用KAN网络可视化变量间非线性关系，发现隐藏物理规律
KAN-Matrix: Visualizing Nonlinear Pairwise and Multivariate Contributions for Physical Insight
- 用KAN构建双变量与多变量贡献矩阵，揭示非线性关联
- 相比皮尔逊相关和互信息，结果更稳健且信息量更大
- 适合需要物理可解释性的科学建模与特征分析场景
复杂数据集的解读仍是科学家面临的主要挑战，尤其在变量高维且存在共线性时。本文提出一种柯尔莫哥洛夫-阿诺德网络（KAN）的新应用，以提升模型可解释性与简洁性，超越传统相关性分析。我们设计了两种可解释的彩色可视化工具：双变量KAN矩阵（PKAN）用于刻画变量对间的非线性关系，多变量KAN贡献矩阵（MKAN）则作为非线性特征排序工具，量化输入变量对目标变量预测的相对贡献。这些工具支持建模流程中的预处理（如特征选择、冗余分析）与后处理（如模型解释、物理洞察）。实验对比表明，PKAN与MKAN相较于皮尔逊相关系数和互信息，能产生更鲁棒、更丰富的结果。通过捕捉关系的强度与函数形式，这些矩阵有助于发现隐藏的物理模式，并推动基于领域知识的模型开发。
原文摘要 · Abstract (English)
Interpreting complex datasets remains a major challenge for scientists, particularly due to high dimensionality and collinearity among variables. We introduce a novel application of Kolmogorov-Arnold Networks (KANs) to enhance interpretability and parsimony beyond what traditional correlation analyses offer. We present two interpretable, color-coded visualization tools: the Pairwise KAN Matrix (PKAN) and the Multivariate KAN Contribution Matrix (MKAN). PKAN characterizes nonlinear associations between pairs of variables, while MKAN serves as a nonlinear feature-ranking tool that quantifies the relative contributions of inputs in predicting a target variable. These tools support pre-processing (e.g., feature selection, redundancy analysis) and post-processing (e.g., model explanation, physical insights) in model development workflows. Through experimental comparisons, we demonstrate that PKAN and MKAN yield more robust and informative results than Pearson Correlation and Mutual Information. By capturing the strength and functional forms of relationships, these matrices facilitate the discovery of hidden physical patterns and promote domain-informed model development.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。