1. Data Analysis using Riemannian Geometry and Applications to Chemical Engineering
- Author
-
Smith, Alexander, Laubach, Benjamin, Castillo, Ivan, and Zavala, Victor M.
- Subjects
Statistics - Applications - 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 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., Comment: 18 pages, 10 figures
- Published
- 2022