Mapper-GIN: Lightweight Structural Graph Abstraction for Corrupted 3D Point Cloud Classification

2026-02-05

AI Summary

This work addresses the limited robustness of 3D point cloud classification under corruptions such as noise and geometric transformations by proposing a lightweight and interpretable paradigm. The approach leverages the Mapper algorithm—equipped with a PCA lens, cubic cover, and density-based clustering—to generate a topological abstraction of the point cloud, from which an overlapping region graph is constructed. Graph Isomorphism Networks (GIN) are then employed for graph classification. Relying solely on structural abstraction, the method avoids large backbone networks and complex data augmentation strategies. Evaluated on the ModelNet40-C benchmark, it achieves competitive robustness with only 0.5 million parameters, substantially improving both computational efficiency and model interpretability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Interpretability, Explainability, and Transparency
• Natural Language Processing: Safety and Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Robust 3D point cloud classification is often pursued by scaling up backbones or relying on specialized data augmentation. We instead ask whether structural abstraction alone can improve robustness, and study a simple topology-inspired decomposition based on the Mapper algorithm. We propose Mapper-GIN, a lightweight pipeline that partitions a point cloud into overlapping regions using Mapper (PCA lens, cubical cover, and followed by density-based clustering), constructs a region graph from their overlaps, and performs graph classification with a Graph Isomorphism Network. On the corruption benchmark ModelNet40-C, Mapper-GIN achieves competitive and stable accuracy under Noise and Transformation corruptions with only 0.5M parameters. In contrast to prior approaches that require heavier architectures or additional mechanisms to gain robustness, Mapper-GIN attains strong corruption robustness through simple region-level graph abstraction and GIN message passing. Overall, our results suggest that region-graph structure offers an efficient and interpretable source of robustness for 3D visual recognition.

Problem

• 3D point cloud classification
• corruption robustness
• structural abstraction
• Mapper algorithm
• graph representation

Innovation

• Mapper algorithm
• graph abstraction
• Graph Isomorphism Network
• 3D point cloud robustness
• lightweight architecture