clustatsum: Compute and format cluster validation statistics

In fpc: Flexible Procedures for Clustering

Compute and format cluster validation statistics

Description

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.

Usage

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,...)

Arguments

datadist	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.
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.
noisecluster	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.
datanp	optional observations times variables data matrix, see npstats.
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.
useboot	logical. If TRUE, a stability index (either nselectboot or prediction.strength) will be involved.
bootclassif	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.
bootmethod	either "nselectboot" or "prediction.strength"; stability index to be used if useboot=TRUE.
bootruns	integer. Number of resampling runs. If useboot=TRUE, passed on as B to nselectboot or M to prediction.strength.
cbmethod	CBI-function (see kmeansCBI); clustering method to be used for stability assessment if useboot=TRUE.
methodpars	parameters to be passed on to cbmethod.
distmethod	logical. In case of useboot=TRUE indicates whether cbmethod will interpret data as distances.
dnnk	nnk-argument to be passed on to distrsimilarity.
pamcrit	pamcrit-argument to be passed on to cqcluster.stats.
...	further arguments to be passed on to cqcluster.stats.

Value

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.

avewithin	average distance within clusters (reweighted so that every observation, rather than every distance, has the same weight).
mnnd	average distance to nnkth nearest neighbour within cluster.
cvnnd	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).
maxdiameter	maximum cluster diameter.
widestgap	widest within-cluster gap or average of cluster-wise widest within-cluster gap, depending on parameter averagegap.
sindex	separation index, see argument sepindex.
minsep	minimum cluster separation.
asw	average silhouette width. See silhouette.
dindex	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).
denscut	this index measures whether cluster boundaries run through density valleys; I-densbound in Sec. 3.6 of Hennig (2019).
highdgap	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).
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).
withinss	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	entropy of the distribution of cluster memberships, see Meila(2007).
pamc	average distance to cluster centroid.
kdnorm	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).
kdunif	Kolmogorov distance between distribution of distances to nnkth nearest within-cluster neighbor and appropriate Gamma-distribution, see Byers and Raftery (1998), aggregated over clusters.
boot	if useboot=TRUE, stability value; stabk for method nselectboot; mean.pred for method prediction.strength.

Author(s)

Christian Hennig [e-mail] https://www.unibo.it/sitoweb/christian.hennig/en/

References

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.

See Also

cqcluster.stats, distrsimilarity

Examples

  
  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)
  

fpc documentation built on Sept. 24, 2024, 9:07 a.m.