Mohajer, Mojgan and Englmeier, KarlHans and Schmid, Volker J. (1. December 2010): A comparison of Gap statistic definitions with and without logarithm function. Department of Statistics: Technical Reports, No.96 

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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 withincluster 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 DCEMR images.
Item Type:  Paper (Technical Report) 

Status:  Submitted Version 
Keywords:  average linkage, Gap statistic, log function, number of clusters, within cluster dispersion 
Collections:  Mathematics, Computer Science and Statistics > Statistics > Technical Reports 
Subjects:  500 Science > 510 Mathematics 
JEL Classification:  C38 
URN:  urn:nbn:de:bvb:19epub119203 
Language:  English 
ID Code:  11920 
Deposited On:  03. Dec 2010 10:42 
Last Modified:  27. Nov 2013 13:01 
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