Genetic Programming for Manifold Learning: Preserving Local Topology

Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. algorithms can discover a much lower-dimensional representation (embedding) high-dimensional dataset through non-linear transformations that preserve the most important structure original data. State-of-the-art manifold directly optimise embedding without mapping between space and discovered embedded space. This makes interpretability - key requirement exploratory data analysis nearly impossible. Recently, genetic programming has emerged as very promising approach to by evolving functional mappings from embedding. However, programming-based struggled match performance other approaches. In this work, we propose new using for learning, which preserves local topology. is expected significantly improve on tasks where neighbourhood (topology) paramount. We compare our proposed with various baseline find it often outperforms methods, including clear improvement over previous These results particularly promising, given potential reusability evolved mappings.