gensilwidth {optpart}

Generalized Silhouette Width

Description

Calculates mean cluster silhouette widths using a generalized mean.

Usage

gensilwidth(clust, dist, p=1)

Arguments

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

Details

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.

Value

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

Author(s)

Attila Lengyel and Zoltan Botta-Dukat wrote the algorithm

David W. Roberts [e-mail] http://ecology.msu.montana.edu/labdsv/R

References

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

See Also

silhouette

Examples

data(shoshveg)
dis.bc <- dsvdis(shoshveg,'bray')
opt.5 <- optpart(5,dis.bc)
gensilwidth(opt.5,dis.bc)