Spherical {intrinsicDimension}

Isotropic Distributions With or Without Noise

Description

Generates a sample from isotropic distributions in d dimensions with n-dimensional noise added to it.

Usage

hyperBall(Ns, d, n = d, sd = 0)
hyperSphere(Ns, d, n = d + 1, sd = 0)
isotropicNormal(Ns, d, n = d, sd = 0)

Arguments

Ns

number of points.

d

intrinsic dimension of the support of the distribution (the manifold.)

n

dimension of noise.

sd

standard deviation of noise.

Details

hyperBall draws a sample from a uniform distribution on a hyper ball of radius 1. hyperSphere draws a sample from a uniform distribution on a hypersphere of radius 1. isotropicNormal draws a sample from a isotropic normal distribution with identity covariance matrix.

Author(s)

Kerstin Johnsson, Lund University

Examples

datap <- hyperSphere(100, 1, 3, sd = .1)
par(mfrow = c(1, 2))
plot(datap[, 1], datap[, 2])
plot(datap[, 1], datap[, 3])