cutHyperSphere {intrinsicDimension}

Piece of Noisy Hypersphere

Description

Generates Ns data points cut out from a noisy hypersphere. n has to be at least d+1, otherwise the function terminates with an error.

Usage

cutHyperSphere(Ns, rat, d, n, sd)

Arguments

Ns

number of data points.

rat

ratio between cut-off radius and radius of sphere.

d

(intrinsic) dimension of hypersphere.

n

dimension of noise.

sd

standard deviation of noise.

Details

The returned data are within distance rat the point 1/\sqrt{d+1}(1 ... 1) and are obtained from a unit distribution on the d-sphere overlaid with n-dimensional normal noise.

The data generated by this function can be used to evaluate the performance of local dimension estimators.

Value

A Ns by n matrix.

Warning

If sd is high, cutHyperSphere will be slow and might not even be able to return a data set. If so, it will return NULL.

Author(s)

Kerstin Johnsson, Lund University

See Also

cutHyperPlane

Examples

datap <- cutHyperSphere(100, rat = .5, 1, 3, 0.01)
par(mfrow = c(1, 2))
plot(datap[, 1], datap[, 2])
plot(datap[, 1], datap[, 3])

datap <- cutHyperSphere(100, rat = 2, 1, 3, 0.11)
par(mfrow = c(1, 2))
plot(datap[, 1], datap[, 2])
plot(datap[, 1], datap[, 3])