The Hoegn Index: a hyperparameter optimizer for low dimensional embeddings of multimodal neurodata

Dimensionality reduction algorithms like DIABLO have become increasingly common across fields like genomics, computational biology, and neuroscience. However, their adoption comes with persistent challenges: different disciplines rely on different quality measures, assume different underlying geometries, and operate across incompatible feature spaces. This makes hyperparameter tuning one of the more overlooked yet consequential steps in any dimensionality reduction workflow. Current approaches tend to be narrow - some optimize for a single metric, others prioritize computational efficiency - and none adequately handles the simultaneous optimization of multiple quality criteria. This thesis proposes a structured pipeline built around two original contributions: the Hoegn Parametrization and the Hoegn Index. The Hoegn Parametrization is an interpolation method designed to fill non-numeric gaps (matrices) in a parameter space, allowing these to undergo sweeping like other hyperparameters. The Hoegn Index aggregates multiple performance metrics into an envelope which identifies what hyperparameters return the most stable combination. The Index is deliberately conservative as it enforces a performance floor given by the envelope of all metrics. The pipeline was tested on a synthetic dataset generated with R::synthpop, structured to reflect a clinical multimodal neuroimaging and neuropsychological dataset from children with ADHD, ASD, and normotypical development. Given that the data is synthetic, no inferential conclusions are drawn - the focus is on demonstrating interpretability and methodological transparency. The result is a practical, reproducible framework that helps researchers make principled embedding decisions, regardless of their field.