Curvature Corrected Nonnegative Manifold Data Factorization

• URL: http://arxiv.org/abs/2502.15124v1
• Date: Fri, 21 Feb 2025 01:00:02 GMT
• Title: Curvature Corrected Nonnegative Manifold Data Factorization
• Authors: Joyce Chew, Willem Diepeveen, Deanna Needell,
• Abstract summary: We propose curvature corrected nonnegative manifold data factorization (CC-NMDF) as a geometry-aware method for extracting interpretable factors from manifold-valued data.<n>We develop an efficient iterative algorithm for computing CC-NMDF and demonstrate our method on real-world diffusion tensor magnetic resonance imaging data.
• Score: 7.136519238386581
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Data with underlying nonlinear structure are collected across numerous application domains, necessitating new data processing and analysis methods adapted to nonlinear domain structure. Riemannanian manifolds present a rich environment in which to develop such tools, as manifold-valued data arise in a variety of scientific settings, and Riemannian geometry provides a solid theoretical grounding for geometric data analysis. Low-rank approximations, such as nonnegative matrix factorization (NMF), are the foundation of many Euclidean data analysis methods, so adaptations of these factorizations for manifold-valued data are important building blocks for further development of manifold data analysis. In this work, we propose curvature corrected nonnegative manifold data factorization (CC-NMDF) as a geometry-aware method for extracting interpretable factors from manifold-valued data, analogous to nonnegative matrix factorization. We develop an efficient iterative algorithm for computing CC-NMDF and demonstrate our method on real-world diffusion tensor magnetic resonance imaging data.

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