揭示扩散映射在实践中的参数陷阱与组件选择误区
Nonlinear Dimensionality Reduction with Diffusion Maps in Practice
- 系统分析预处理与参数设置对流形的影响
- 发现前几个主成分未必最具代表性
- 推荐新方法识别真正关键的降维组件
扩散映射是一种谱方法，能从高维数据中揭示非线性子流形，已广泛应用于生物、工程和社科等领域。然而，数据预处理、参数设定及分量选择对结果流形有显著影响，而这一问题尚未在文献中得到充分讨论。本文提供面向实践的扩散映射综述，揭示潜在陷阱，并展示一种新提出的识别关键分量的技术。结果表明，前几项分量并不一定是最相关者。
原文摘要 · Abstract (English)
Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology, engineering, and social sciences. But data preprocessing, parameter settings and component selection have a significant influence on the resulting manifold, something which has not been comprehensively discussed in the literature so far. We provide a practice oriented review of the Diffusion Map technique, illustrate pitfalls and showcase a recently introduced technique for identifying the most relevant components. Our results show that the first components are not necessarily the most relevant ones.
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