Exact 多参数持久同调中的滤波学习及时间序列数据的分类
最优化与控制
2024-10-08 v2 代数拓扑
机器学习
摘要
要分析给定离散数据的拓扑性质，需要考虑称为滤波的连续变换。持久同调作为跟踪滤波中同调变化的工具。数据拓扑分析的结果因滤波选择的不同而异，使得滤波选择至关重要。滤波学习旨在找到最小化损失函数的优化滤波。最近提出的 Exact 多参数持久同调 (EMPH) 特别适用于拓扑时间序列分析，利用秩不变式的精确公式代替计算。本文提出了 EMPH 滤波学习的框架。我们 formulating an optimization problem and propose an algorithm for solving the problem. We then apply the proposed algorithm to several classification problems. Particularly, we derive the exact formula of the gradient of the loss function with respect to the filtration parameters, which makes it possible to directly update the filtration without using automatic differentiation, significantly enhancing the learning process.
关键词
引用
@article{arxiv.2406.19587,
title = {Filtration learning in exact multi-parameter persistent homology and classification of time-series data},
author = {Keunsu Kim and Jae-Hun Jung},
journal= {arXiv preprint arXiv:2406.19587},
year = {2024}
}
备注
26 pages, Version 2