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Riemann

Riemann is an R package for learning with data on Riemannian manifolds. In statistics and machine learning, the term manifold appears in two realms; one is dimensionality reduction where we assume that low-dimensional data manifold is embedded in high-dimensional Euclidean space. The other is statistics on manifolds - data lie on some Riemannian manifolds that we are already well aware of. Riemann aims to achieve the latter. If you are interested in dimension reduction, please check another R package Rdimtools.

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")

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Version

Install

install.packages('Riemann')

Monthly Downloads

621

Version

0.1.6

License

MIT + file LICENSE

Maintainer

Kisung You

Last Published

September 26th, 2025

Functions in Riemann (0.1.6)

Data : EEG Covariances for Event-Related Potentials

grassmann.optmacg

Estimation of Distribution Algorithm with MACG Distribution

Data : Gorilla Skull

Angular Central Gaussian Distribution

predict.m2skreg

Prediction for Manifold-to-Scalar Kernel Regression

S3 method for mixture model : predict labels

Distance between Two Curves on Manifolds

Data : Normal Vectors to the Orbital Planes of the 9 Planets

Data : Left Hands

Data : Passiflora Leaves

Dynamic Time Warping Distance

Data : Populated Cities in the U.S.

K-Means Clustering

Geodesic Interpolation

Hierarchical Agglomerative Clustering

Competitive Learning Riemannian Quantization

grassmann.runif

Generate Uniform Samples on Grassmann Manifold

grassmann.utest

Test of Uniformity on Grassmann Manifold

K-Means Clustering with Lightweight Coreset

Principal Geodesic Analysis

Multidimensional Scaling

Finite Mixture of Spherical Laplace Distributions

Finite Mixture of Spherical Normal Distributions

Compute Pairwise Distances for Data

Compute Pairwise Distances for Two Sets of Data

Isometric Feature Mapping

Geodesic Interpolation of Multiple Points

S3 method for mixture model : evaluate density

Riemannian Manifold Metric Learning

Find K-Nearest Neighbors

Kernel Principal Component Analysis

riem.wasserstein

Wasserstein Distance between Empirical Measures

Generate Random Samples from Multivariate Normal Distribution

Fréchet Median and Variation

Spectral Clustering by Shi and Malik (2000)

Fréchet Analysis of Variance

Nonlinear Mean Shift

S3 method for mixture model : log-likelihood

Pairwise Distance on SPD Manifold

Spectral Clustering with Unnormalized Laplacian

Supported Geometries on SPD Manifold

Matrix Angular Central Gaussian Distribution

K-Means++ Clustering

Prepare Data on (Compact) Stiefel Manifold

Generate Uniform Samples on Sphere

Test of Uniformity on Sphere

Test of Uniformity on Stiefel Manifold

Prepare Data on SPD Manifold of Fixed-Rank

wrap.correlation

Prepare Data on Correlation Manifold

Simulated Annealing on Stiefel Manifold

Prepare Data on Sphere

Spectral Clustering by Ng, Jordan, and Weiss (2002)

Convert between Cartesian Coordinates and Geographic Coordinates

Wasserstein Barycenter of SPD Matrices

Spectral Clustering by Zelnik-Manor and Perona (2005)

Wrap Landmark Data on Shape Space

K-Medoids Clustering

Manifold-to-Scalar Kernel Regression with K-Fold Cross Validation

Manifold-to-Scalar Kernel Regression

Find the Smallest Enclosing Ball

Fréchet Mean and Variation

wrap.multinomial

Prepare Data on Multinomial Manifold

Generate Uniform Samples on Stiefel Manifold

Prepare Data on Grassmann Manifold

t-distributed Stochastic Neighbor Embedding

Prepare Data on Euclidean Space

Two-Sample Test with Wasserstein Metric

Prepare Data on Rotation Group

Spherical Laplace Distribution

Two-Sample Test modified from Biswas and Ghosh (2014)

Spherical Normal Distribution

Prepare Data on Symmetric Positive-Definite (SPD) Manifold

riem.coreset18B

Build Lightweight Coreset