提出周期时间序列的不变量，基于权重连续性与最大多样性原理。
Maximum diversity and weighting for invariants of periodic time series
- 通过权重连续性构建周期时间序列的数学不变量
- 在真实数据上验证了新不变量提升机器学习性能
- 适合对时序数据建模和拓扑数据分析的研究者
幅度作为富范畴欧拉特征的特例，代表度量空间的大小，与基数、维数和体积等经典概念相关。尽管已有研究从多角度解释幅度意义，连续性也提供了重要视角。本文聚焦于权重（其总和为幅度）的连续性及其与最大多样性的关联。近期研究揭示了幅度理论在点云或模型参数集数据分析中的应用潜力。本文进一步将其应用于周期时间序列分析，提出一类新的不变量，其不变性直接源于连续性结果。以真实世界数据为例的简单机器学习实验表明，所提不变量显著提升了模型性能。
原文摘要 · Abstract (English)
Magnitude, obtained as a special case of Euler characteristic of enriched category, represents a sense of the size of metric spaces and is related to classical notions such as cardinality, dimension, and volume. While the studies have explained the meaning of magnitude from various perspectives, continuity also gives a valuable view of magnitude. Based on established results about continuity of magnitude and maximum diversity, this article focuses on continuity of weighting, a distribution whose totality is magnitude, and its variation corresponding to maximum diversity. Meanwhile, recent studies also illuminated the connection between magnitude and data analysis by applying magnitude theory to point clouds representing the data or the set of model parameters. This article will also provide an application for time series analysis by introducing a new kind of invariants of periodic time series, where the invariance follows directly from the continuity results. As a use-case, a simple machine learning experiment is conducted with real-world data, in which the suggested invariants improved the performance.
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