# Learning with Data on Riemannian Manifolds

## Documentation for package ‘Riemann’ version 0.1.4

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

acg | Angular Central Gaussian Distribution
cities | Data : Populated Cities in the U.S.
dacg | Angular Central Gaussian Distribution
density | S3 method for mixture model : evaluate density
density.moSL | Finite Mixture of Spherical Laplace Distributions
density.moSN | Finite Mixture of Spherical Normal Distributions
dmacg | Matrix Angular Central Gaussian Distribution
dsplaplace | Spherical Laplace Distribution
dspnorm | Spherical Normal Distribution
ERP | Data : EEG Covariances for Event-Related Potentials
gorilla | Data : Gorilla Skull
grassmann.optmacg | Estimation of Distribution Algorithm with MACG Distribution
grassmann.runif | Generate Uniform Samples on Grassmann Manifold
grassmann.utest | Test of Uniformity on Grassmann Manifold
hands | Data : Left Hands
label | S3 method for mixture model : predict labels
label.moSL | Finite Mixture of Spherical Laplace Distributions
label.moSN | Finite Mixture of Spherical Normal Distributions
loglkd | S3 method for mixture model : log-likelihood
loglkd.moSL | Finite Mixture of Spherical Laplace Distributions
loglkd.moSN | Finite Mixture of Spherical Normal Distributions
macg | Matrix Angular Central Gaussian Distribution
mle.acg | Angular Central Gaussian Distribution
mle.macg | Matrix Angular Central Gaussian Distribution
mle.splaplace | Spherical Laplace Distribution
mle.spnorm | Spherical Normal Distribution
moSL | Finite Mixture of Spherical Laplace Distributions
moSN | Finite Mixture of Spherical Normal Distributions
orbital | Data : Normal Vectors to the Orbital Planes of the 9 Planets
passiflora | Data : Passiflora Leaves
predict.m2skreg | Prediction for Manifold-to-Scalar Kernel Regression
racg | Angular Central Gaussian Distribution
riem.clrq | Competitive Learning Riemannian Quantization
riem.coreset18B | Build Lightweight Coreset
riem.distlp | Distance between Two Curves on Manifolds
riem.dtw | Dynamic Time Warping Distance
riem.fanova | Fréchet Analysis of Variance
riem.fanovaP | Fréchet Analysis of Variance
riem.hclust | Hierarchical Agglomerative Clustering
riem.interp | Geodesic Interpolation
riem.interps | Geodesic Interpolation of Multiple Points
riem.isomap | Isometric Feature Mapping
riem.kmeans | K-Means Clustering
riem.kmeans18B | K-Means Clustering with Lightweight Coreset
riem.kmeanspp | K-Means++ Clustering
riem.kmedoids | K-Medoids Clustering
riem.knn | Find K-Nearest Neighbors
riem.kpca | Kernel Principal Component Analysis
riem.m2skreg | Manifold-to-Scalar Kernel Regression
riem.m2skregCV | Manifold-to-Scalar Kernel Regression with K-Fold Cross Validation
riem.mds | Multidimensional Scaling
riem.mean | Fréchet Mean and Variation
riem.median | Fréchet Median and Variation
riem.nmshift | Nonlinear Mean Shift
riem.pdist | Compute Pairwise Distances for Data
riem.pdist2 | Compute Pairwise Distances for Two Sets of Data
riem.pga | Principal Geodesic Analysis
riem.phate | PHATE
riem.rmml | Riemannian Manifold Metric Learning
riem.sammon | Sammon Mapping
riem.sc05Z | Spectral Clustering by Zelnik-Manor and Perona (2005)
riem.scNJW | Spectral Clustering by Ng, Jordan, and Weiss (2002)
riem.scSM | Spectral Clustering by Shi and Malik (2000)
riem.scUL | Spectral Clustering with Unnormalized Laplacian
riem.seb | Find the Smallest Enclosing Ball
riem.test2bg14 | Two-Sample Test modified from Biswas and Ghosh (2014)
riem.test2wass | Two-Sample Test with Wasserstein Metric
riem.tsne | t-distributed Stochastic Neighbor Embedding
riem.wasserstein | Wasserstein Distance between Empirical Measures
rmacg | Matrix Angular Central Gaussian Distribution
rmvnorm | Generate Random Samples from Multivariate Normal Distribution
rsplaplace | Spherical Laplace Distribution
rspnorm | Spherical Normal Distribution
spd.geometry | Supported Geometries on SPD Manifold
spd.pdist | Pairwise Distance on SPD Manifold
spd.wassbary | Wasserstein Barycenter of SPD Matrices
sphere.convert | Convert between Cartesian Coordinates and Geographic Coordinates
sphere.geo2xyz | Convert between Cartesian Coordinates and Geographic Coordinates
sphere.runif | Generate Uniform Samples on Sphere
sphere.utest | Test of Uniformity on Sphere
sphere.xyz2geo | Convert between Cartesian Coordinates and Geographic Coordinates
splaplace | Spherical Laplace Distribution
spnorm | Spherical Normal Distribution
stiefel.optSA | Simulated Annealing on Stiefel Manifold
stiefel.runif | Generate Uniform Samples on Stiefel Manifold
stiefel.utest | Test of Uniformity on Stiefel Manifold
wrap.correlation | Prepare Data on Correlation Manifold
wrap.euclidean | Prepare Data on Euclidean Space
wrap.grassmann | Prepare Data on Grassmann Manifold
wrap.landmark | Wrap Landmark Data on Shape Space
wrap.multinomial | Prepare Data on Multinomial Manifold
wrap.rotation | Prepare Data on Rotation Group
wrap.spd | Prepare Data on Symmetric Positive-Definite (SPD) Manifold
wrap.spdk | Prepare Data on SPD Manifold of Fixed-Rank
wrap.sphere | Prepare Data on Sphere
wrap.stiefel | Prepare Data on (Compact) Stiefel Manifold