gensilwidth calculates mean cluster silhouette widths using a generalized
mean. The scaling parameter can be set between \([-\infty,\infty]\) where values
less than one emphasize connectivity, and values greater than one emphasize
compactedness. Individual sample unit silhouette widths are still calculated as
\(s _i = (b_i - a_i) / \max(b_i,a_i)\) where \(a_i\) is the mean dissimilarity of a
sample unit to the cluster to which it is assigned, and \(b_i\) is the mean
dissimilarity to the nearest neighbor cluster. Given \(s_i\) for all members of a cluster,
the generalized mean is calculated as
$$\bar s = \left( {1\over n} \sum_{k=1}^n s_k^p \right)^{1/p}$$
Exceptions exist for specific values:
for p=0 $$s_i = \left( \prod_{k=1}^n s_k \right)^{1/n}$$
for p=\(-\infty\) $$s_i = \min_{k=1}^n s_k$$
for p=\(\infty\) $$s_i = \max_{k=1}^n s_k$$
\(p=-1\) = harmonic mean, \(p=0\) = geometric mean, and \(p=1\) = arithmetic mean.