This CRAN Task View contains a list of packages that can be
used for finding groups in data and modeling unobserved
crosssectional heterogeneity. Many packages provide functionality for
more than one of the topics listed below, the section headings are
mainly meant as quick starting points rather than an ultimate
categorization. Except for packages stats and cluster (which ship with
base R and hence are part of every R installation), each package is
listed only once.
Most of the packages listed in this CRAN Task View, but not all are
distributed under the GPL. Please have a look at the DESCRIPTION file
of each package to check under which license it is distributed.
Hierarchical Clustering:

Functions
hclust()
from package stats and
agnes()
from
cluster
are the primary
functions for agglomerative hierarchical clustering, function
diana()
can be used for divisive hierarchical
clustering. Faster alternatives to
hclust()
are
provided by the packages
fastcluster
and
flashClust.

Function
dendrogram()
from stats and associated
methods can be used for improved visualization for cluster
dendrograms.

The
dendextend
package provides functions for easy
visualization (coloring labels and branches, etc.), manipulation
(rotating, pruning, etc.) and comparison of dendrograms (tangelgrams
with heuristics for optimal branch rotations, and tree correlation
measures with bootstrap and permutation tests for
significance).

Package
dynamicTreeCut
contains methods for detection
of clusters in hierarchical clustering dendrograms.

Package
genieclust
implements a fast hierarchical
clustering algorithm with a linkage criterion which is a variant of
the single linkage method combining it with the Gini inequality
measure to robustify the linkage method while retaining
computational efficiency to allow for the use of larger data
sets.

Package
idendr0
allows to interactively explore
hierarchical clustering dendrograms and the clustered data. The data
can be visualized (and interacted with) in a builtin heat map, but
also in GGobi dynamic interactive graphics (provided by
rggobi), or base R plots.

Package
isopam
uses an algorithm which is based on
the classification of ordination scores from isometric feature
mapping. The classification is performed either as a hierarchical,
divisive method or as nonhierarchical partitioning.

Package
mdendro
provides an alternative
implementation of agglomerative hierarchical clustering.
The package natively handles similarity matrices,
calculates variablegroup dendrograms, which solve the
nonuniqueness problem that arises when there are ties in the data,
and calculates five descriptors for the final dendrogram: cophenetic
correlation coefficient, space distortion ratio, agglomerative
coefficient, chaining coefficient, and tree balance.

The package
protoclust
implements a form of
hierarchical clustering that associates a prototypical element with
each interior node of the dendrogram. Using the package's
plot()
function, one can produce dendrograms that are
prototypelabeled and are therefore easier to interpret.

pvclust
is a package for assessing the uncertainty in
hierarchical cluster analysis. It provides approximately
unbiased pvalues as well as bootstrap pvalues.
Partitioning Clustering:

Function
kmeans()
from package stats provides
several algorithms for computing partitions with respect to
Euclidean distance.

Function
pam()
from package
cluster
implements
partitioning around medoids and can work with arbitrary
distances. Function
clara()
is a
wrapper to
pam()
for larger data sets. Silhouette plots
and spanning ellipses can be used for visualization.

Package
apcluster
implements Frey's and Dueck's
Affinity Propagation clustering. The algorithms in the package are analogous
to the Matlab code published by Frey and Dueck.

Package
ClusterR
implements kmeans,
minibatchkmeans, kmedoids, affinity propagation clustering and
Gaussian mixture models with the option to plot, validate, predict
(new data) and estimate the optimal number of clusters. The package
takes advantage of RcppArmadillo to speed up the
computationally intensive parts of the functions.

Package
clusterSim
allows to search for the optimal
clustering procedure for a given dataset.

Package
clustMixType
implements Huang's kprototypes
extension of kmeans for mixed type data.

Package
evclust
implements various clustering
algorithms that produce a credal partition, i.e., a set of
DempsterShafer mass functions representing the membership of
objects to clusters.

Package
flexclust
provides kcentroid cluster
algorithms for arbitrary distance measures, hard competitive
learning, neural gas and QT clustering. Neighborhood graphs and
image plots of partitions are available for visualization. Some of
this functionality is also provided by package
cclust.

Package
kernlab
provides a weighted kernel version of
the kmeans algorithm by
kkmeans
and spectral
clustering by
specc.

Package
kml
provides kmeans
clustering specifically for longitudinal (joint) data.

Package
skmeans
allows spherical kMeans Clustering,
i.e. kmeans clustering with cosine similarity. It features several
methods, including a genetic and a simple fixedpoint algorithm and
an interface to the CLUTO vcluster program for clustering
highdimensional datasets.

