用字典学习剔除时间序列冗余样本，提升系统辨识效率
Dictionary-Learning-Based Data Pruning for System Identification
- 基于字典学习将时间序列表示为代表性原子，通过相关性筛选有用样本
- 在模拟与两个基准数据集上，模型系数决定系数（R²）接近原数据
- 适合处理高冗余时间序列数据的高效降维场景
系统辨识通常通过时间移位和非线性化（如多项式基）扩充时间序列数据，这会引入特征与样本层面的冗余。现有研究多关注特征冗余的削减，对样本冗余的关注较少。本文提出一种基于字典学习的数据剪枝方法——mini-batch FastCan，通过字典学习将时间序列表示为一组代表性样本（称作原子），依据样本与原子的相关性选择有效样本。该方法在1个模拟数据集和2个基准数据集上进行测试。采用全数据集与剪枝后数据集训练模型的系数决定系数（R-squared）作为评估指标。结果表明，所提方法显著优于随机剪枝。
原文摘要 · Abstract (English)
System identification is normally involved in augmenting time series data by time shifting and nonlinearisation (e.g., polynomial basis), both of which introduce redundancy in features and samples. Many research works focus on reducing redundancy feature-wise, while less attention is paid to sample-wise redundancy. This paper proposes a novel data pruning method, called mini-batch FastCan, to reduce sample-wise redundancy based on dictionary learning. Time series data is represented by some representative samples, called atoms, via dictionary learning. The useful samples are selected based on their correlation with the atoms. The method is tested on one simulated dataset and two benchmark datasets. The R-squared between the coefficients of models trained on the full datasets and the coefficients of models trained on pruned datasets is adopted to evaluate the performance of data pruning methods. It is found that the proposed method significantly outperforms the random pruning method.
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