Scientific Paper¶
This section highlights the scientific foundation behind the Riemannian STATS package.
Riemannian Principal Component Analysis¶
R-PCA is a novel extension of Principal Component Analysis designed to operate on datasets that reside on non-Euclidean spaces. Instead of assuming a flat Euclidean structure, R-PCA leverages local geometric information, derived via the UMAP algorithm, to define a Riemannian manifold over the data. This allows for more accurate dimensionality reduction and statistical analysis that respects the intrinsic structure of complex datasets.
Applications include:
High-dimensional structured data
Clustering with geometric consistency
Real-world datasets such as image sets (e.g., Olivetti Faces)
R-PCA improves interpretability, variance capture, and clustering performance compared to standard PCA especially in cases where local metrics vary significantly across the dataset.
📄 Link to the complete paper: "Riemannian Principal Component Analysis"Watch the official presentation introducing the concepts behind R-PCA. (Video in Spanish)