A comparison of Gap statistic definitions with and without logarithm function
A comparison of Gap statistic definitions with and without logarithm function
复制标题
使用和不使用对数函数的 Gap 统计量定义的比较
DOI：
10.5282/ubm/epub.11920
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Volker J Schmid
中科院分区：
文献类型：
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作者：
Mojgan Mohajer;K. Englmeier;Volker J Schmid
差距统计是确定一组数据中聚类数量的标准方法。差距统计量通过将 $\log(W_{k})$ 的图与适当的数据空参考分布下的期望进行比较，对 $\log(W_{k})$ 进行标准化，其中 $W_{k}$ 是簇内离散度。我们建议使用 $W_{k}$ 代替 $\log(W_{k})$，并将其与空参考分布下的 $W_{k}$ 的期望进行比较。事实上，每当一个数满足原始的 Gap 统计不等式时，这个数也满足使用 $W_{k}$ 的 Gap 统计不等式，但不满足 \textit{反之亦然}。间隙函数的两个定义在几个模拟数据集和 DCE-MR 图像的真实数据上进行评估。
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.