Package
Spectrum
implements a selftuning spectral
clustering method for single or multiview data and uses either the
eigengap or multimodality gap heuristics to determine the number of
clusters. The method is sufficiently flexible to cluster a wide
range of Gaussian and nonGaussian structures with automatic
selection of K.

Package
tclust
allows for trimmed
kmeans clustering. In addition using this package other covariance
structures can also be specified for the clusters.
ModelBased Clustering:

ML estimation:

For semi or partially supervised problems, where for a part of
the observations labels are given with certainty or with some
probability, package
bgmm
provides beliefbased and
softlabel mixture modeling for mixtures of Gaussians with the EM
algorithm.

EMCluster
provides EM algorithms and several
efficient initialization methods for modelbased clustering of
finite mixture Gaussian distribution with unstructured dispersion in
unsupervised as well as semisupervised learning situation.

Packages
funHDDC
and
funFEM
implement modelbased functional data
analysis.
The
funFEM
package implements the
funFEM
algorithm which allows to cluster time series or, more generally,
functional data. It is based on a discriminative functional mixture
model which allows the clustering of the data in a unique and
discriminative functional subspace. This model presents the
advantage to be parsimonious and can therefore handle long time
series.
The
funHDDC
package implements the funHDDC algorithm
which allows the clustering of functional data within groupspecific
functional subspaces. The funHDDC algorithm is based on a functional
mixture model which models and clusters the data into groupspecific
functional subspaces. The approach allows afterward meaningful
interpretations by looking at the groupspecific functional
curves.

Package
GLDEX
fits mixtures of generalized lambda
distributions and for grouped conditional data package
mixdist
can be used.

Package
GMCM
fits Gaussian mixture copula models for
unsupervised clustering and metaanalysis.

Package
HDclassif
provides function
hddc
to fit Gaussian mixture model to highdimensional data where it is
assumed that the data lives in a lower dimension than the original
space.

Package
teigen
allows to fit multivariate
tdistribution mixture models (with eigendecomposed covariance
structure) from a clustering or classification point of
view.

Package
mclust
fits mixtures of Gaussians using the EM
algorithm. It allows fine control of volume and shape of covariance
matrices and agglomerative hierarchical clustering based on maximum
likelihood. It provides comprehensive strategies using hierarchical
clustering, EM and the Bayesian Information Criterion (BIC) for
clustering, density estimation, and discriminant analysis. Package
Rmixmod
provides tools for fitting mixture models of
multivariate Gaussian or multinomial components to a given data set
with either a clustering, a density estimation or a discriminant
analysis point of view. Package
mclust
as well as packages
mixture
and
Rmixmod
provide all 14 possible
variancecovariance structures based on the eigenvalue
decomposition.

Package
MetabolAnalyze
fits mixtures of probabilistic
principal component analysis with the EM algorithm.

For grouped conditional data package
mixdist
can be
used.

Package
MixAll
provides EM estimation of diagonal
Gaussian, gamma, Poisson and categorical mixtures combined based on
the conditional independence assumption using different EM variants
and allowing for missing observations. The package accesses the
clustering part of the Statistical ToolKit
STK++
.

Package
mixR
performs maximum likelihood estimation
of finite mixture models for raw or binned data for families
including Normal, Weibull, Gamma and Lognormal using the EM
algorithm, together with the NewtonRaphson algorithm or the
bisection method when necessary. The package also provides
information criteria or the bootstrap likelihood ratio test for
model selection and the model fitting process is accelerated using
package Rcpp.

mixtools
provides fitting with the EM algorithm for
parametric and nonparametric (multivariate) mixtures. Parametric
mixtures include mixtures of multinomials, multivariate normals,
normals with repeated measures, Poisson regressions and Gaussian
regressions (with random effects). Nonparametric mixtures include
the univariate semiparametric case where symmetry is imposed for
identifiability and multivariate nonparametric mixtures with
conditional independent assumption. In addition fitting mixtures of
Gaussian regressions with the MetropolisHastings algorithm is
available.

Fitting finite mixtures of uni and multivariate scale mixtures
of skewnormal distributions with the EM algorithm is provided by
package
mixsmsn.

Package
MoEClust
fits parsimonious finite
multivariate Gaussian mixtures of experts models via the EM
algorithm. Covariates may influence the mixing proportions and/or
component densities and all 14 constrained covariance
parameterizations from package
mclust
are
implemented.

Package
movMF
fits finite mixtures of von
MisesFisher distributions with the EM algorithm.

mritc
provides tools for classification using normal
mixture models and (higher resolution) hidden Markov normal mixture
models fitted by various methods.

prabclus
clusters a presenceabsence matrix
object by calculating an MDS
from the distances, and applying maximum likelihood Gaussian
mixtures clustering to the MDS
points.

