Easy Guides

Factoextra R Package: Easy Multivariate Data Analyses and Elegant Visualization

Sun, 19 Feb 2017 17:10:58 +0100

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 easy-to-use R package named factoextra.

The R package factoextra has flexible and easy-to-use methods to extract quickly, in a human readable standard data format, the analysis results from the different packages mentioned above.
It produces a ggplot2-based 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: https://www.sthda.com/english/rpkgs/factoextra.

Contents

Why using factoextra?
Installing FactoMineR
Installing and loading factoextra
Main functions in the factoextra package
Dimension reduction and factoextra
Cluster analysis and factoextra
Acknoweledgment
References
Infos

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 (https://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.

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 <- decathlon2[1:23, 1:10]

Principal component analysis

library("FactoMineR")
res.pca <- PCA(df,  graph = FALSE)

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))

factoextra

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")

factoextra

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
             )

factoextra

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)

factoextra

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)
             )

factoextra

# Biplot of individuals and variables
fviz_pca_biplot(res.pca, repel = TRUE)

factoextra

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
             )

factoextra

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 <- CA(housetasks, graph = FALSE)

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)

factoextra

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 <- MCA(poison, quanti.sup = 1:2,
              quali.sup = 3:4, graph=FALSE)

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 <- as.factor(poison[, "Vomiting"])
fviz_mca_ind(res.mca,  habillage = grp,
             addEllipses = TRUE, repel = TRUE)

factoextra

Graph of variable categories:

fviz_mca_var(res.mca, repel = TRUE)

factoextra

Biplot of individuals and variables:

fviz_mca_biplot(res.mca, repel = TRUE)

factoextra

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, density-based clustering and model-based 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 <- scale(USArrests)

# 2. Compute k-means
set.seed(123)
km.res <- kmeans(scale(USArrests), 4, nstart = 25)

# 3. Visualize
library("factoextra")
fviz_cluster(km.res, data = df,
             palette = c("#00AFBB","#2E9FDF", "#E7B800", "#FC4E07"),
             ggtheme = theme_minimal(),
             main = "Partitioning Clustering Plot"
             )

factoextra

library("factoextra")
# Compute hierarchical clustering and cut into 4 clusters
res <- hcut(USArrests, k = 4, stand = TRUE)

# Visualize
fviz_dend(res, rect = TRUE, cex = 0.5,
          k_colors = c("#00AFBB","#2E9FDF", "#E7B800", "#FC4E07"))

factoextra

# Optimal number of clusters for k-means
library("factoextra")
my_data <- scale(USArrests)
fviz_nbclust(my_data, kmeans, method = "gap_stat")

factoextra

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, Springer-Verlag 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. Springer-Verlag 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), 1-18. 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)

fviz_pca: Quick Principal Component Analysis data visualization - R software and data mining

Thu, 12 Nov 2015 01:15:35 +0100

Description
Install and load factoextra
Usage
Arguments
Value
Examples
Infos

Description

Draw the graph of individuals/variables from the output of Principal Component Analysis (PCA).

The following functions, from factoextra package are use:

fviz_pca_ind(): Graph of individuals
fviz_pca_var(): Graph of variables
fviz_pca_biplot() (or fviz_pca()): Biplot of individuals and variables

Install and load factoextra

The package devtools is required for the installation as factoextra is hosted on github.

# install.packages("devtools")
library("devtools")
install_github("kassambara/factoextra")

Load factoextra :

library("factoextra")

Usage

# Graph of individuals
fviz_pca_ind(X, axes = c(1, 2), geom = c("point", "text"),
       label = "all", invisible = "none", labelsize = 4,
       pointsize = 2, habillage = "none",
       addEllipses = FALSE, ellipse.level = 0.95, 
       col.ind = "black", col.ind.sup = "blue", alpha.ind = 1,
       select.ind = list(name = NULL, cos2 = NULL, contrib = NULL),
       jitter = list(what = "label", width = NULL, height = NULL),  ...)

