AI 中文总结
研究针对轨迹集合数据，提出聚类加权多元多尺度样本熵（CWMMSE），可分组轨迹并加权其动态复杂性，分离个体复杂性和总体多样性，通过多系统验证其排序与平均法不同，表明应测量总体复杂性而非求平均。
AI 中文摘要
在物理和生命科学中，数据越来越多地以轨迹集合的形式出现。现有的样本熵度量用于刻画单个时间序列，而对集合求平均会忽略总体结构，无法区分冗余和多样性。我们引入聚类加权多元多尺度样本熵（CWMMSE），它将轨迹分组为行为模式并根据其动态复杂性加权。CWMMSE是总体模式分布的加权熵，其经验插件估计器对于固定有限划分是强一致的，能分离个体复杂性和总体多样性这两个在实际数据中可能不同的成分。在11个物理、环境、工程和生物医学系统中，CWMMSE的排序与平均法不同，如能识别大地震导致的系统复杂性崩溃等。结果表明应测量而非平均总体复杂性。
英文摘要
Across the physical and life sciences, data increasingly appear as ensembles of trajectories, from chaotic flows and satellite constellations to clinical cohorts. Established sample-entropy measures characterize individual time series, while averaging across an ensemble discards population structure and cannot distinguish redundancy from diversity. We introduce clustering-weighted multivariate multiscale sample entropy (CWMMSE), which groups trajectories into behavioral patterns and weights each by its dynamical complexity. CWMMSE is a weighted entropy of the population's pattern distribution. Its empirical plug-in estimator is strongly consistent for a fixed finite partition, and it separates two components that can diverge in real data: individual complexity and population diversity. Both are essential. Averaging ignores diversity, whereas spread alone can mistake a varied but predictable population for a complex one. Across eleven physical, environmental, engineering, and biomedical systems, CWMMSE ranks a calm ocean region above an energetic but individually more complex one, identifies a major earthquake as a collapse in system complexity, and reverses the conclusion from averaging in cardiac cohorts, where disease reduces population diversity. Supported by an open, reproducible implementation, these results show that population complexity should be measured rather than averaged.
