Data Analysis using Riemannian Geometry and Applications to Chemical Engineering

TL;DR

This paper applies Riemannian geometry to analyze symmetric positive definite matrices in chemical engineering, improving tasks like classification and dimensionality reduction through manifold-aware techniques.

Contribution

It introduces the use of Riemannian geometry for SPD matrix analysis in chemical engineering, demonstrating benefits in anomaly detection and data analysis tasks.

Findings

Enhanced anomaly detection in process monitoring

Improved dimensionality reduction techniques

Effective analysis of SPD matrices on Riemannian manifolds

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.