# Graph of variables
fviz_pca_var(X, axes = c(1, 2), geom = c("arrow", "text"),
       label = "all", invisible = "none", labelsize = 4,
       col.var = "black", alpha.var = 1, col.quanti.sup = "blue",
       col.circle = "grey70",
       select.var = list(name =NULL, cos2 = NULL, contrib = NULL),
       jitter = list(what = "label", width = NULL, height = NULL))

# Biplot of individuals and variables
fviz_pca_biplot(X, axes = c(1, 2), geom = c("point", "text"),
   label = "all", invisible = "none", labelsize = 4, pointsize = 2,
    habillage = "none", addEllipses = FALSE, ellipse.level = 0.95,
    col.ind = "black", col.ind.sup = "blue", alpha.ind = 1,
    col.var = "steelblue", alpha.var = 1, col.quanti.sup = "blue",
    col.circle = "grey70", 
    select.var = list(name = NULL, cos2 = NULL, contrib= NULL), 
    select.ind = list(name = NULL, cos2 = NULL, contrib = NULL),
    jitter = list(what = "label", width = NULL, height = NULL), ...)

# An alias of fviz_pca_biplot()
fviz_pca(X, ...)

Arguments

Argument	Description
X	an object of class PCA [FactoMineR]; prcomp and princomp [stats]; dudi and pca [ade4].
axes	a numeric vector of length 2 specifying the dimensions to be plotted.
geom	a text specifying the geometry to be used for the graph. Allowed values are the combination of c(“point”, “arrow”, “text”). Use “point” (to show only points); “text” to show only labels; c(“point”, “text”) or c(“arrow”, “text”) to show both types.
label	a text specifying the elements to be labelled. Default value is “all”. Allowed values are “none” or the combination of c(“ind”, “ind.sup”, “quali”, “var”, “quanti.sup”). “ind” can be used to label only active individuals. “ind.sup” is for supplementary individuals. “quali” is for supplementary qualitative variables. “var” is for active variables. “quanti.sup” is for quantitative supplementary variables.
invisible	a text specifying the elements to be hidden on the plot. Default value is “none”. Allowed values are the combination of c(“ind”, “ind.sup”, “quali”, “var”, “quanti.sup”).
labelsize	font size for the labels.
pointsize	the size of points.
habillage	an optional factor variable for coloring the observations by groups. Default value is “none”. If X is a PCA object from FactoMineR package, habillage can also specify the supplementary qualitative variable (by its index or name) to be used for coloring individuals by groups (see ?PCA in FactoMineR).
addEllipses	logical value. If TRUE, draws ellipses around the individuals when habillage != “none”.
ellipse.level	the size of the concentration ellipse in normal probability.
col.ind,col.var	colors for individuals and variables, respectively. Possible values include also : “cos2”, “contrib”, “coord”, “x” or “y”. In this case, the colors for individuals/variables are automatically controlled by their qualities of representation (“cos2”), contributions (“contrib”), coordinates (x^2 + y^2, “coord”), x values (“x”) or y values (“y”). To use automatic coloring (by cos2, contrib, ….), make sure that habillage =“none”.
col.ind.sup	color for supplementary individuals.
alpha.ind,alpha.var	controls the transparency of individual and variable colors, respectively. The value can variate from 0 (total transparency) to 1 (no transparency). Default value is 1. Possible values include also : “cos2”, “contrib”, “coord”, “x” or “y”. In this case, the transparency for the individual/variable colors are automatically controlled by their qualities (“cos2”), contributions (“contrib”), coordinates (x^2 + y^2 , “coord”), x values(“x”) or y values(“y”). To use this, make sure that habillage =“none”.
select.ind,select.var	a selection of individuals/variables to be drawn. Allowed values are NULL or a list containing the arguments name, cos2 or contrib: name: is a character vector containing individuals/variables to be drawn cos2: if cos2 is in [0, 1], ex: 0.6, then individuals/variables with a cos2 > 0.6 are drawn. if cos2 > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn. contrib: if contrib > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn
jitter	a parameter used to jitter the points in order to reduce overplotting. It’s a list containing the objects what, width and height (Ex.; jitter = list(what, width, height)). what: the element to be jittered. Possible values are “point” or “p”; “label” or “l”; “both” or “b”. width: degree of jitter in x direction (ex: 0.2). height: degree of jitter in y direction (ex: 0.2).
col.quanti.sup	a color for the quantitative supplementary variables.
col.circle	a color for the correlation circle.
…	Arguments to be passed to the function fviz_pca_biplot().

