Profiling Psychological Traits in Kernel Space: from the 2D Plane to the Reproducing Kernel Hilbert Space (RKHS)

• DOI: 10.31234/osf.io/hvxfm_v2
• Publication Date: 2025-05-22T18:44:38Z
• Authors: Agnieszka Szymańska
• Keywords: Kernel (algebra); Profiling (computer programming)

The article presents a new methodology of psychological profiling in the Hilbert space with reproducing kernel (RKHS), which individuals — rather than variables become basis for verifying models. A transformation classical trait profiles into geometric points relational is presented, and coefficient~$\eta^\star$ introduced as measure fit space. model analyzed spatial structure individuals, allows its verification through localization persons relative to theoretical trajectory.In contrast methods based on variable covariation, proposed approach reconfigures very measurement itself, introducing radial tool transforming data topology higher dimensions. RKHS makes it possible reveal deep arrangement their mutual similarities raw values.The coefficient~$\eta^\star$, being an extension Aranowska’s formula, assess whether given profile realizes or fits empirical distribution. This method opens possibility models not at level correlation matrix, but defined by themselves vectors.The thus constitutes proposal epistemology from person space, classification localization, analysis relations.