Factoextra R Package: Easy Multivariate Data Analyses and Elegant Visualization
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factoextra is an R package making easy to extract and visualize the output of exploratory multivariate data analyses, including:

Principal Component Analysis (PCA), which is used to summarize the information contained in a continuous (i.e, quantitative) multivariate data by reducing the dimensionality of the data without loosing important information.

Correspondence Analysis (CA), which is an extension of the principal component analysis suited to analyse a large contingency table formed by two qualitative variables (or categorical data).

Multiple Correspondence Analysis (MCA), which is an adaptation of CA to a data table containing more than two categorical variables.

Multiple Factor Analysis (MFA) dedicated to datasets where variables are organized into groups (qualitative and/or quantitative variables).

Hierarchical Multiple Factor Analysis (HMFA): An extension of MFA in a situation where the data are organized into a hierarchical structure.

Factor Analysis of Mixed Data (FAMD), a particular case of the MFA, dedicated to analyze a data set containing both quantitative and qualitative variables.
There are a number of R packages implementing principal component methods. These packages include: FactoMineR, ade4, stats, ca, MASS and ExPosition.
However, the result is presented differently according to the used packages. To help in the interpretation and in the visualization of multivariate analysis – such as cluster analysis and dimensionality reduction analysis – we developed an easytouse R package named factoextra.

The R package factoextra has flexible and easytouse methods to extract quickly, in a human readable standard data format, the analysis results from the different packages mentioned above.

It produces a ggplot2based elegant data visualization with less typing.
 It contains also many functions facilitating clustering analysis and visualization.
We’ll use i) the FactoMineR package (Sebastien Le, et al., 2008) to compute PCA, (M)CA, FAMD, MFA and HCPC; ii) and the factoextra package for extracting and visualizing the results.
FactoMineR is a great and my favorite package for computing principal component methods in R. It’s very easy to use and very well documented. The official website is available at: http://factominer.free.fr/. Thanks to François Husson for his impressive work.
The figure below shows methods, which outputs can be visualized using the factoextra package. The official online documentation is available at: http://www.sthda.com/english/rpkgs/factoextra.
Why using factoextra?

The factoextra R package can handle the results of PCA, CA, MCA, MFA, FAMD and HMFA from several packages, for extracting and visualizing the most important information contained in your data.
 After PCA, CA, MCA, MFA, FAMD and HMFA, the most important row/column elements can be highlighted using :
 their cos2 values corresponding to their quality of representation on the factor map
 their contributions to the definition of the principal dimensions.
If you want to do this, the factoextra package provides a convenient solution.
 PCA and (M)CA are used sometimes for prediction problems : one can predict the coordinates of new supplementary variables (quantitative and qualitative) and supplementary individuals using the information provided by the previously performed PCA or (M)CA. This can be done easily using the FactoMineR package.
If you want to make predictions with PCA/MCA and to visualize the position of the supplementary variables/individuals on the factor map using ggplot2: then factoextra can help you. It’s quick, write less and do more…
 Several functions from different packages – FactoMineR, ade4, ExPosition, stats – are available in R for performing PCA, CA or MCA. However, The components of the output vary from package to package.
No matter the package you decided to use, factoextra can give you a human understandable output.
Installing FactoMineR
The FactoMineR package can be installed and loaded as follow:
# Install install.packages("FactoMineR") # Load library("FactoMineR")
Installing and loading factoextra
 factoextra can be installed from CRAN as follow:
install.packages("factoextra")
 Or, install the latest version from Github
if(!require(devtools)) install.packages("devtools") devtools::install_github("kassambara/factoextra")
 Load factoextra as follow :
library("factoextra")
Main functions in the factoextra package
See the online documentation (http://www.sthda.com/english/rpkgs/factoextra) for a complete list.
Visualizing dimension reduction analysis outputs
Functions  Description 

