Package index • Riemann

Prepare Data on Manifolds

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

Common Functions on All Supported Manifolds

[1] Basic Operations

riem.interp(): Geodesic Interpolation

riem.interps(): Geodesic Interpolation of Multiple Points

riem.pdist(): Compute Pairwise Distances for Data

riem.pdist2(): Compute Pairwise Distances for Two Sets of Data

riem.wasserstein(): Wasserstein Distance between Empirical Measures

[2] Statistical Inference

predict(<m2skreg>): Prediction for Manifold-to-Scalar Kernel Regression

riem.fanova() riem.fanovaP(): Fréchet Analysis of Variance

riem.m2skreg(): Manifold-to-Scalar Kernel Regression

riem.m2skregCV(): Manifold-to-Scalar Kernel Regression with K-Fold Cross Validation

riem.mean(): Fréchet Mean and Variation

riem.median(): Fréchet Median and Variation

riem.test2bg14(): Two-Sample Test modified from Biswas and Ghosh (2014)

riem.test2wass(): Two-Sample Test with Wasserstein Metric

[3] Clustering

riem.clrq(): Competitive Learning Riemannian Quantization

riem.hclust(): Hierarchical Agglomerative Clustering

riem.kmeans(): K-Means Clustering

riem.kmeans18B(): K-Means Clustering with Lightweight Coreset

riem.kmeanspp(): K-Means++ Clustering

riem.kmedoids(): K-Medoids Clustering

riem.nmshift(): Nonlinear Mean Shift

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

[5] Visualization and Dimension Reduction

riem.isomap(): Isometric Feature Mapping

riem.kpca(): Kernel Principal Component Analysis

riem.mds(): Multidimensional Scaling

riem.pga(): Principal Geodesic Analysis

riem.phate(): PHATE

riem.sammon(): Sammon Mapping

riem.tsne(): t-distributed Stochastic Neighbor Embedding

[6] Curves

riem.distlp(): Distance between Two Curves on Manifolds

riem.dtw(): Dynamic Time Warping Distance

[7] Spatial Analysis

[8] Other Methods

riem.coreset18B(): Build Lightweight Coreset

riem.knn(): Find K-Nearest Neighbors

riem.rmml(): Riemannian Manifold Metric Learning

riem.seb(): Find the Smallest Enclosing Ball

Functions on Specific Manifolds

Sphere

moSL() loglkd(<moSL>) label(<moSL>) density(<moSL>): Finite Mixture of Spherical Laplace Distributions

moSN() loglkd(<moSN>) label(<moSN>) density(<moSN>): Finite Mixture of Spherical Normal Distributions

sphere.geo2xyz() sphere.xyz2geo(): Convert between Cartesian Coordinates and Geographic Coordinates

sphere.runif(): Generate Uniform Samples on Sphere

sphere.utest(): Test of Uniformity on Sphere

Stiefel

stiefel.optSA(): Simulated Annealing on Stiefel Manifold

stiefel.runif(): Generate Uniform Samples on Stiefel Manifold

stiefel.utest(): Test of Uniformity on Stiefel Manifold

Grassmann

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

SPD

spd.geometry(): Supported Geometries on SPD Manifold

spd.pdist(): Pairwise Distance on SPD Manifold

spd.wassbary(): Wasserstein Barycenter of SPD Matrices

Probability Distributions

dacg() racg() mle.acg(): Angular Central Gaussian Distribution

dmacg() rmacg() mle.macg(): Matrix Angular Central Gaussian Distribution

dsplaplace() rsplaplace() mle.splaplace(): Spherical Laplace Distribution

dspnorm() rspnorm() mle.spnorm(): Spherical Normal Distribution

Data

ERP: Data : EEG Covariances for Event-Related Potentials

cities: Data : Populated Cities in the U.S.

gorilla: Data : Gorilla Skull

hands: Data : Left Hands

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

passiflora: Data : Passiflora Leaves

Others

density(): S3 method for mixture model : evaluate density

label(): S3 method for mixture model : predict labels

loglkd(): S3 method for mixture model : log-likelihood

rmvnorm(): Generate Random Samples from Multivariate Normal Distribution