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Data analysis using Riemannian geometry and applications to chemical engineering.
- Source :
-
Computers & Chemical Engineering . Dec2022, Vol. 168, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- We explore the use of tools from Riemannian geometry for the analysis of symmetric positive definite matrices (SPD). An SPD matrix is a versatile data representation that is commonly used in chemical engineering (e.g., covariance/correlation/Hessian matrices and images) and powerful techniques are available for its analysis (e.g., principal component analysis). A key observation that motivates this work is that SPD matrices live on a Riemannian manifold and that implementing techniques that exploit this basic property can yield significant benefits in data-centric tasks such as classification and dimensionality reduction. We demonstrate this via a couple of case studies that conduct anomaly detection in the context of process monitoring and image analysis. • Mathematical introduction to Riemannian manifolds and their geometric analysis. • Framework (and code) for the analysis of SPD matrices through Riemannian geometry. • Benefits of geometric approach to data analysis illustrated through two real world case studies. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00981354
- Volume :
- 168
- Database :
- Academic Search Index
- Journal :
- Computers & Chemical Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 161014775
- Full Text :
- https://doi.org/10.1016/j.compchemeng.2022.108023