fviz_eig (or fviz_eigenvalue)  Extract and visualize the eigenvalues/variances of dimensions. 
fviz_pca  Graph of individuals/variables from the output of Principal Component Analysis (PCA). 
fviz_ca  Graph of column/row variables from the output of Correspondence Analysis (CA). 
fviz_mca  Graph of individuals/variables from the output of Multiple Correspondence Analysis (MCA). 
fviz_mfa  Graph of individuals/variables from the output of Multiple Factor Analysis (MFA). 
fviz_famd  Graph of individuals/variables from the output of Factor Analysis of Mixed Data (FAMD). 
fviz_hmfa  Graph of individuals/variables from the output of Hierarchical Multiple Factor Analysis (HMFA). 
fviz_ellipses  Draw confidence ellipses around the categories. 
fviz_cos2  Visualize the quality of representation of the row/column variable from the results of PCA, CA, MCA functions. 
fviz_contrib  Visualize the contributions of row/column elements from the results of PCA, CA, MCA functions. 
Extracting data from dimension reduction analysis outputs
Functions  Description 

get_eigenvalue  Extract and visualize the eigenvalues/variances of dimensions. 
get_pca  Extract all the results (coordinates, squared cosine, contributions) for the active individuals/variables from Principal Component Analysis (PCA) outputs. 
get_ca  Extract all the results (coordinates, squared cosine, contributions) for the active column/row variables from Correspondence Analysis outputs. 
get_mca  Extract results from Multiple Correspondence Analysis outputs. 
get_mfa  Extract results from Multiple Factor Analysis outputs. 
get_famd  Extract results from Factor Analysis of Mixed Data outputs. 
get_hmfa  Extract results from Hierarchical Multiple Factor Analysis outputs. 
facto_summarize  Subset and summarize the output of factor analyses. 
Clustering analysis and visualization
Functions  Description 