Package
psychomix
estimates mixtures of the
dichotomous Rasch model (via conditional ML) and the BradleyTerry
model. Package
mixRasch
estimates mixture Rasch models,
including the dichotomous Rasch model, the rating scale model, and
the partial credit model with joint maximum likelihood estimation.

Package
rebmix
implements the REBMIX algorithm to fit
mixtures of conditionally independent normal, lognormal, Weibull,
gamma, binomial, Poisson, Dirac or von Mises component densities as
well as mixtures of multivariate normal component densities with
unrestricted variancecovariance matrices.

Bayesian estimation:

Bayesian estimation of finite mixtures of multivariate Gaussians
is possible using package
bayesm. The package provides
functionality for sampling from such a mixture as well as estimating
the model using Gibbs sampling. Additional functionality for
analyzing the MCMC chains is available for averaging
the moments over MCMC draws, for determining the marginal densities,
for clustering observations and for plotting the uni and bivariate
marginal densities.

Package
bayesmix
provides Bayesian estimation using
JAGS.

Package
Bmix
provides Bayesian Sampling for
stickbreaking mixtures.

Package
bmixture
provides Bayesian estimation of
finite mixtures of univariate Gamma and normal distributions.

Package
GSM
fits mixtures of gamma distributions.

Package
IMIFA
fits Infinite Mixtures of Infinite
Factor Analyzers and a flexible suite of related models for
clustering highdimensional data. The number of clusters
and/or number of clusterspecific latent factors can be
nonparametrically inferred, without recourse to model selection
criteria.

Package
mcclust
implements methods for processing a
sample of (hard) clusterings, e.g. the MCMC output of a Bayesian
clustering model. Among them are methods that find a single best
clustering to represent the sample, which are based on the posterior
similarity matrix or a relabeling algorithm.

Package
mixAK
contains a mixture of statistical
methods including the MCMC methods to analyze normal mixtures with
possibly censored data.

Package
NPflow
fits Dirichlet process mixtures of
multivariate normal, skew normal or skew tdistributions. The
package was developed oriented towards flowcytometry data
preprocessing applications.

Package
PReMiuM
is a package for profile regression,
which is a Dirichlet process Bayesian clustering where the response
is linked nonparametrically to the covariate profile.

Package
rjags
provides an interface to the JAGS
MCMC library which includes a module for mixture modelling.

Other estimation methods:

Package
AdMit
allows to fit an adaptive mixture of Studentt
distributions to approximate a target density through its kernel
function.

Circular and orthogonal regression clustering using redescending
Mestimators is provided by package
edci.
Other Cluster Algorithms and Clustering Suites:

Package
ADPclust
allows to cluster high dimensional
data based on a two dimensional decision plot. This densitydistance
plot plots for each data point the local density against the
shortest distance to all observations with a higher local density
value. The cluster centroids of this noniterative procedure can be
selected using an interactive or automatic selection mode.

Package
amap
provides alternative implementations
of kmeans and agglomerative hierarchical clustering.

Package
biclust
provides several algorithms to find
biclusters in twodimensional data.

Package
cba
implements clustering techniques for
business analytics like "rock" and "proximus".

Package
CHsharp
clusters 3dimensional data into
their local modes based on a convergent form of Choi and Hall's
(1999) data sharpening method.

Package
clue
implements ensemble methods for both
hierarchical and partitioning cluster methods.

Package
CoClust
implements a cluster algorithm that
is based on copula functions and therefore allows to group
observations according to the multivariate dependence structure of
the generating process without any assumptions on the margins.

Package
compHclust
provides complimentary
hierarchical clustering which was especially designed for microarray
data to uncover structures present in the data that arise from
'weak' genes.

Package
DatabionicSwarm
implements a swarm system
called Databionic swarm (DBS) for selforganized clustering. This
method is able to adapt itself to structures of highdimensional
data such as natural clusters characterized by distance and/or
density based structures in the data space.

Package
dbscan
provides a fast reimplementation of
the DBSCAN (densitybased spatial clustering of applications with
noise) algorithm using a kdtree.

Fuzzy clustering and bagged clustering are available in package
e1071. Further and more extensive tools for fuzzy
clustering are available in package
fclust.

Package
FactoClass
performs a combination of
factorial methods and cluster analysis.

Package
FCPS
provides many conventional clustering
algorithms with consistent input and output, several statistical
approaches for the estimation of the number of clusters as well as
the mirrored density plot (MDplot) of clusterability and offers a
variety of clustering challenges any algorithm should be able to handle
when facing real world data.

The
hopach
algorithm is a hybrid between
hierarchical methods and PAM and builds a tree by
recursively partitioning a data set.

For graphs and networks modelbased clustering approaches are
implemented in
latentnet.

