Learning with Data on Riemannian Manifolds
Angular Central Gaussian Distribution
S3 method for mixture model : evaluate density
Estimation of Distribution Algorithm with MACG Distribution
Generate Uniform Samples on Grassmann Manifold
Test of Uniformity on Grassmann Manifold
S3 method for mixture model : predict labels
S3 method for mixture model : log-likelihood
Matrix Angular Central Gaussian Distribution
Finite Mixture of Spherical Laplace Distributions
Finite Mixture of Spherical Normal Distributions
Prediction for Manifold-to-Scalar Kernel Regression
Competitive Learning Riemannian Quantization
Build Lightweight Coreset
Distance between Two Curves on Manifolds
Dynamic Time Warping Distance
Fréchet Analysis of Variance
Hierarchical Agglomerative Clustering
Geodesic Interpolation
Geodesic Interpolation of Multiple Points
Isometric Feature Mapping
K-Means Clustering
K-Means Clustering with Lightweight Coreset
K-Means++ Clustering
K-Medoids Clustering
Find K-Nearest Neighbors
Kernel Principal Component Analysis
Manifold-to-Scalar Kernel Regression
Manifold-to-Scalar Kernel Regression with K-Fold Cross Validation
Multidimensional Scaling
Fréchet Mean and Variation
Fréchet Median and Variation
Nonlinear Mean Shift
Compute Pairwise Distances for Data
Compute Pairwise Distances for Two Sets of Data
Principal Geodesic Analysis
PHATE
Riemannian Manifold Metric Learning
Sammon Mapping
Spectral Clustering by Zelnik-Manor and Perona (2005)
Spectral Clustering by Ng, Jordan, and Weiss (2002)
Spectral Clustering by Shi and Malik (2000)
Spectral Clustering with Unnormalized Laplacian
Find the Smallest Enclosing Ball
Two-Sample Test modified from Biswas and Ghosh (2014)
Two-Sample Test with Wasserstein Metric
t-distributed Stochastic Neighbor Embedding
Wasserstein Distance between Empirical Measures
Generate Random Samples from Multivariate Normal Distribution
Supported Geometries on SPD Manifold
Pairwise Distance on SPD Manifold
Wasserstein Barycenter of SPD Matrices
Convert between Cartesian Coordinates and Geographic Coordinates
Generate Uniform Samples on Sphere
Test of Uniformity on Sphere
Spherical Laplace Distribution
Spherical Normal Distribution
Simulated Annealing on Stiefel Manifold
Generate Uniform Samples on Stiefel Manifold
Test of Uniformity on Stiefel Manifold
Prepare Data on Correlation Manifold
Prepare Data on Euclidean Space
Prepare Data on Grassmann Manifold
Wrap Landmark Data on Shape Space
Prepare Data on Multinomial Manifold
Prepare Data on Rotation Group
Prepare Data on Symmetric Positive-Definite (SPD) Manifold
Prepare Data on SPD Manifold of Fixed-Rank
Prepare Data on Sphere
Prepare Data on (Compact) Stiefel Manifold
We provide a variety of algorithms for manifold-valued data, including Fréchet summaries, hypothesis testing, clustering, visualization, and other learning tasks. See Bhattacharya and Bhattacharya (2012) <doi:10.1017/CBO9781139094764> for general exposition to statistics on manifolds.