  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.
