$[20$ points$]$ Hierarchical clustering

In Figure $3$ there are two clusters A $($red$)$ and B $($blue$),$ each has four members and plotted in

Figure $3.$ The coordinates of each member are labeled in the figure. Compute the distance

between two clusters using Euclidean distance.

Figure $3$: Scatter plot samples in two clusters

a$.$ What is the distance between the two farthest members? $($max or complete link$)($round to four decimal places here, and next $2$ problems$)$

$\_$ a$.$ What is the distance between the two farthest members? $($max or complete link$)($round to four decimal places here, and next $2$ problems$)$

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b$.$ What is the distance between the two closest members? $($min or single link$)$

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c$.$ What is the average distance between all pairs?

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d$.$ What is the center distance between two clusters?

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e$.$ Among all four distances above, which one is robust to noise? Answer either $$complete$,$single$,$average$,$ and "center"?

b$.$ What is the distance between the two closest members? $($min or single link$)$

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c$.$ What is the average distance between all pairs?

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d$.$ What is the center distance between two clusters?

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e$.$ Among all four distances above, which one is robust to noise? Answer either $$complete$,$single$,$average$,$ and "center"?