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factoextra : Extract and Visualize the Results of Multivariate Data Analyses

factoextra is an R package making easy to extract and visualize the output of exploratory multivariate data analyses, including:

  1. 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.

  2. 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).

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

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

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

  6. 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 easy-to-use R package named factoextra.

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.

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.

factoextra R package
factoextra R package

Why using factoextra?

  1. 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.

  2. After PCA, CA, MCA, MFA, FAMD and HMFA, the most important row/column elements can be highlighted using :

If you want to do this, the factoextra package provides a convenient solution.

  1. 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…

  1. 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

install.packages("factoextra")
if(!require(devtools)) install.packages("devtools")
devtools::install_github("kassambara/factoextra")
library("factoextra")
#> Loading required package: ggplot2
#> Welcome! Related Books: `Practical Guide To Cluster Analysis in R` at https://goo.gl/13EFCZ

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 Model-based Clustering Results
fviz_silhouette Visualize Silhouette Information from Clustering.
hcut Computes Hierarchical Clustering and Cut the Tree
hkmeans (hkmeans_tree, print.hkmeans) Hierarchical k-means 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.

dimension reduction and factoextra
dimension reduction and factoextra

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

Read more about computing and interpreting principal component analysis at: Principal Component Analysis (PCA).

  1. Loading data
library("factoextra")
data("decathlon2")
df <- decathlon2[1:23, 1:10]
  1. Principal component analysis
library("FactoMineR")
res.pca <- PCA(df,  graph = FALSE)
  1. 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 <- get_pca_var(res.pca)
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
             )
  1. 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)

  1. Extract and visualize results for individuals:
# Extract the results for individuals
ind <- get_pca_ind(res.pca)
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)
  1. Color individuals by groups:
# Compute PCA on the iris data set
# The variable Species (index = 5) is removed
# before PCA analysis
iris.pca <- PCA(iris[,-5], graph = FALSE)

# Visualize
# Use habillage to specify groups for coloring
fviz_pca_ind(iris.pca,
             label = "none", # hide individual labels
             habillage = iris$Species, # color by groups
             palette = c("#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE # Concentration ellipses
             )