arXiv:2602.03967cs.LGcs.NE2026-02

用进化策略优化非线性主成分分析,保留可解释性且效果更优。

Non-linear PCA via Evolution Strategies: a Novel Objective Function

  • 用神经网络参数化变量变换,进化策略优化非可微特征分解。
  • 新目标函数提升各变量方差贡献,解释力比传统方法强。
  • 支持分类/有序变量,无需独热编码,适合需要可解释性的场景。

主成分分析(PCA)是常用降维技术,但其线性特性难以捕捉真实数据的复杂结构。虽然核主成分分析(kPCA)能处理非线性,却牺牲了可解释性并面临超参数选择难题。本文提出一种融合PCA可解释性与神经网络灵活性的新型非线性PCA框架。通过神经网络参数化变量变换,并使用进化策略(ES)优化,解决特征分解不可微问题。设计了一种细粒度目标函数,最大化每个变量的个体方差贡献,提供更强学习信号。该方法原生处理分类和有序变量,避免独热编码导致的维度爆炸。在合成与真实数据集上,本方法显著优于线性PCA和kPCA,在解释方差方面表现更佳。同时保持了PCA的可解释性,可使用双标图等标准工具可视化特征贡献。代码已开源。

原文摘要 · Abstract (English)

Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA) addresses non-linearity, it sacrifices interpretability and struggles with hyperparameter selection. In this paper, we propose a robust non-linear PCA framework that unifies the interpretability of PCA with the flexibility of neural networks. Our method parametrizes variable transformations via neural networks, optimized using Evolution Strategies (ES) to handle the non-differentiability of eigendecomposition. We introduce a novel, granular objective function that maximizes the individual variance contribution of each variable providing a stronger learning signal than global variance maximization. This approach natively handles categorical and ordinal variables without the dimensional explosion associated with one-hot encoding. We demonstrate that our method significantly outperforms both linear PCA and kPCA in explained variance across synthetic and real-world datasets. At the same time, it preserves PCA's interpretability, enabling visualization and analysis of feature contributions using standard tools such as biplots. The code can be found on GitHub.

非线性降维进化策略可解释性主成分分析

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