Genetic Programming for Manifold Learning: Preserving Local Topology
提出一种新的遗传编程方法用于流形学习，通过保持局部拓扑结构来提升降维性能，同时保留可解释性，适合探索性数据分析。
Manifold learning (MaL) methods are an invaluable tool in today’s world of increasingly huge datasets. MaL algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through nonlinear transformations that preserve the most important structure of the original data. State-of-the-art MaL methods directly optimize an embedding without mapping between the original space and the discovered embedded space. This makes interpretability—a key requirement in exploratory data analysis—nearly impossible. Recently, genetic programming has emerged as a very promising approach to MaL by evolving functional mappings from the original space to an embedding. However, genetic programming-based MaL has struggled to match the performance of other approaches. In this work, we propose a new approach to using genetic programming for MaL, which preserves local topology. This is expected to significantly improve performance on tasks where local neighborhood structure (topology) is paramount. We compare our proposed approach with various baseline MaL methods and find that it often outperforms other methods, including a clear improvement over previous genetic programming approaches. These results are particularly promising, given the potential interpretability and reusability of the evolved mappings.