Value

A ggplot2 plot

Examples

Principal component analysis

A principal component analysis (PCA) is performed using the built-in R function prcomp() and iris data:

data(iris)
head(iris)

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

# The variable Species (index = 5) is removed
# before the PCA analysis
res.pca <- prcomp(iris[, -5],  scale = TRUE)

fviz_pca_ind(): Graph of individuals

# Default plot
fviz_pca_ind(res.pca)

# Change title and axis labels
fviz_pca_ind(res.pca) +
  labs(title ="PCA", x = "PC1", y = "PC2")

# Change axis limits by specifying the min and max
fviz_pca_ind(res.pca) +
   xlim(-4, 4) + ylim (-4, 4)

# Use text only
fviz_pca_ind(res.pca, geom="text")

# Use points only
fviz_pca_ind(res.pca, geom="point")

# Change the size of points
fviz_pca_ind(res.pca, geom="point", pointsize = 4)

# Change point color and theme
fviz_pca_ind(res.pca, col.ind = "blue")+
   theme_minimal()

# Control automatically the color of individuals
# using the cos2 or the contributions
# cos2 = the quality of the individuals on the factor map
fviz_pca_ind(res.pca, col.ind="cos2")

# Gradient color
fviz_pca_ind(res.pca, col.ind="cos2") +
      scale_color_gradient2(low="white", mid="blue",
      high="red", midpoint=0.6)

# Change the theme and use only points
fviz_pca_ind(res.pca, col.ind="cos2", geom = "point") +
      scale_color_gradient2(low="white", mid="blue",
      high="red", midpoint=0.6)+ theme_minimal()

# Color by the contributions
fviz_pca_ind(res.pca, col.ind="contrib") +
      scale_color_gradient2(low="white", mid="blue",
      high="red", midpoint=4)

# Control the transparency of the color by the
# contributions
fviz_pca_ind(res.pca, alpha.ind="contrib") +
     theme_minimal()

# Color individuals by groups
fviz_pca_ind(res.pca, label="none", habillage=iris$Species)

# Add ellipses
p <- fviz_pca_ind(res.pca, label="none", habillage=iris$Species,
             addEllipses=TRUE, ellipse.level=0.95)
print(p)

# Change group colors using RColorBrewer color palettes
p + scale_color_brewer(palette="Dark2") +
     theme_minimal()

p + scale_color_brewer(palette="Paired") +
     theme_minimal()

p + scale_color_brewer(palette="Set1") +
     theme_minimal()

# Change color manually
p + scale_color_manual(values=c("#999999", "#E69F00", "#56B4E9"))

# Select and visualize individuals with cos2 > 0.96
fviz_pca_ind(res.pca, select.ind = list(cos2 = 0.96))

# Select the top 20 according the cos2
fviz_pca_ind(res.pca, select.ind = list(cos2 = 20))

# Select the top 20 contributing individuals
fviz_pca_ind(res.pca, select.ind = list(contrib = 20))

# Select by names
fviz_pca_ind(res.pca,
select.ind = list(name = c("23", "42", "119")))

fviz_pca_var(): Graph of variables

# Default plot
fviz_pca_var(res.pca)

# Use points and text
fviz_pca_var(res.pca, geom = c("point", "text"))

# Change color and theme
fviz_pca_var(res.pca, col.var="steelblue")+
 theme_minimal()

# Control variable colors using their contributions
fviz_pca_var(res.pca, col.var="contrib")+
 scale_color_gradient2(low="white", mid="blue",
           high="red", midpoint=96) +
 theme_minimal()

# Control the transparency of variables using their contributions
fviz_pca_var(res.pca, alpha.var="contrib") +
   theme_minimal()

# Select and visualize variables with cos2 >= 0.96
fviz_pca_var(res.pca, select.var = list(cos2 = 0.96))

# Select the top 3 contributing variables
fviz_pca_var(res.pca, select.var = list(contrib = 3))

# Select by names
fviz_pca_var(res.pca,
   select.var= list(name = c("Sepal.Width", "Petal.Length")))

fviz_pca_biplot(): Biplot of individuals of variables

fviz_pca_biplot(res.pca)

# Keep only the labels for variables
fviz_pca_biplot(res.pca, label ="var")

# Keep only labels for individuals
fviz_pca_biplot(res.pca, label ="ind")

# Hide variables
fviz_pca_biplot(res.pca, invisible ="var")

# Hide individuals
fviz_pca_biplot(res.pca, invisible ="ind")

# Control automatically the color of individuals using the cos2
fviz_pca_biplot(res.pca, label ="var", col.ind="cos2") +
       theme_minimal()

# Change the color by groups, add ellipses
fviz_pca_biplot(res.pca, label="var", habillage=iris$Species,
               addEllipses=TRUE, ellipse.level=0.95)

# Select the top 30 contributing individuals
fviz_pca_biplot(res.pca, label="var",
               select.ind = list(contrib = 30))

Infos

This analysis has been performed using R software (ver. 3.2.1) and factoextra (ver. 1.0.3)

fviz_mca: Quick Multiple Correspondence Analysis data visualization - R software and data mining

Thu, 12 Nov 2015 01:09:40 +0100

Description
Install and load factoextra
Usage
Arguments
Details
Value
Examples
Infos

Description

Draw the graph of individuals/variables from the output of Multiple Correspondence Analysis (MCA).

