Last updated on 2021-08-15
by Friedrich Leisch, Bettina Gruen
This CRAN Task View contains a list of packages that can be
used for finding groups in data and modeling unobserved
cross-sectional 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.
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
provided by the packages fastcluster and
dendrogram() from stats and associated
methods can be used for improved visualization for cluster
- 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
- 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
- Package idendr0 allows to interactively explore
hierarchical clustering dendrograms and the clustered data. The data
can be visualized (and interacted with) in a built-in 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 non-hierarchical partitioning.
- Package mdendro provides an alternative
implementation of agglomerative hierarchical clustering.
The package natively handles similarity matrices,
calculates variable-group dendrograms, which solve the
non-uniqueness 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
prototype-labeled and are therefore easier to interpret.
- pvclust is a package for assessing the uncertainty in
hierarchical cluster analysis. It provides approximately
unbiased p-values as well as bootstrap p-values.
kmeans() from package stats provides
several algorithms for computing partitions with respect to
pam() from package cluster implements
partitioning around medoids and can work with arbitrary
clara() is a
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 k-means,
mini-batch-kmeans, k-medoids, 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 k-prototypes
extension of k-means for mixed type data.
- Package evclust implements various clustering
algorithms that produce a credal partition, i.e., a set of
Dempster-Shafer mass functions representing the membership of
objects to clusters.
- Package flexclust provides k-centroid 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 k-means algorithm by
kkmeans and spectral
- Package kml provides k-means
clustering specifically for longitudinal (joint) data.
- Package skmeans allows spherical k-Means Clustering,
i.e. k-means clustering with cosine similarity. It features several
methods, including a genetic and a simple fixed-point algorithm and
an interface to the CLUTO vcluster program for clustering
- Package Spectrum implements a self-tuning spectral
clustering method for single or multi-view 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 non-Gaussian structures with automatic
selection of K.
- Package tclust allows for trimmed
k-means clustering. In addition using this package other covariance
structures can also be specified for the clusters.
- 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 belief-based and
soft-label mixture modeling for mixtures of Gaussians with the EM
- EMCluster provides EM algorithms and several
efficient initialization methods for model-based clustering of
finite mixture Gaussian distribution with unstructured dispersion in
unsupervised as well as semi-supervised learning situation.
- Packages funHDDC and funFEM
implement model-based functional data
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
The funHDDC package implements the funHDDC algorithm
which allows the clustering of functional data within group-specific
functional subspaces. The funHDDC algorithm is based on a functional
mixture model which models and clusters the data into group-specific
functional subspaces. The approach allows afterward meaningful
interpretations by looking at the group-specific functional
- 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 meta-analysis.
- Package HDclassif provides function
to fit Gaussian mixture model to high-dimensional data where it is
assumed that the data lives in a lower dimension than the original
- Package teigen allows to fit multivariate
t-distribution mixture models (with eigen-decomposed covariance
structure) from a clustering or classification point of
- 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
variance-covariance structures based on the eigenvalue
- Package MetabolAnalyze fits mixtures of probabilistic
principal component analysis with the EM algorithm.
- For grouped conditional data package mixdist can be
- 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 Newton-Raphson 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
- mixtools provides fitting with the EM algorithm for
parametric and non-parametric (multivariate) mixtures. Parametric
mixtures include mixtures of multinomials, multivariate normals,
normals with repeated measures, Poisson regressions and Gaussian
regressions (with random effects). Non-parametric mixtures include
the univariate semi-parametric case where symmetry is imposed for
identifiability and multivariate non-parametric mixtures with
conditional independent assumption. In addition fitting mixtures of
Gaussian regressions with the Metropolis-Hastings algorithm is
- Fitting finite mixtures of uni- and multivariate scale mixtures
of skew-normal distributions with the EM algorithm is provided by
- 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
- Package movMF fits finite mixtures of von
Mises-Fisher 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 presence-absence matrix
object by calculating an MDS
from the distances, and applying maximum likelihood Gaussian
mixtures clustering to the MDS
- Package psychomix estimates mixtures of the
dichotomous Rasch model (via conditional ML) and the Bradley-Terry
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 variance-covariance 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
- Package bayesmix provides Bayesian estimation using
- Package Bmix provides Bayesian Sampling for
- 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 high-dimensional data. The number of clusters
and/or number of cluster-specific latent factors can be
non-parametrically inferred, without recourse to model selection
- 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 t-distributions. The
package was developed oriented towards flow-cytometry data
- Package PReMiuM is a package for profile regression,
which is a Dirichlet process Bayesian clustering where the response
is linked non-parametrically 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 Student-t
distributions to approximate a target density through its kernel
- Circular and orthogonal regression clustering using redescending
M-estimators 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 density-distance
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 non-iterative procedure can be
selected using an interactive or automatic selection mode.
- Package amap provides alternative implementations
of k-means and agglomerative hierarchical clustering.
- Package biclust provides several algorithms to find
biclusters in two-dimensional data.
- Package cba implements clustering techniques for
business analytics like "rock" and "proximus".
- Package CHsharp clusters 3-dimensional 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
- Package DatabionicSwarm implements a swarm system
called Databionic swarm (DBS) for self-organized clustering. This
method is able to adapt itself to structures of high-dimensional
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 (density-based spatial clustering of applications with
noise) algorithm using a kd-tree.
- 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 (MD-plot) 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 model-based 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 2-step cluster analysis
where first hierarchical clustering is performed to determine the
initial partition for the subsequent k-means clustering
- Package ProjectionBasedClustering implements
projection-based clustering (PBC) for high-dimensional datasets in
which clusters are formed by both distance and density structures
- 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
- Package RPMM fits recursively partitioned mixture
models for Beta and Gaussian Mixtures. This is a model-based
clustering algorithm that returns a hierarchy of classes, similar to
hierarchical clustering, but also similar to finite mixture
- Self-organizing maps are available in package
- Several packages provide cluster algorithms which have been
developed for bioinformatics applications. These packages include
FunCluster for profiling microarray expression data
for order-restricted information-based clustering.
- Package crimCV fits finite mixtures
of zero-inflated Poisson models for longitudinal data with time
- 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 user-extensible
framework for EM-estimation of mixtures of regression models,
including mixtures of (generalized) linear models.
- Package fpc provides fixed-point methods both for
model-based 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 one-variable
regressions and provides the bootstrap test for the number of
- mixPHM fits mixtures of proportional hazard models
with the EM algorithm.
- 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 1-D and
2-D 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
- 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
- Package clustvarsel provides variable selection for
Gaussian model-based clustering. Variable selection for latent
class analysis for clustering multivariate categorical data is
implemented in package LCAvarsel.
Package VarSelLCM provides variable selection for
model-based clustering of continuous, count, categorical or
mixed-type data with missing values where the models used impose a
conditional independence assumption given group membership.
- Package factoextra provides some easy-to-use
functions to extract and visualize the output of multivariate data
analyses in general including also heuristic and model-based cluster
analysis. The package also contains functions for simplifying some
cluster analysis steps and uses ggplot2-based
- Functionality to compare the similarity between two cluster
solutions is provided by
cluster.stats() in package
- The stability of k-centroid clustering solutions fitted using
functions from package flexclust can also be validated
bootFlexclust() using bootstrap methods.
- Package MOCCA provides methods to analyze cluster
alternatives based on multi-objective optimization of cluster
- 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
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.