clustatsum computes cluster validation statistics by running
cqcluster.stats,
and potentially distrsimilarity, and collecting some key
statistics values with a somewhat different nomenclature.
This was implemented as a helper function for use inside of
clusterbenchstats and cgrestandard.
clustatsum(datadist=NULL,clustering,noisecluster=FALSE,
datanp=NULL,npstats=FALSE,useboot=FALSE,
bootclassif=NULL,
bootmethod="nselectboot",
bootruns=25, cbmethod=NULL,methodpars=NULL,
distmethod=NULL,dnnk=2,
pamcrit=TRUE,...)clustatsum returns a list. The components, as listed below, are
outputs of summary.cquality with default parameters,
which means that they are partly transformed versions of those given
out by cqcluster.stats, i.e., their range is between 0
and 1 and large values are good. Those from
distrsimilarity are computed with
largeisgood=TRUE, correspondingly.
average distance within clusters (reweighted so that every observation, rather than every distance, has the same weight).
average distance to nnkth nearest neighbour within
cluster.
coefficient of variation of dissimilarities to
nnkth nearest wthin-cluster neighbour, measuring uniformity of
within-cluster densities, weighted over all clusters, see Sec. 3.7 of
Hennig (2019).
maximum cluster diameter.
widest within-cluster gap or average of cluster-wise
widest within-cluster gap, depending on parameter averagegap.
separation index, see argument sepindex.
minimum cluster separation.
average silhouette
width. See silhouette.
this index measures to what extent the density decreases from the cluster mode to the outskirts; I-densdec in Sec. 3.6 of Hennig (2019).
this index measures whether cluster boundaries run through density valleys; I-densbound in Sec. 3.6 of Hennig (2019).
this measures whether there is a large within-cluster gap with high density on both sides; I-highdgap in Sec. 3.6 of Hennig (2019).
correlation between distances and a 0-1-vector where 0 means same cluster, 1 means different clusters. "Normalized gamma" in Halkidi et al. (2001).
a generalisation of the within clusters sum
of squares (k-means objective function), which is obtained if
d is a Euclidean distance matrix. For general distance
measures, this is half
the sum of the within cluster squared dissimilarities divided by the
cluster size.
entropy of the distribution of cluster memberships, see Meila(2007).
average distance to cluster centroid.
Kolmogorov distance between distribution of within-cluster Mahalanobis distances and appropriate chi-squared distribution, aggregated over clusters (I am grateful to Agustin Mayo-Iscar for the idea).
Kolmogorov distance between distribution of distances to
nnkth nearest within-cluster neighbor and appropriate
Gamma-distribution, see Byers and Raftery (1998), aggregated over
clusters.
if useboot=TRUE, stability value; stabk for
method nselectboot; mean.pred for method
prediction.strength.
distances on which validation-measures are based, dist
object or distance matrix. If NULL, this is computed from
datanp; at least one of datadist and datanp
must be specified.
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.
logical. If TRUE, it is assumed that the
largest cluster number in clustering denotes a 'noise
class', i.e. points that do not belong to any cluster. These points
are not taken into account for the computation of all functions of
within and between cluster distances including the validation
indexes.
optional observations times variables data matrix, see
npstats.
logical. If TRUE, distrsimilarity
is called and the two statistics computed there are added to the
output. These are based on datanp and require datanp
to be specified.
logical. If TRUE, a stability index (either
nselectboot or prediction.strength) will be involved.
If useboot=TRUE, a string indicating the
classification method to be used with the stability index, see the
classification argument of nselectboot and
prediction.strength.
either "nselectboot" or
"prediction.strength"; stability index to be used if
useboot=TRUE.
integer. Number of resampling runs. If
useboot=TRUE, passed on as B to
nselectboot or
M to prediction.strength.
CBI-function (see kmeansCBI); clustering
method to be used for
stability assessment if useboot=TRUE.
parameters to be passed on to cbmethod.
logical. In case of useboot=TRUE indicates
whether cbmethod will interpret data as distances.
nnk-argument to be passed on to
distrsimilarity.
pamcrit-argument to be passed on to
cqcluster.stats.
further arguments to be passed on to
cqcluster.stats.
Christian Hennig christian.hennig@unibo.it https://www.unibo.it/sitoweb/christian.hennig/en/
Akhanli, S. and Hennig, C. (2020) Calibrating and aggregating cluster validity indexes for context-adapted comparison of clusterings. Statistics and Computing, 30, 1523-1544, https://link.springer.com/article/10.1007/s11222-020-09958-2, https://arxiv.org/abs/2002.01822
Halkidi, M., Batistakis, Y., Vazirgiannis, M. (2001) On Clustering Validation Techniques, Journal of Intelligent Information Systems, 17, 107-145.
Hennig, C. (2019) Cluster validation by measurement of clustering characteristics relevant to the user. In C. H. Skiadas (ed.) Data Analysis and Applications 1: Clustering and Regression, Modeling-estimating, Forecasting and Data Mining, Volume 2, Wiley, New York 1-24, https://arxiv.org/abs/1703.09282
Kaufman, L. and Rousseeuw, P.J. (1990). "Finding Groups in Data: An Introduction to Cluster Analysis". Wiley, New York.
Meila, M. (2007) Comparing clusterings?an information based distance, Journal of Multivariate Analysis, 98, 873-895.
cqcluster.stats, distrsimilarity
set.seed(20000)
options(digits=3)
face <- rFace(20,dMoNo=2,dNoEy=0,p=2)
dface <- dist(face)
complete3 <- cutree(hclust(dface),3)
clustatsum(dface,complete3)
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