The following functions, from factoextra package are use:

fviz_mca_ind(): Graph of individuals
fviz_mca_var(): Graph of variable categories
fviz_mca_biplot() (or fviz_mca()): Biplot of individuals and variable categories

Install and load factoextra

The package devtools is required for the installation as factoextra is hosted on github.

# install.packages("devtools")
library("devtools")
install_github("kassambara/factoextra")

Load factoextra :

library("factoextra")

Usage

# Graph of individuals
fviz_mca_ind(X, axes = c(1, 2), 
  geom = c("point", "text"), label = "all", invisible = "none",
  labelsize = 4, pointsize = 2, habillage = "none",
  addEllipses = FALSE, ellipse.level = 0.95, col.ind = "blue",
  col.ind.sup = "darkblue", alpha.ind = 1, shape.ind = 19,
  select.ind = list(name = NULL, cos2 = NULL, contrib = NULL),
  map = "symmetric", 
  jitter = list(what = "label", width = NULL, height = NULL), ...)

# Graph of variables
fviz_mca_var(X, axes = c(1, 2),
  geom = c("point", "text"), label = "all",
  invisible = "none", labelsize = 4, pointsize = 2, col.var = "red",
  alpha.var = 1, shape.var = 17, col.quanti.sup = "blue",
  col.quali.sup = "darkgreen", col.circle = "grey70",
  select.var = list(name = NULL, cos2 = NULL, contrib = NULL),
  map = "symmetric", 
  jitter = list(what = "label", width = NULL, height = NULL))

# Biplot of individuals and variables
fviz_mca_biplot(X, axes = c(1, 2), geom = c("point", "text"),
  label = "all", invisible = "none", labelsize = 4, pointsize = 2,
  habillage = "none", addEllipses = FALSE, ellipse.level = 0.95,
  col.ind = "blue", col.ind.sup = "darkblue", alpha.ind = 1,
  col.var = "red", alpha.var = 1, col.quanti.sup = "blue",
  col.quali.sup = "darkgreen", shape.ind = 19, shape.var = 17,
  select.var = list(name = NULL, cos2 = NULL, contrib = NULL),
  select.ind = list(name = NULL, cos2 = NULL, contrib = NULL),
  map = "symmetric", arrows = c(FALSE, FALSE), 
  jitter = list(what = "label", width = NULL, height = NULL), ...)

