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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] 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