# PointHop: An Explainable Machine Learning Method for Point Cloud Classification

arXiv: https://arxiv.org/abs/1907.12766 · HTML: https://mlsanity.com/paper/1907.12766/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2019.

## Built on by (most cited first, 30 of 46)

- [LIF-Seg: LiDAR and Camera Image Fusion for 3D LiDAR Semantic Segmentation](https://mlsanity.com/paper/2108.07511/) (2021)
- [Masked Autoencoders in 3D Point Cloud Representation Learning](https://mlsanity.com/paper/2207.01545/) (2022)
- [Green Learning: Introduction, Examples and Outlook](https://mlsanity.com/paper/2210.00965/) (2022)
- [R-PointHop: A Green, Accurate, and Unsupervised Point Cloud Registration Method](https://mlsanity.com/paper/2103.08129/) (2021)
- [On Supervised Feature Selection from High Dimensional Feature Spaces](https://mlsanity.com/paper/2203.11924/) (2022)
- [VoxelHop: Successive Subspace Learning for ALS Disease Classification Using Structural MRI](https://mlsanity.com/paper/2101.05131/) (2021)
- [Surrogate Model-Based Explainability Methods for Point Cloud NNs](https://mlsanity.com/paper/2107.13459/) (2021)
- [3D-OAE: Occlusion Auto-Encoders for Self-Supervised Learning on Point Clouds](https://mlsanity.com/paper/2203.14084/) (2022)
- [AnomalyHop: An SSL-based Image Anomaly Localization Method](https://mlsanity.com/paper/2105.03797/) (2021)
- [X-3D: Explicit 3D Structure Modeling for Point Cloud Recognition](https://mlsanity.com/paper/2404.15010/) (2024)
- [PointMCD: Boosting Deep Point Cloud Encoders via Multi-view Cross-modal Distillation for 3D Shape Recognition](https://mlsanity.com/paper/2207.03128/) (2022)
- [E-PixelHop: An Enhanced PixelHop Method for Object Classification](https://mlsanity.com/paper/2107.02966/) (2021)
- [Geo-DefakeHop: High-Performance Geographic Fake Image Detection](https://mlsanity.com/paper/2110.09795/) (2021)
- [CP-Net: Contour-Perturbed Reconstruction Network for Self-Supervised Point Cloud Learning](https://mlsanity.com/paper/2201.08215/) (2022)
- [TGHop: An Explainable, Efficient and Lightweight Method for Texture Generation](https://mlsanity.com/paper/2107.04020/) (2021)
- [Segmentation of Cardiac Structures via Successive Subspace Learning with Saab Transform from Cine MRI](https://mlsanity.com/paper/2107.10718/) (2021)
- [GSIP: Green Semantic Segmentation of Large-Scale Indoor Point Clouds](https://mlsanity.com/paper/2109.11835/) (2021)
- [A-PixelHop: A Green, Robust and Explainable Fake-Image Detector](https://mlsanity.com/paper/2111.04012/) (2021)
- [Fast and Simple Explainability for Point Cloud Networks](https://mlsanity.com/paper/2403.07706/) (2024)
- [DefakeHop++: An Enhanced Lightweight Deepfake Detector](https://mlsanity.com/paper/2205.00211/) (2022)
- [PAGER: Progressive Attribute-Guided Extendable Robust Image Generation](https://mlsanity.com/paper/2206.00162/) (2022)
- [Bridging Gap between Image Pixels and Semantics via Supervision: A Survey](https://mlsanity.com/paper/2107.13757/) (2021)
- [GreenPCO: An Unsupervised Lightweight Point Cloud Odometry Method](https://mlsanity.com/paper/2112.04054/) (2021)
- [PCRP: Unsupervised Point Cloud Object Retrieval and Pose Estimation](https://mlsanity.com/paper/2202.07843/) (2022)
- [GENHOP: An Image Generation Method Based on Successive Subspace Learning](https://mlsanity.com/paper/2210.03689/) (2022)
- [Explainability of Point Cloud Neural Networks Using SMILE: Statistical Model-Agnostic Interpretability with Local Explanations](https://mlsanity.com/paper/2410.15374/) (2024)
- [Design of Supervision-Scalable Learning Systems: Methodology and Performance Benchmarking](https://mlsanity.com/paper/2206.09061/) (2022)
- [S3I-PointHop: SO(3)-Invariant PointHop for 3D Point Cloud Classification](https://mlsanity.com/paper/2302.11506/) (2023)
- [Enhancing Edge Intelligence with Highly Discriminant LNT Features](https://mlsanity.com/paper/2312.14968/) (2023)
- [Robustifying Point Cloud Networks by Refocusing](https://mlsanity.com/paper/2308.05525/) (2023)

## Abstract (arXiv)

An explainable machine learning method for point cloud classification, called the PointHop method, is proposed in this work. The PointHop method consists of two stages: 1) local-to-global attribute building through iterative one-hop information exchange, and 2) classification and ensembles. In the attribute building stage, we address the problem of unordered point cloud data using a space partitioning procedure and developing a robust descriptor that characterizes the relationship between a point and its one-hop neighbor in a PointHop unit. When we put multiple PointHop units in cascade, the attributes of a point will grow by taking its relationship with one-hop neighbor points into account iteratively. Furthermore, to control the rapid dimension growth of the attribute vector associated with a point, we use the Saab transform to reduce the attribute dimension in each PointHop unit. In the classification and ensemble stage, we feed the feature vector obtained from multiple PointHop units to a classifier. We explore ensemble methods to improve the classification performance furthermore. It is shown by experimental results that the PointHop method offers classification performance that is comparable with state-of-the-art methods while demanding much lower training complexity.