dist(fviz_dist, get_dist)  Enhanced Distance Matrix Computation and Visualization. 
get_clust_tendency  Assessing Clustering Tendency. 
fviz_nbclust(fviz_gap_stat)  Determining and Visualizing the Optimal Number of Clusters. 
fviz_dend  Enhanced Visualization of Dendrogram 
fviz_cluster  Visualize Clustering Results 
fviz_mclust  Visualize Modelbased Clustering Results 
fviz_silhouette  Visualize Silhouette Information from Clustering. 
hcut  Computes Hierarchical Clustering and Cut the Tree 
hkmeans (hkmeans_tree, print.hkmeans)  Hierarchical kmeans clustering. 
eclust  Visual enhancement of clustering analysis 
Dimension reduction and factoextra
As depicted in the figure below, the type of analysis to be performed depends on the data set formats and structures.
In this section we start by illustrating classical methods – such as PCA, CA and MCA – for analyzing a data set containing continuous variables, contingency table and qualitative variables, respectively.
We continue by discussing advanced methods – such as FAMD, MFA and HMFA – for analyzing a data set containing a mix of variables (qualitatives & quantitatives) organized or not into groups.
Finally, we show how to perform hierarchical clustering on principal components (HCPC), which useful for performing clustering with a data set containing only qualitative variables or with a mixed data of qualitative and quantitative variables.
Principal component analysis
 Data: decathlon2 [in factoextra package]
 PCA function: FactoMineR::PCA()
 Visualization factoextra::fviz_pca()
Read more about computing and interpreting principal component analysis at: Principal Component Analysis (PCA).
 Loading data
library("factoextra") data("decathlon2") df
 Principal component analysis
library("FactoMineR") res.pca
 Extract and visualize eigenvalues/variances:
# Extract eigenvalues/variances get_eig(res.pca) ## eigenvalue variance.percent cumulative.variance.percent ## Dim.1 4.1242133 41.242133 41.24213 ## Dim.2 1.8385309 18.385309 59.62744 ## Dim.3 1.2391403 12.391403 72.01885 ## Dim.4 0.8194402 8.194402 80.21325 ## Dim.5 0.7015528 7.015528 87.22878 ## Dim.6 0.4228828 4.228828 91.45760 ## Dim.7 0.3025817 3.025817 94.48342 ## Dim.8 0.2744700 2.744700 97.22812 ## Dim.9 0.1552169 1.552169 98.78029 ## Dim.10 0.1219710 1.219710 100.00000 # Visualize eigenvalues/variances fviz_screeplot(res.pca, addlabels = TRUE, ylim = c(0, 50))
4.Extract and visualize results for variables:
# Extract the results for variables var ## Principal Component Analysis Results for variables ## =================================================== ## Name Description ## 1 "$coord" "Coordinates for the variables" ## 2 "$cor" "Correlations between variables and dimensions" ## 3 "$cos2" "Cos2 for the variables" ## 4 "$contrib" "contributions of the variables" # Coordinates of variables head(var$coord) ## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 ## X100m 0.8506257 0.17939806 0.3015564 0.03357320 0.1944440 ## Long.jump 0.7941806 0.28085695 0.1905465 0.11538956 0.2331567 ## Shot.put 0.7339127 0.08540412 0.5175978 0.12846837 0.2488129 ## High.jump 0.6100840 0.46521415 0.3300852 0.14455012 0.4027002 ## X400m 0.7016034 0.29017826 0.2835329 0.43082552 0.1039085 ## X110m.hurdle 0.7641252 0.02474081 0.4488873 0.01689589 0.2242200 # Contribution of variables head(var$contrib) ## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 ## X100m 17.544293 1.7505098 7.338659 0.13755240 5.389252 ## Long.jump 15.293168 4.2904162 2.930094 1.62485936 7.748815 ## Shot.put 13.060137 0.3967224 21.620432 2.01407269 8.824401 ## High.jump 9.024811 11.7715838 8.792888 2.54987951 23.115504 ## X400m 11.935544 4.5799296 6.487636 22.65090599 1.539012 ## X110m.hurdle 14.157544 0.0332933 16.261261 0.03483735 7.166193 # Graph of variables: default plot fviz_pca_var(res.pca, col.var = "black")
It’s possible to control variable colors using their contributions (“contrib”) to the principal axes:
# Control variable colors using their contributions fviz_pca_var(res.pca, col.var="contrib", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), repel = TRUE # Avoid text overlapping )
 Variable contributions to the principal axes:
# Contributions of variables to PC1 fviz_contrib(res.pca, choice = "var", axes = 1, top = 10) # Contributions of variables to PC2 fviz_contrib(res.pca, choice = "var", axes = 2, top = 10)
 Extract and visualize results for individuals:
