比较不同聚类的指标

最新推荐文章于 2025-01-11 19:30:45 发布

weixin_30472035

最新推荐文章于 2025-01-11 19:30:45 发布

阅读量210

点赞数

CC 4.0 BY-SA版权

本文详细介绍了Jaccard指数的概念及其在聚类分析中的应用，包括与Fowlkes和Mallows指数的关系，以及与其他评价指标的区别。重点讨论了如何使用Jaccard指数来评估聚类结果的有效性和一致性。

Jaccard Index
The Jaccard index (also known as Jaccard similarity coefficient) between partitions A and B is defined as the size of the intersection divided by the size of the union of the sample sets: $Jaccard_{AB}=\frac{a}{a+b+c}$
where a, b, c and d are the entries in the mismatch matrix.
Fowlkes and Mallows
Another method for comparing clusters was proposed by Fowlkes and Mallows (1983) as an alternative for Rand index. The Fowlkes and Mallows index can be defined as $FM_{AB}=\frac{a}{\sqrt{(a+b)(a+c)}}$ Actually, the Wallace coefficient was derived from this index (Wallace, 1983) and therefore it can be rewritten as $FM_{AB}=\sqrt{W_{A\rightarrow B}\times W_{B\rightarrow A}}$
Mirkin Metric
This coefficient assumes null value for identical clusterings and positive values otherwise. It corresponds to the Hamming distance between the binary vector representation of each partition. $Mirkin_{AB}=2(b+c)=N(N-1)(1-Rand)$ It provides an alternative adjusted form of Rand index. However, unlike Hubert and Arabie's adjusted Rand (Hubert, 1985) it doesn't provide a correction for chance agreement. Meila (2005) also proposed a bounded version of this index: $Mirkin_{AB}^'=\frac{Mirkin}{N^2}$
NMI (normalized mutual information)

where cA ( cB ) i s t he number of groups in the partition A ( B),Ci· ( C·j ) i s t he sum of elements of C in row i (column j),
and N is the number of nodes.
If A = B, t hen I ( A,B) = 1; if A and B are completely different, t hen I ( A,B) = 0.

（to be continued...）