用张量方法高效计算拓扑特征，支持高维数据的快速处理
Tensor Computation of Euler Characteristic Functions and Transforms
- 基于张量框架实现拓扑描述子的高效计算
- 在二维和三维数据上相比现有方法速度提升显著
- 支持任意维度单纯复形与立方复形，适合高性能计算
加权欧拉特征变换（WECT）和欧拉特征函数（ECF）在多个应用中已被证明是有效的工具。然而，当前计算这些描述子的方法要么不适用于GPU加速，要么无法扩展到高维情形。本文提出一种基于张量的通用框架，可高效实现对任意维度单纯复形与立方复形的拓扑描述子计算，且高度适配GPU架构。实验表明，在多种二维与三维数据集上，该框架在计算WECT与ECF时相比现有方法有显著加速。相关计算已实现在公开的Python工具包pyECT中。
原文摘要 · Abstract (English)
The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for computing these functions are either not optimized for GPU computation or do not scale to higher-dimensional settings. In this work, we present a tensor-based framework for computing such topological descriptors which is highly optimized for GPU architectures and works in full generality across simplicial and cubical complexes of arbitrary dimension. Experimentally, the framework demonstrates significant speedups over existing methods when computing the WECT and ECF across a variety of two- and three-dimensional datasets. Computation of these transforms is implemented in a publicly available Python package called pyECT.
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