基于高斯加权线性变换的可解释非线性降维

Interpretable non-linear dimensionality reduction using gaussian weighted linear transformation

April 24, 2025

作者: Erik Bergh

cs.AI

摘要

降维技术是分析和可视化高维数据的基础。现有方法如t-SNE和PCA在表征能力与可解释性之间存在权衡。本文提出了一种新颖方法，通过将线性方法的可解释性与非线性变换的表达力相结合，弥合了这一差距。所提出的算法通过一系列由高斯函数加权的线性变换，构建了高维与低维空间之间的非线性映射。这种架构在保持线性方法可解释性优势的同时，实现了复杂的非线性变换，因为每个变换都可以独立分析。最终模型不仅提供了强大的降维能力，还提供了对变换空间的透明洞察。本文还介绍了解释学习到的变换的技术，包括识别被抑制维度的方法以及空间如何扩展和收缩。这些工具使实践者能够理解算法在降维过程中如何保持和修改几何关系。为确保该算法的实际应用价值，本文强调了开发用户友好软件包的重要性，以促进其在学术界和工业界的采用。

English

Dimensionality reduction techniques are fundamental for analyzing and visualizing high-dimensional data. With established methods like t-SNE and PCA presenting a trade-off between representational power and interpretability. This paper introduces a novel approach that bridges this gap by combining the interpretability of linear methods with the expressiveness of non-linear transformations. The proposed algorithm constructs a non-linear mapping between high-dimensional and low-dimensional spaces through a combination of linear transformations, each weighted by Gaussian functions. This architecture enables complex non-linear transformations while preserving the interpretability advantages of linear methods, as each transformation can be analyzed independently. The resulting model provides both powerful dimensionality reduction and transparent insights into the transformed space. Techniques for interpreting the learned transformations are presented, including methods for identifying suppressed dimensions and how space is expanded and contracted. These tools enable practitioners to understand how the algorithm preserves and modifies geometric relationships during dimensionality reduction. To ensure the practical utility of this algorithm, the creation of user-friendly software packages is emphasized, facilitating its adoption in both academia and industry.