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**Mohajer, Mojgan, Englmeier, Karl-Hans and Schmid, Volker J. ORCID: https://orcid.org/0000-0003-2195-8130 (1. December 2010): A comparison of Gap statistic definitions with and without logarithm function. Department of Statistics: Technical Reports, No.96 [PDF, 766kB]**

## Abstract

The Gap statistic is a standard method for determining the number of clusters in a set of data. The Gap statistic standardizes the graph of $\log(W_{k})$, where $W_{k}$ is the within-cluster dispersion, by comparing it to its expectation under an appropriate null reference distribution of the data. We suggest to use $W_{k}$ instead of $\log(W_{k})$, and to compare it to the expectation of $W_{k}$ under a null reference distribution. In fact, whenever a number fulfills the original Gap statistic inequality, this number also fulfills the inequality of a Gap statistic using $W_{k}$, but not \textit{vice versa}. The two definitions of the Gap function are evaluated on several simulated data set and on a real data of DCE-MR images.

Item Type: | Paper |
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Form of publication: | Submitted Version |

Keywords: | average linkage, Gap statistic, log function, number of clusters, within cluster dispersion |

Faculties: | Mathematics, Computer Science and Statistics > Statistics > Technical Reports Mathematics, Computer Science and Statistics > Statistics > Chairs/Working Groups > Bioimaging |

Subjects: | 000 Computer science, information and general works > 000 Computer science, knowledge, and systems 500 Science > 510 Mathematics 600 Technology > 610 Medicine and health |

JEL Classification: | C38 |

URN: | urn:nbn:de:bvb:19-epub-11920-3 |

Language: | English |

Item ID: | 11920 |

Date Deposited: | 03. Dec 2010 10:42 |

Last Modified: | 04. Nov 2020 12:52 |

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