Description Usage Arguments Details Value Warning Author(s) See Also Examples

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.

1 | ```
cutHyperPlane(Ns, d, n, sd)
``` |

`Ns` |
number of data points. |

`d` |
dimension of hyperplane. |

`n` |
dimension of noise. |

`sd` |
standard deviation of noise. |

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.

A `Ns`

x `n`

matrix.

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`

.

Kerstin Johnsson, Lund University

1 2 3 4 |

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