Supervisors: Steen Thorbjørnsen (AU) and Jacob von Bornemann Hjelmborg (SDU)
This project seeks to integrate two recently developed approaches to data analysis. The first method, introduced by the Japanese researcher Yuka Hashimoto and collaborators, applies concepts from operator algebras—particularly the theory of Hilbert C*-modules—to the study of concrete datasets. Their work suggests that this framework can capture structural attributes such as continuity and differentiability in certain classes of data more effectively than many traditional statistical techniques.
The second method builds on the celebrated Johnson–Lindenstrauss lemma, employing random projections to map high-dimensional datasets into spaces of significantly lower dimension while largely preserving their essential geometric and statistical properties. This dimensionality reduction has become a powerful tool in modern data analysis due to its efficiency and theoretical robustness.
By combining these two approaches, we expect to develop statistical methods that retain the structural sensitivity of the framework proposed by Hashimoto and co-authors, while achieving greater computational tractability and conceptual simplicity. We anticipate that this synthesis will broaden the applicability of operator-algebraic techniques and offer new insights into complex datasets.
The methods developed in the project will ultimately be applied to real-world data, including twin studies, with the broader aim of improving our understanding of factors involved in the prevention of certain forms of cancer.
Earliest start date: 1 August 2026
