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For cluster analysis, the distance between two clusters was measured by Ward's method (Ward, 1963).
When the minimal distance between two clusters was larger than 1 Å, the clustering was stopped.
(The UPGMA used because the distance between two clusters was calculated as the average distance between all pairs of objects in two different clusters).
The cluster analysis was done using the complete linkage clustering [ 20] where the distance between two clusters was measured as a maximum distance between a point in one cluster and a point in another cluster.
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(3) The gateways between two clusters are located on the boundary lines. .
The distance between two clusters is given by the height of the horizontal line connecting two clusters.
Average-linkage: The distance between two clusters is defined as the average of all distances between the observations in one cluster and the other cluster: average- linkage dist ance=frac{1}{N_X{N}_Y}{displaystyle sum_{xin X}}{displaystyle sum_{yin Y}} distleft x,yright); where X and Y are two different clusters; N X,N Y are the corresponding numbers of observations.
Single-linkage: The distance between two clusters is defined as the minimum of all distances between the observations in one cluster and the other cluster: single- linkage distance= minleft{ distleft x,yright):xin X,kern0.75em yin Yright}; where X and Y are two different clusters.
Complete-linkage: The distance between two clusters is defined as the maximum of all distances between the observations in one cluster and the other cluster: complete- linkage distance= maxleft{ distleft x,yright):xin X,kern0.75em yin Yright}; where X and Y are two different clusters.
Transitions between two clusters were counted if dimer conformations traversed to another cluster in the subsequent time step (frame).
In complete linkage clustering, the distance between two clusters is defined as the largest distance between two elements, one in each cluster.
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