Clustering by merging Gaussian mixture components; computes all methods introduced in Hennig (2010) from an initial mclust clustering. See details section for details.
mergenormals(xdata, mclustsummary=NULL,
clustering, probs, muarray, Sigmaarray, z,
method=NULL, cutoff=NULL, by=0.005,
numberstop=NULL, renumber=TRUE, M=50, ...) # S3 method for mergenorm
summary(object, ...)
# S3 method for summary.mergenorm
print(x, ...)
mergenormals gives out an object of class mergenorm,
which is a List with components
integer vector. Final clustering.
vector of numbers of remaining clusters. These
are given in terms of the original clusters even of
renumber=TRUE, in which case they may be needed to understand
the numbering of some further components, see below.
vector of numbers of components that were "merged away".
vector of values of the merging criterion (see details) at which components were merged.
vector of numbers of clusters to which the original components were merged.
a list, if mclustsummary was provided. Entry
no. i refers to number i in clusternumbers. The list entry i
contains the parameters of the original mixture components that
make up cluster i, as extracted by
extract.mixturepars.
vector of prediction strength values for
clusternumbers from 1 to the number of components in the original
mixture, if method=="predictive". See
mixpredictive.
square matrix with entries giving the original values of the merging criterion (see details) for every pair of original mixture components.
square matrix as orig.decisionmatrix,
but with final entries; numbering of rows and columns corresponds to
clusternumbers; all entries corresponding to other rows and
columns can be ignored.
final cluster values of probs (see arguments)
for merged components, generated by (potentially repeated) execution
of mergeparameters out of the original
ones. Numbered according to clusternumbers.
final cluster means, analogous to probs.
final cluster covariance matrices, analogous to
probs.
final matrix of posterior probabilities of observations
belonging to the clusters, analogous to probs.
logical. If TRUE, there was a noise component
fitted in the initial mclust clustering (see help for
initialization in mclustBIC). In this
case, a cluster number 0 indicates noise. noise is ignored by the
merging methods and kept as it was originally.
as above.
as above.
summary.mergenorm gives out a list with components
clustering, clusternumbers, defunct.components, valuemerged,
mergedtonumbers, predvalues, probs, muarray, Sigmaarray, z, noise,
method, cutoff as above, plus onc (original number of
components) and mnc (number of clusters after merging).
data (something that can be coerced into a matrix).
output object from
summary.mclustBIC for xdata. Either
mclustsummary or all of clustering,
probs, muarray, Sigmaarray and z need
to be specified (the latter are obtained from mclustsummary
if they are not provided). I am not aware of restrictions of the
usage of
mclustBIC to produce an initial clustering;
covariance matrix models can be restricted and a noise component can be
included if desired, although I have probably not tested all
possibilities.
vector of integers. Initial assignment of data to mixture components.
vector of component proportions (for all components; should sum up to one).
matrix of component means (rows).
array of component covariance matrices (third dimension refers to component number).
matrix of observation- (row-)wise posterior probabilities of belonging to the components (columns).
one of "bhat", "ridge.uni",
"ridge.ratio", "demp", "dipuni",
"diptantrum", "predictive". See details.
numeric between 0 and 1. Tuning constant, see details and Hennig (2010). If not specified, the default values given in (9) in Hennig (2010) are used.
real between 0 and 1. Interval width for density computation
along the ridgeline, used for methods "ridge.uni" and
"ridge.ratio". Methods "dipuni" and
"diptantrum" require ridgeline computations and use it as well.
integer. If specified, cutoff is ignored and
components are merged until the number of clusters specified here is
reached.
logical. If TRUE merged clusters are renumbered
from 1 to their number. If not, numbers of the original clustering
are used (numbers of components that were merged into others then
will not appear).
integer. Number of times the dataset is divided into two
halves. Used if method="predictive".
additional optional parameters to pass on to
ridgeline.diagnosis or mixpredictive (in
mergenormals).
object of class mergenorm, output of
mergenormals.
object of class summary.mergenorm, output of
summary.mergenorm.
Christian Hennig christian.hennig@unibo.it https://www.unibo.it/sitoweb/christian.hennig/en/
Mixture components are merged in a hierarchical fashion. The merging
criterion is computed for all pairs of current clusters and the two
clusters with the highest criterion value (lowest, respectively, for
method="predictive") are merged. Then criterion values are
recomputed for the merged cluster. Merging is continued until the
criterion value to merge is below (or above, for
method="predictive") the cutoff value. Details are given in
Hennig (2010). The following criteria are offered, specified by the
method-argument.
components are only merged if their mixture is
unimodal according to Ray and Lindsay's (2005) ridgeline theory,
see ridgeline.diagnosis. This ignores argument
cutoff.
ratio between density minimum between
components and minimum of density maxima according to Ray and
Lindsay's (2005) ridgeline theory, see
ridgeline.diagnosis.
Bhattacharyya upper bound on misclassification
probability between two components, see
bhattacharyya.matrix.
direct estimation of misclassification probability between components, see Hennig (2010).
this uses method="ridge.ratio" to decide
which clusters to merge but stops merging according to the p-value of
the dip test computed as in Hartigan and Hartigan (1985), see
dip.test.
as "dipuni", but p-value of dip test
computed as in Tantrum, Murua and Stuetzle (2003), see
dipp.tantrum.
this uses method="demp" to decide which
clusters to merge but stops merging according to the value of
prediction strength (Tibshirani and Walther, 2005) as computed in
mixpredictive.
J. A. Hartigan and P. M. Hartigan (1985) The Dip Test of Unimodality, Annals of Statistics, 13, 70-84.
Hennig, C. (2010) Methods for merging Gaussian mixture components, Advances in Data Analysis and Classification, 4, 3-34.
Ray, S. and Lindsay, B. G. (2005) The Topography of Multivariate Normal Mixtures, Annals of Statistics, 33, 2042-2065.
Tantrum, J., Murua, A. and Stuetzle, W. (2003) Assessment and Pruning of Hierarchical Model Based Clustering, Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, Washington, D.C., 197-205.
Tibshirani, R. and Walther, G. (2005) Cluster Validation by Prediction Strength, Journal of Computational and Graphical Statistics, 14, 511-528.
require(mclust)
require(MASS)
options(digits=3)
data(crabs)
dc <- crabs[,4:8]
cm <- mclustBIC(crabs[,4:8],G=9,modelNames="EEE")
scm <- summary(cm,crabs[,4:8])
cmnbhat <- mergenormals(crabs[,4:8],scm,method="bhat")
summary(cmnbhat)
cmndemp <- mergenormals(crabs[,4:8],scm,method="demp")
summary(cmndemp)
# Other methods take a bit longer, but try them!
# The values of by and M below are still chosen for reasonably fast execution.
# cmnrr <- mergenormals(crabs[,4:8],scm,method="ridge.ratio",by=0.05)
# cmd <- mergenormals(crabs[,4:8],scm,method="dip.tantrum",by=0.05)
# cmp <- mergenormals(crabs[,4:8],scm,method="predictive",M=3)
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