Package
pdfCluster
provides tools to perform cluster
analysis via kernel density estimation. Clusters are associated to
the maximally connected components with estimated density above a
threshold. In addition a tree structure associated with the
connected components is obtained.

Package
prcr
implements the 2step cluster analysis
where first hierarchical clustering is performed to determine the
initial partition for the subsequent kmeans clustering
procedure.

Package
ProjectionBasedClustering
implements
projectionbased clustering (PBC) for highdimensional datasets in
which clusters are formed by both distance and density structures
(DDS).

Package
randomLCA
provides the fitting of latent
class models which optionally also include a random effect. Package
poLCA
allows for polytomous variable latent class
analysis and regression.
BayesLCA
allows to fit Bayesian
LCA models employing the EM algorithm, Gibbs sampling or variational
Bayes methods.

Package
RPMM
fits recursively partitioned mixture
models for Beta and Gaussian Mixtures. This is a modelbased
clustering algorithm that returns a hierarchy of classes, similar to
hierarchical clustering, but also similar to finite mixture
models.

Selforganizing maps are available in package
som.

Several packages provide cluster algorithms which have been
developed for bioinformatics applications. These packages include
FunCluster
for profiling microarray expression data
and
ORIClust
for orderrestricted informationbased clustering.
Clusterwise Regression:

Package
crimCV
fits finite mixtures
of zeroinflated Poisson models for longitudinal data with time
as covariate.

Multigroup mixtures of latent Markov models on mixed categorical
and continuous data (including time series) can be fitted using
depmix
or
depmixS4. The parameters are
optimized using a general purpose optimization routine given linear
and nonlinear constraints on the parameters.

Package
flexmix
implements an userextensible
framework for EMestimation of mixtures of regression models,
including mixtures of (generalized) linear models.

Package
fpc
provides fixedpoint methods both for
modelbased clustering and linear regression. A collection of
asymmetric projection methods can be used to plot various
aspects of a clustering.

Package
lcmm
fits a latent class linear mixed model
which is also known as growth mixture model or heterogeneous linear
mixed model using a maximum likelihood method.

Package
mixreg
fits mixtures of onevariable
regressions and provides the bootstrap test for the number of
components.

mixPHM
fits mixtures of proportional hazard models
with the EM algorithm.
Additional Functionality:

Package
clusterGeneration
contains functions for
generating random clusters and random covariance/correlation
matrices, calculating a separation index (data and population
version) for pairs of clusters or cluster distributions, and 1D and
2D projection plots to visualize clusters.
Alternatively
MixSim
generates a finite mixture model
with Gaussian components for prespecified levels of maximum and/or
average overlaps. This model can be used to simulate data for
studying the performance of cluster algorithms.

Package
clusterCrit
computes various clustering
validation or quality criteria and partition comparison
indices.

For cluster validation package
clusterRepro
tests the
reproducibility of a cluster. Package
clv
contains
popular internal and external cluster validation methods ready to
use for most of the outputs produced by functions from package
cluster
and
clValid
calculates several
stability measures.

Package
clustvarsel
provides variable selection for
Gaussian modelbased clustering. Variable selection for latent
class analysis for clustering multivariate categorical data is
implemented in package
LCAvarsel.
Package
VarSelLCM
provides variable selection for
modelbased clustering of continuous, count, categorical or
mixedtype data with missing values where the models used impose a
conditional independence assumption given group membership.

Package
factoextra
provides some easytouse
functions to extract and visualize the output of multivariate data
analyses in general including also heuristic and modelbased cluster
analysis. The package also contains functions for simplifying some
cluster analysis steps and uses
ggplot2
based
visualization.

Functionality to compare the similarity between two cluster
solutions is provided by
cluster.stats()
in package
fpc.

The stability of kcentroid clustering solutions fitted using
functions from package
flexclust
can also be validated
via
bootFlexclust()
using bootstrap methods.

Package
MOCCA
provides methods to analyze cluster
alternatives based on multiobjective optimization of cluster
validation indices.

Package
NbClust
implements 30 different indices which
evaluate the cluster structure and should help to determine on a
suitable number of clusters.

Mixtures of univariate normal distributions can be printed
and plotted using package
nor1mix.

Package
seriation
provides
dissplot()
for
visualizing dissimilarity matrices using seriation and matrix shading.
This also allows to inspect cluster quality by restricting objects
belonging to the same cluster to be displayed in consecutive order.

Package
sigclust
provides a statistical method for
testing the significance of clustering results.

Package
treeClust
calculates dissimilarities
between data points based on their leaf memberships in regression or
classification trees for each variable. It also performs the cluster
analysis using the resulting dissimilarity matrix with available
heuristic clustering algorithms in R.