Navigating high-dimensional spaces in chemistry and beyond with a reference-based coordinate assignment

High-dimensional representations underpin modern machine learning across chemistry, biology, and data science, yet their rapidly increasing dimensionality limits scalability, interpretability, and computational e!ciency. Here we introduce the reference-based coordinate assignment (RCA), a geometric framework that reconstitutes dimensionality reduction as a positioning problem. Instead of deriving coordinates through global variance maximisation or optimisation-based projections, RCA determines positions from distances between investigated and reference samples, forming a new coordinate system. Using multilateration, data points are embedded relative to these references, enabling deterministic and pointwise embedding. Across diverse domains-including molecular datasets, image recognition, and speech classification-RCA produces compact representations that preserve the predictive power of machine learning models while dramatically reducing their computational cost. These results show that such reference distances can serve as scalable coordinates for complex data, providing an e!cient and interpretable framework for navigating high-dimensional spaces. How much, or how little information is necessary to represent a molecule to a machine to enable e!cient learning, su!ciently accurate property prediction, and accelerated discovery? Modern molecular representations encode structural and electronic information through hundreds or thou