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arXiv · 2203.12471

Data Analysis using Riemannian Geometry and Applications to Chemical Engineering

Alexander Smith·Benjamin Laubach·Ivan Castillo·Victor M. Zavala
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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.

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Alexander Smith, Benjamin Laubach, Ivan Castillo, Victor M. Zavala. 2022-03-23. Data Analysis using Riemannian Geometry and Applications to Chemical Engineering. https://arxiv.org/abs/2203.12471

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