# Extract the results for individuals ind ## Principal Component Analysis Results for individuals ## =================================================== ## Name Description ## 1 "$coord" "Coordinates for the individuals" ## 2 "$cos2" "Cos2 for the individuals" ## 3 "$contrib" "contributions of the individuals" # Coordinates of individuals head(ind$coord) ## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 ## SEBRLE 0.1955047 1.5890567 0.6424912 0.08389652 1.16829387 ## CLAY 0.8078795 2.4748137 1.3873827 1.29838232 0.82498206 ## BERNARD 1.3591340 1.6480950 0.2005584 1.96409420 0.08419345 ## YURKOV 0.8889532 0.4426067 2.5295843 0.71290837 0.40782264 ## ZSIVOCZKY 0.1081216 2.0688377 1.3342591 0.10152796 0.20145217 ## McMULLEN 0.1212195 1.0139102 0.8625170 1.34164291 1.62151286 # Graph of individuals # 1. Use repel = TRUE to avoid overplotting # 2. Control automatically the color of individuals using the cos2 # cos2 = the quality of the individuals on the factor map # Use points only # 3. Use gradient color fviz_pca_ind(res.pca, col.ind = "cos2", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), repel = TRUE # Avoid text overlapping (slow if many points) )
# Biplot of individuals and variables fviz_pca_biplot(res.pca, repel = TRUE)
 Color individuals by groups:
# Compute PCA on the iris data set # The variable Species (index = 5) is removed # before PCA analysis iris.pca
Correspondence analysis
 Data: housetasks [in factoextra]
 CA function FactoMineR::CA()
 Visualize with factoextra::fviz_ca()
Read more about computing and interpreting correspondence analysis at: Correspondence Analysis (CA).
 Compute CA:
# Loading data data("housetasks") # Computing CA library("FactoMineR") res.ca
 Extract results for row/column variables:
# Result for row variables get_ca_row(res.ca) # Result for column variables get_ca_col(res.ca)
 Biplot of rows and columns
fviz_ca_biplot(res.ca, repel = TRUE)
To visualize only row points or column points, type this:
# Graph of row points fviz_ca_row(res.ca, repel = TRUE) # Graph of column points fviz_ca_col(res.ca) # Visualize row contributions on axes 1 fviz_contrib(res.ca, choice ="row", axes = 1) # Visualize column contributions on axes 1 fviz_contrib(res.ca, choice ="col", axes = 1)
Multiple correspondence analysis
 Data: poison [in factoextra]
 MCA function FactoMineR::MCA()
 Visualization factoextra::fviz_mca()
Read more about computing and interpreting multiple correspondence analysis at: Multiple Correspondence Analysis (MCA).
 Computing MCA:
library(FactoMineR) data(poison) res.mca
 Extract results for variables and individuals:
# Extract the results for variable categories get_mca_var(res.mca) # Extract the results for individuals get_mca_ind(res.mca)
 Contribution of variables and individuals to the principal axes:
# Visualize variable categorie contributions on axes 1 fviz_contrib(res.mca, choice ="var", axes = 1) # Visualize individual contributions on axes 1 # select the top 20 fviz_contrib(res.mca, choice ="ind", axes = 1, top = 20)
 Graph of individuals
# Color by groups # Add concentration ellipses # Use repel = TRUE to avoid overplotting grp
 Graph of variable categories:
fviz_mca_var(res.mca, repel = TRUE)
 Biplot of individuals and variables:
fviz_mca_biplot(res.mca, repel = TRUE)
Advanced methods
The factoextra R package has also functions that support the visualization of advanced methods such:
 Factor Analysis of Mixed Data (FAMD): : FAMD Examples
 Multiple Factor Analysis (MFA): MFA Examples
 Hierarchical Multiple Factor Analysis (HMFA): HMFA Examples
 Hierachical Clustering on Principal Components (HCPC)
Cluster analysis and factoextra
To learn more about cluster analysis, you can refer to the book available at: Practical Guide to Cluster Analysis in R
The main parts of the book include:
 distance measures,
 partitioning clustering,
 hierarchical clustering,
 cluster validation methods, as well as,
 advanced clustering methods such as fuzzy clustering, densitybased clustering and modelbased clustering.
The book presents the basic principles of these tasks and provide many examples in R. It offers solid guidance in data mining for students and researchers.
Partitioning clustering
# 1. Loading and preparing data data("USArrests") df
Hierarchical clustering
library("factoextra") # Compute hierarchical clustering and cut into 4 clusters res
Determine the optimal number of clusters
# Optimal number of clusters for kmeans library("factoextra") my_data
Acknoweledgment
I would like to thank Fabian Mundt for his active contributions to factoextra.
We sincerely thank all developers for their efforts behind the packages that factoextra depends on, namely, ggplot2 (Hadley Wickham, SpringerVerlag New York, 2009), FactoMineR (Sebastien Le et al., Journal of Statistical Software, 2008), dendextend (Tal Galili, Bioinformatics, 2015), cluster (Martin Maechler et al., 2016) and more …..
References
 H. Wickham (2009). ggplot2: Elegant Graphics for Data Analysis. SpringerVerlag New York.
 Maechler, M., Rousseeuw, P., Struyf, A., Hubert, M., Hornik, K.(2016). cluster: Cluster Analysis Basics and Extensions. R package version 2.0.5.
 Sebastien Le, Julie Josse, Francois Husson (2008). FactoMineR: An R Package for Multivariate Analysis. Journal of Statistical Software, 25(1), 118. 10.18637/jss.v025.i01
 Tal Galili (2015). dendextend: an R package for visualizing, adjusting, and comparing trees of hierarchical clustering. Bioinformatics. DOI: 10.1093/bioinformatics/btv428
Infos
This analysis has been performed using R software (ver. 3.3.2) and factoextra (ver. 1.0.4.999)
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