Intrinsic Structure

Intrinsic structure research focuses on uncovering and representing the underlying organization within complex datasets, aiming to extract meaningful features and relationships obscured by high dimensionality or noise. Current efforts employ diverse techniques, including manifold learning (e.g., Isomap), robust factor analysis (e.g., matrix-variate t-distribution based models), and nonnegative tensor factorization enhanced with Wasserstein distance and manifold regularization, to reveal this structure in various data types, from dislocation networks to biomedical images. These advancements enable improved data analysis, classification, and generative modeling, with applications ranging from materials science and medical imaging to mathematical constant discovery and taxonomy expansion.