cutHyperPlane {intrinsicDimension}

Piece of Noisy Hyperplane

Description

Generates Ns data points within the unit ball from a hyperplane through the origin with noise added. n has to be at least d, otherwise the function terminates with an error.

Usage

cutHyperPlane(Ns, d, n, sd)

Arguments

Ns

number of data points.

d

dimension of hyperplane.

n

dimension of noise.

sd

standard deviation of noise.

Details

The data set is generated the following way: First data points are sampled uniformly in a d-ball. After this, (n-d)-dimensional orthogonal noise with standard deviation sd in each direction is added. No noise is added in the directions parallel to the hyperplane since on an infinite plane adding isotropic noise to a uniform distribution does not change the distribution. Finally all data points within distance 1 from the origin are considered as candidates for the data set that will be returned, out of the candidates Ns data points are chosen randomly to be returned. If there are less than Ns candidates more candidates will be generated in the same way.

The data generated by this function can be used to evaluate how much local dimension estimators are affected by noise.

Value

A Ns x n matrix.

Warning

If sd is high, cutHyperPlane 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

cutHyperSphere

Examples

datap <- cutHyperPlane(100, 2, 3, 0.01)
par(mfrow = c(1, 2))
plot(datap[, 1], datap[, 2])
plot(datap[, 1], datap[, 3])