COMPLEX provides the first two-sided distortion bounds for multiparameter topological features, enabling certified embeddings where you can mathematically verify that the embedding preserves data relationships—a critical missing piece for trustworthy topological machine learning.
COMPLEX is a new method for converting multiparameter persistence modules (a topological data analysis tool) into embeddings that can be used for machine learning. Unlike previous approaches, it provides both upper and lower bounds on how well features are preserved, making it possible to verify that similar data stays similar in the embedding.