cluster.stats {fpc} | R Documentation |
Computes a number of distance based statistics which can be used for cluster validation, comparison between clusterings and decision about the number of clusters: cluster sizes, cluster diameters, average distances within and between clusters, cluster separation, average silhouette widths, the Calinski and Harabasz index, the best distance based statistics to decide about the number of clusters in a study of Milligan and Cooper (1985), Hubert's gamma coefficient, the Dunn index and two indexes to assess the similarity of two clusterings, namely the corrected Rand index and Meila's VI.
cluster.stats(d,clustering,alt.clustering=NULL, silhouette=TRUE,G2=FALSE,G3=FALSE, compareonly=FALSE)
d |
a distance object (as generated by |
clustering |
an integer vector of length of the number of cases, which indicates a clustering. The clusters have to be numbered from 1 to the number of clusters. |
alt.clustering |
an integer vector such as for
|
silhouette |
logical. If |
G2 |
logical. If |
G3 |
logical. If |
compareonly |
logical. If |
cluster.stats
returns a list containing the components
n, cluster.number, cluster.size, diameter,
average.distance, median.distance, separation, average.toother,
separation.matrix, average.between, average.within,
n.between, n.within, within.cluster.ss, clus.avg.silwidths, avg.silwidth,
g2, g3, pearsongamma, dunn, entropy, wb.ratio, ch,
corrected.rand, vi
except if compareonly=TRUE
, in which case
only the last two components are computed.
n |
number of cases. |
cluster.number |
number of clusters. |
cluster.size |
vector of cluster sizes (number of points). |
diameter |
vector of cluster diameters (maximum within cluster distances). |
average.distance |
vector of clusterwise within cluster average distances. |
median.distance |
vector of clusterwise within cluster distance medians. |
separation |
vector of clusterwise minimum distances of a point in the cluster to a point of another cluster. |
average.toother |
vector of clusterwise average distances of a point in the cluster to the points of other clusters. |
separation.matrix |
matrix of separation values between all pairs of clusters. |
average.between |
average distance between clusters. |
average.within |
average distance within clusters. |
n.between |
number of distances between clusters. |
n.within |
number of distances within clusters. |
within.cluster.ss |
a generalisation of the within clusters sum
of squares (k-means objective function), which is obtained if
|
clus.avg.silwidths |
vector of cluster average silhouette
widths. See
|
avg.silwidth |
average silhouette
width. See
|
g2 |
Goodman and Kruskal's Gamma coefficient. See Milligan and Cooper (1985), Gordon (1999, p. 62). |
g3 |
G3 coefficient. See Gordon (1999, p. 62). |
pearsongamma |
correlation between distances and a 0-1-vector where 0 means same cluster, 1 means different clusters. "Normalized gamma" in Halkidi et al. (2001). |
dunn |
minimum separation / maximum diameter. Dunn index, see Haldiki et al. (2002). |
entropy |
entropy of the distribution of cluster memberships, see Meila(2007). |
wb.ratio |
|
ch |
Calinski and Harabasz index (Calinski and Harabasz 1974, optimal in Milligan and Cooper 1985; generalised for dissimilarites in Hennig and Liao 2010) |
corrected.rand |
corrected Rand index (if |
vi |
variation of information (VI) index (if |
Christian Hennig chrish@stats.ucl.ac.uk http://www.homepages.ucl.ac.uk/~ucakche/
Calinski, R. B., and Harabasz, J. (1974) A Dendrite Method for Cluster Analysis, Communications in Statistics, 3, 1-27.
Gordon, A. D. (1999) Classification, 2nd ed. Chapman and Hall.
Halkidi, M., Batistakis, Y., Vazirgiannis, M. (2001) On Clustering Validation Techniques, Journal of Intelligent Information Systems, 17, 107-145.
Hennig, C. and Liao, T. (2010) Comparing latent class and dissimilarity based clustering for mixed type variables with application to social stratification. Research report no. 308, Department of Statistical Science, UCL. http://www.ucl.ac.uk/Stats/research/reports/psfiles/rr308.pdf
Meila, M. (2007) Comparing clusterings?an information based distance, Journal of Multivariate Analysis, 98, 873-895.
Milligan, G. W. and Cooper, M. C. (1985) An examination of procedures for determining the number of clusters. Psychometrika, 50, 159-179.
silhouette
, dist
, calinhara
,
clusterboot
computes clusterwise stability statistics by
resampling.
set.seed(20000) face <- rFace(200,dMoNo=2,dNoEy=0,p=2) dface <- dist(face) complete3 <- cutree(hclust(dface),3) cluster.stats(dface,complete3, alt.clustering=as.integer(attr(face,"grouping")))