用拓扑工具提升点云图数据的机器学习效率
Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform
- 用欧拉特征变换提取几何拓扑特征
- 实现对点云、图、网格的更高效建模
- 适合对拓扑与深度学习交叉研究感兴趣者
本文阐述了拓扑概念如何增强机器学习研究。以欧拉特征变换（ECT）——一种几何拓扑不变量——为实例，展示了其在点云、图和网格数据分析中的多种应用，可构建更高效的模型。此外，文章展望了未来可能方向：（1）在拓扑空间上学习函数，（2）构建融合拓扑知识的神经网络混合模型，（3）分析神经网络的定性性质。当前已有研究涉及其中部分方向，本文旨在为这一新兴领域提供入门引导与邀请。
原文摘要 · Abstract (English)
This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use cases that result in more efficient models for analyzing point clouds, graphs, and meshes. Moreover, I outline a vision for how topological concepts could be used in the future, comprising (1) the learning of functions on topological spaces, (2) the building of hybrid models that imbue neural networks with knowledge about the topological information in data, and (3) the analysis of qualitative properties of neural networks. With current research already addressing some of these aspects, this article thus serves as an introduction and invitation to this nascent area of research.
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