Manifold learning techniques play a pivotal role in machine learning by
revealing lower-dimensional embeddings within high-dimensional data, thus
enhancing both the efficiency and interpretability of data analysis by
transforming the data into a lower-dimensional representation. However, a
notable challenge with current manifold learning methods is their lack of
explicit functional mappings, crucial for explainability in many real-world
applications. Genetic programming, known for its interpretable functional
tree-based models, has emerged as a promising approach to address this
challenge. Previous research leveraged multi-objective GP to balance manifold
quality against embedding dimensionality, producing functional mappings across
a range of embedding sizes. Yet, these mapping trees often became complex,
hindering explainability. In response, in this paper, we introduce Genetic
Programming for Explainable Manifold Learning (GP-EMaL), a novel approach that
directly penalises tree complexity. Our new method is able to maintain high
manifold quality while significantly enhancing explainability and also allows
customisation of complexity measures, such as symmetry balancing, scaling, and
node complexity, catering to diverse application needs. Our experimental
analysis demonstrates that GP-EMaL is able to match the performance of the
existing approach in most cases, while using simpler, smaller, and more
interpretable tree structures. This advancement marks a significant step
towards achieving interpretable manifold learning.

使用遗传编程进行可解释流形学习，直接惩罚树结构的复杂性，提高流形质量和可解释性，并允许自定义复杂度度量，标志着实现可解释流形学习的重要进展。