This CRAN Task View contains a list of packages that can be used for finding groups in data and modelling 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.

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. A faster alternative to hclust() is provided by flashClust.
• Function dendrogram() from stats and associated methods can be used for improved visualization for cluster dendrograms.
• pvclust is a package for assessing the uncertainty in hierarchical cluster analysis. It provides approximately unbiased p-values as well as bootstrap p-values.
• hybridHclust implements hybrid hierarchical clustering via mutual clusters.
• Package dynamicTreeCut contains methods for detection of clusters in hierarchical clustering dendrograms.
• Package LLAhclust provides likelihood linkage analysis hierarchical clustering.

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 clusterSim allows to search for the optimal clustering procedure for a given dataset.
• 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 trimcluster provides trimmed k-means clustering.
• Package bayesclust allows to test and search for clusters in a hierarchical Bayes model.
• Package clues provides a clustering method based on local shrinking.
• 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 high-dimensional datasets.

Model-based Clustering:

• ML estimation:
  • 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.
  • prabclus clusters a presence-absence matrix object by calculating an MDS from the distances, and applying maximum likelihood Gaussian mixtures clustering to the MDS points.
  • Package MFDA implements model-based functional data analysis.
  • Package GLDEX fits mixtures of generalized lambda distributions and for grouped conditional data package mixdist can be used.
  • 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.
• 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. Bayesian estimation using a variational approach for multivariate Gaussian distributions with a diagonal covariance matrix is provided by package vabayelMix.
  • Package Bmix provides Bayesian Sampling for stick-breaking mixtures.
  • Package bclust allows Bayesian clustering using a spike-and-slab hierarchical model and is suitable for clustering high-dimensional data.
  • Package mixAK contains a mixture of statistical methods including the MCMC methods to analyze normal mixtures with possibly censored data.
  • Package EMCC provides evolutionary Monte Carlo (EMC) methods for clustering.
  • Package GSM fits mixtures of gamma distributions.
  • 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 relabelling algorithm.
  • 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 function.
  • Robust estimation using Weighted Likelihood can be done with package wle.
  • Package pendensity estimates densities with a penalized mixture approach.

Other Cluster Algorithms:

• 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.
• Fuzzy clustering and bagged clustering are available in package e1071.
• 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 FactoClass performs a combination of factorial methods and cluster analysis.
• 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 packages latentnet and mixer.
• Package nnclust allows fast clustering of large data sets by constructing a minimum spanning tree for each cluster. For each cluster the procedure is stopped when the nearest-neighbour distance rises above a specified threshold. A set of clusters and a set of "outliers" not in any cluster is returned. The algorithm works best for well-separated clusters in up to 8 dimensions, and sample sizes up to hundreds of thousands.
• 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.
• 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 models.
• Package segclust fits a segmentation/clustering model. A mixture of univariate gaussian distributions is used for the cluster structure and segments are assumed to arise because switching between clusters over time occurs.
• Self-organizing maps are available in package som.
• Several packages provide cluster algorithms which have been developped for bioinformatics applications. These packages include FunCluster for profiling microarray expression data, MMG for mixture models on graphcs, ORIClust for order-restricted information-based clustering and varmixt for mixture models on the variance.

Additional Functionality:

• Mixtures of univariate normal distributions can be printed and plotted using package nor1mix.
• Packages gcExplorer and clusterfly allow to visualise the results of clustering algorithms.
• 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.
• 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 clustTool provides a GUI for clustering data with spatial information.
• Package clustvarsel provides variable selection for model-based clustering.

Cluster-wise Regression:

• 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.
• 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 mixreg fits mixtures of one-variable regressions and provides the bootstrap test for the number of components.
• Mixed-mode latent class regression with special focus on longitudinal data is implemented by mmlcr. The components can follow a multivariate distribution of a (censored) Gaussian, multinomial, negative binomial or Poisson distribution. In addition concomitant variables can be specified to model the priors.
• moc fits mixture models to multivariate mixed data using a Newton-type algorithm. The component specific distribution may have one, two or three parameters. Covariates and concomitant variables can be specified as well as constraints for the parameters.
• mixtools provides fitting with the EM algorithm of mixtures of multinomials, multivariate normals, normals with repeated measures, Poisson regressions and Gaussian regressions (with random effects) and with the Metropolis-Hastings algorithm of mixtures of Gaussian regressions.
• mixPHM fits mixtures of proportional hazard models with the EM algorithm.
• Package gamlss.mx fits finite mixtures of of gamlss family distributions.