fpc: clustatsum – R documentation

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clustatsum

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 `nnk`th nearest neighbour within cluster.
`cvnnd`	coefficient of variation of dissimilarities to `nnk`th 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); low values are good.
`denscut`	this index measures whether cluster boundaries run through density valleys; I-densbound in Sec. 3.6 of Hennig (2019); low values are good.
`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); low values are good.
`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 `nnk`th 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 christian.hennig@unibo.it 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.

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

Flexible Procedures for Clustering

v2.2-9

GPL

Authors

Christian Hennig <christian.hennig@unibo.it>

Initial release

2020-12-06