Validity index | Equation | Type |
---|---|---|
Xie-Beni index (XB) [47] measures | \({XB=\frac {\sum \limits _{k=1}^{K}\sum \limits _{i=1}^{n} D^{2}(z_{k}, x_{i})}{ n \times \min _{k\neq l}\{D^{2}(z_{k}, z_{l})\}}} \) | Minimisation |
the quotient between the total | Â | |
variance and the minimum | Â | |
separation of the elements | Â | |
in the clusters. | Â | |
Overall cluster deviation (Dev) [48] | \(Dev= \sum \limits _{k=1}^{K} \sum \limits _{x_{i} \in C_{k}} D(z_{k}, x_{i})\) | Minimisation |
is defined as the overall summed | Â | |
distances between genes and their | Â | |
corresponding cluster medoid. | Â | |
Cluster separation (Sep) [49] is | \( Sep= \frac {2}{K(K-1)}\sum \limits _{k=1}^{K} \sum \limits _{j=1, j\not =i}^{K} D^{2}(z_{i}, z_{j})\) | Maximization |
defined as inter-cluster distances | Â | |
between cluster medoids. | Â |