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

Estimates local manifold dimension using the largest singular values of the covariance matrix.

1 2 |

`data` |
a local data set for which dimension should be estimated. |

`ver` |
possible values: |

`alphaFO` |
only for |

`alphaFan` |
only for |

`betaFan` |
only for |

`PFan` |
only for |

`ngap` |
only for |

`maxdim` |
only for |

`verbose` |
should information about the process be printed out? |

Version `'FO'`

is the method by Fukunaga-Olsen, version `'fan'`

is the method by Fan et al..

Version `'maxgap'`

returns the position of the largest relative gap in the sequence of singular values.

Version `'cal'`

considers the positions of the `ngap`

largest relative gaps in the
sequence of singular values and generates calibration data to determine which one of them is most likely.

All versions assume that the data is local, i.e. that it is a neighborhood taken from a larger data set, such that the curvature and the noise within the neighborhood is relatively small. In the ideal case (no noise, no curvature) this is equivalent to the data being uniformly distributed over a hyper ball.

A `DimEst`

object with slots:

`dim.est` |
the dimension estimate |

`gap.size` |
if |

`likelihood` |
if |

Kerstin Johnsson, Lund University

Fukunaga, K. and Olsen, D. R. (1971). An algorithm for finding intrinsic dimensionality
of data. *IEEE Trans. Comput.*, **c-20**(2):176-183.

Fan, M. et al. (2010). Intrinsic dimension estimation of data by principal component
analysis. *arXiv preprint* 1002.2050.

1 2 3 4 | ```
data <- cutHyperPlane(100, 4, 10, .05)
pcaLocalDimEst(data, 'fan')
pcaLocalDimEst(data, 'FO')
pcaLocalDimEst(data, 'maxgap')
``` |

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