Generalized Silhouette Width
Calculates mean cluster silhouette widths using a generalized mean.
gensilwidth(clust, dist, p=1)
clust |
an integer vector of cluster memberships or a classification object of class ‘clustering’ |
dist |
an object of class ‘dist’ |
p |
the scaling parameter of the analysis |
gensilwidth calculates mean cluster silhouette widths using a generalized mean. The scaling parameter can be set between [-∞,∞] 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 = ≤ft( {1\over n} ∑_{k=1}^n s_k^p \right)^{1/p}
Exceptions exist for specific values:
for p=0
s_i = ≤ft( ∏_{k=1}^n s_k \right)^{1/n}
for p=-∞
s_i = \min_{k=1}^n s_k
for p=∞
s_i = \max_{k=1}^n s_k
p=-1 = harmonic mean, p=0 = geometric mean, and p=1 = arithmetic mean.
an object of class ‘silhouette’, a list with components
cluster |
the assigned cluster for each sample unit |
neighbor |
the identity of the nearest neighbor cluster for each sample unit |
sil_width |
the silhouette width for each sample unit |
Attila Lengyel and Zoltan Botta-Dukat wrote the algorithm
David W. Roberts droberts@montana.edu http://ecology.msu.montana.edu/labdsv/R
Lengyel, A. and Z. Botta-Dukat. 2019. Silhouette width using generalized mean: A flexible method for assessing clustering efficiency. Ecology and Evolution https://doi.org/10.1002/ece3.5774
data(shoshveg) dis.bc <- dsvdis(shoshveg,'bray') opt.5 <- optpart(5,dis.bc) gensilwidth(opt.5,dis.bc)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.