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Question

Formula for silhouette coefficient

Calculate the silhouette coefficient of point Pi from the above image.

To apply the given formula, how to know which is a(i) and b(i)?

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a(i) : the average distance between 'i' and all other data within the same cluster (source)

b(i) : the lowest average distance of 'i' to all points in any other cluster, of which 'i' is not a member (source)

So, from the question, a(i) will be 24 as point 'Pi' belongs to cluster A and b(i) will be 48 as it is the least average distance that 'Pi' has from any other cluster than A (to which it belongs).

So, as a(i) < b(i), silhouette coefficient s(i) = 1 - 24/48 = 0.5

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$a_i = 24$

$b_i = (48 + 72)/2=60$

$1 - 24/60 =.6$

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