Papers › Toroidal PCA via density ridges
Toroidal PCA via density ridges
Eduardo García-Portugués, Arturo Prieto-Tirado
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Principal Component Analysis (PCA) is a well-known linear dimension-reduction technique designed for Euclidean data. In a wide spectrum of applied fields, however, it is common to observe multivariate circular data (also known as toroidal data), rendering spurious the use of PCA on it due to the periodicity of its support. This paper introduces Toroidal Ridge PCA (TR-PCA), a novel construction of PCA for bivariate circular data that leverages the concept of density ridges as a flexible first principal component analog. Two reference bivariate circular distributions, the bivariate sine von Mises and the bivariate wrapped Cauchy, are employed as the parametric distributional basis of TR-PCA. Efficient algorithms are presented to compute density ridges for these two distribution models. A complete PCA methodology adapted to toroidal data (including scores, variance decomposition, and resolution of edge cases) is introduced and implemented in the companion R package ridgetorus. The usefulness of TR-PCA is showcased with a novel case study involving the analysis of ocean currents on the coast of Santa Barbara.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections