Data for Indoor Scene Understanding](https://mlsanity.com/paper/1702.01105/) (2017)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [PointASNL: Robust Point Clouds Processing using Nonlocal Neural Networks with Adaptive Sampling](https://mlsanity.com/paper/2003.00492/) (2020)
- [SO-Net: Self-Organizing Network for Point Cloud Analysis](https://mlsanity.com/paper/1803.04249/) (2018)
- [Point Convolutional Neural Networks by Extension Operators](https://mlsanity.com/paper/1803.10091/) (2018)
- [Modeling Point Clouds with Self-Attention and Gumbel Subset Sampling](https://mlsanity.com/paper/1904.03375/) (2019)
- [ShellNet: Efficient Point Cloud Convolutional Neural Networks using Concentric Shells Statistics](https://mlsanity.com/paper/1908.06295/) (2019)
- [DensePoint: Learning Densely Contextual Representation for Efficient Point Cloud Processing](https://mlsanity.com/paper/1909.03669/) (2019)
- [Grid-GCN for Fast and Scalable Point Cloud Learning](https://mlsanity.com/paper/1912.02984/) (2019)
- [Point2Sequence: Learning the Shape Representation of 3D Point Clouds with an Attention-based Sequence to Sequence Network](https://mlsanity.com/paper/1811.02565/) (2018)
- [A Closer Look at Local Aggregation Operators in Point Cloud Analysis](https://mlsanity.com/paper/2007.01294/) (2020)

## Abstract (arXiv)

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.