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Riemann

Riemann brings established learning algorithms for manifold-valued data together through a common R interface. It provides clustering, tangent PCA, scalar-response kernel regression, descriptive summaries, inference, and probability models for observations such as positive-definite matrices, directions, and landmark shapes. The implementation combines R, native C++, and selected R-package backends.

Version 0.2.0

This documentation describes development version 0.2.0, available from GitHub and requiring R 4.4 or later. Its core workflow records the selected geometry in fitted means, medians, tangent PCA, clustering, and scalar-response kernel regression. Prediction reuses the training geometry and reference. See the release notes for the changes and numerical corrections in this version.

library(Riemann)
x <- wrap.spd(list(diag(c(1, 2)), diag(c(2, 3)), diag(c(4, 1))))
fit <- riem.pga(x, ndim = 2, geometry = "log_euclidean")
predict(fit, x)
#>             PC1         PC2
#> [1,] -0.6218966 -0.32076986
#> [2,] -0.2887207  0.40987969
#> [3,]  0.9106173 -0.08910983
summary(fit)$geometry
#> Geometry: log_euclidean on spd
#> Representation: 2 x 2 ; intrinsic dimension: 3
#> Validation: core_contract

Read the geometry workflows, migration guide, and descriptive data applications. riem.capabilities() reports available geometric operations; the method contracts distinguish the consolidated core from bounded legacy contracts and experimental routines. Intrinsic Stiefel and correlation computations are currently unavailable. Landmark shape workflows permit reflections through the full orthogonal group.

License

The author-owned software in the September 21, 2026 revision of version 0.2.0 is licensed under GPL-3. Earlier MIT releases and preserved archives retain their original license. Third-party notices are retained in inst/COPYRIGHTS; dependencies and the separate manuscript/replication workspace retain their own license notices.

Installation

  • Option 1 : released version from CRAN.
install.packages("Riemann")
  • Option 2 : development version from GitHub.
if (!require("devtools")) {
  install.packages("devtools")
}
devtools::install_github("kisungyou/Riemann")

Contact

Report bugs through GitHub issues or contact Kisung You.