wrap.sphere: Prepare Data on Sphere In Riemann: Learning with Data on Riemannian Manifolds

Description

The unit hypersphere (sphere, for short) is one of the most fundamental curved space in studying geometry. Precisely, we denote (p-1) sphere in \mathbf{R}^p by

\mathcal{S}^{p-1} = \lbrace x \in \mathbf{R}^p ~ \vert ~ x^\top x = \|x\|^2 = 1 \rbrace

where vectors are of unit norm. In wrap.sphere, normalization is applied when each data point is not on the unit sphere.

Usage

 1 wrap.sphere(input)

Arguments

 input data vectors to be wrapped as riemdata class. Following inputs are considered, matrixan (n \times p) matrix of row observations of unit norm. lista length-n list whose elements are length-p vectors of unit norm.

Value

a named riemdata S3 object containing

data

a list of (p\times 1) matrices in \mathcal{S}^{p-1}.

size

dimension of the ambient space.

name

name of the manifold of interests, "sphere"

Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 #------------------------------------------------------------------- # Checker for Two Types of Inputs # # Generate 5 observations in S^2 embedded in R^3. #------------------------------------------------------------------- ## DATA GENERATION d1 = array(0,c(5,3)) d2 = list() for (i in 1:5){ single = stats::rnorm(3) d1[i,] = single d2[[i]] = single } ## RUN test1 = wrap.sphere(d1) test2 = wrap.sphere(d2)

Riemann documentation built on June 20, 2021, 5:07 p.m.