Created by Didong Li, June 2018

The function GeoDist is designed to estimate the geodesic distance between samples assuming the data lie in some d-dimensional Riemannian manifold embedded in R^p See more details about the spherical distance and spherelets here: https://arxiv.org/abs/1706.08263

Input:

• X = data set, represented by n by p matrix where n is the sample size, p is the number of features
• k = number of neighbors used in k-nearest neighbors
• d = intrinsic dimension

Output:

• D = Euclidean pairwise distance matrix
• SD = spherical pairwise distance matrix

functions pca, SPCA and LocalDist are all necessary to run GeoDist.