# An alias of fviz_mca_biplot()
fviz_mca(X, ...)

Arguments

Argument	Description
X	an object of class MCA [FactoMineR]; mca [ade4].
axes	a numeric vector of length 2 specifying the dimensions to be plotted.
geom	a text specifying the geometry to be used for the graph. Allowed values are the combination of c(“point”, “arrow”, “text”). Use “point” (to show only points); “text” to show only labels; c(“point”, “text”) or c(“arrow”, “text”) to show both types.
label	a text specifying the elements to be labelled. Default value is “all”. Allowed values are “none” or the combination of c(“ind”, “ind.sup”,“var”, “quali.sup”, “quanti.sup”). “ind” can be used to label only active individuals. “ind.sup” is for supplementary individuals. “var” is for active variable categories. “quali.sup” is for supplementary qualitative variable categories. “quanti.sup” is for quantitative supplementary variables.
invisible	a text specifying the elements to be hidden on the plot. Default value is “none”. Allowed values are the combination of c(“ind”, “ind.sup”,“var”, “quali.sup”, “quanti.sup”).
labelsize	font size for the labels.
pointsize	the size of points.
habillage	an optional factor variable for coloring the observations by groups. Default value is “none”. If X is a MCA object from FactoMineR package, habillage can also specify the supplementary qualitative variable (by its index or name) to be used for coloring individuals by groups (see ?MCA in FactoMineR).
addEllipses	logical value. If TRUE, draws ellipses around the individuals when habillage != “none”.
ellipse.level	the size of the concentration ellipse in normal probability.
col.ind,col.var	colors for individuals and variables, respectively. Possible values include also : “cos2”, “contrib”, “coord”, “x” or “y”. In this case, the colors for individuals/variables are automatically controlled by their qualities of representation (“cos2”), contributions (“contrib”), coordinates (x^2 + y^2 , “coord”), x values (“x”) or y values (“y”). To use automatic coloring (by cos2, contrib, ….), make sure that habillage =“none”.
col.ind.sup	color for supplementary individuals.
alpha.ind,alpha.var	controls the transparency of individual and variable colors, respectively. The value can variate from 0 (total transparency) to 1 (no transparency). Default value is 1. Possible values include also : “cos2”, “contrib”, “coord”, “x” or “y”. In this case, the transparency for the individual/variable colors are automatically controlled by their qualities (“cos2”), contributions (“contrib”), coordinates (x^2+y2 , “coord”), x values(“x”) or y values(“y”). To use this, make sure that habillage =“none”.
select.ind,select.var	a selection of individuals/variables to be drawn. Allowed values are NULL or a list containing the arguments name, cos2 or contrib: name: is a character vector containing individuals/variables to be drawn cos2: if cos2 is in [0, 1], ex: 0.6, then individuals/variables with a cos2 > 0.6 are drawn. if cos2 > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn. contrib: if contrib > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn
map	character string specifying the map type. Allowed options include: "symmetric", "rowprincipal", "colprincipal", "symbiplot", "rowgab", "colgab", "rowgreen" and "colgreen". See details
jitter	a parameter used to jitter the points in order to reduce overplotting. It’s a list containing the objects what, width and height (Ex.; jitter = list(what, width, height)). what: the element to be jittered. Possible values are “point” or “p”; “label” or “l”; “both” or “b”. width: degree of jitter in x direction (ex: 0.2). height: degree of jitter in y direction (ex: 0.2).
col.quanti.sup, col.quali.sup	a color for the quantitative/qualitative supplementary variables.
arrows	Vector of two logicals specifying if the plot should contain points (FALSE, default) or arrows (TRUE). First value sets the rows and the second value sets the columns.
…	Arguments to be passed to the function fviz_mca_biplot().

Details

The default plot of MCA is a “symmetric” plot in which both rows and columns are in principal coordinates. In this situation, it’s not possible to interpret the distance between row points and column points. To overcome this problem, the simplest way is to make an asymmetric plot. This means that, the column profiles must be presented in row space or vice-versa. The allowed options for the argument map are:

“rowprincipal” or “colprincipal”: asymmetric plots with either rows in principal coordinates and columns in standard coordinates, or vice versa. These plots preserve row metric or column metric respectively.
“symbiplot”: Both rows and columns are scaled to have variances equal to the singular values (square roots of eigenvalues), which gives a symmetric biplot but does not preserve row or column metrics.
“rowgab” or “colgab”: Asymmetric maps, proposed by Gabriel & Odoroff (1990), with rows (respectively, columns) in principal coordinates and columns (respectively, rows) in standard coordinates multiplied by the mass of the corresponding point.
“rowgreen” or “colgreen”: The so-called contribution biplots showing visually the most contributing points (Greenacre 2006b). These are similar to “rowgab” and “colgab” except that the points in standard coordinates are multiplied by the square root of the corresponding masses, giving reconstructions of the standardized residuals.

Value

A ggplot2 plot

Examples

Multiple Correspondence Analysis

A Multiple Correspondence Analysis (MCA) is performed using the function MCA() [in FactoMineR] and poison data [in FactoMineR]:

# Install and load FactoMineR to compute MCA
# install.packages("FactoMineR")
library("FactoMineR")
data(poison)
poison.active <- poison[1:55, 5:15]
head(poison.active[, 1:6])

    Nausea Vomiting Abdominals   Fever   Diarrhae   Potato
1 Nausea_y  Vomit_n     Abdo_y Fever_y Diarrhea_y Potato_y
2 Nausea_n  Vomit_n     Abdo_n Fever_n Diarrhea_n Potato_y
3 Nausea_n  Vomit_y     Abdo_y Fever_y Diarrhea_y Potato_y
4 Nausea_n  Vomit_n     Abdo_n Fever_n Diarrhea_n Potato_y
5 Nausea_n  Vomit_y     Abdo_y Fever_y Diarrhea_y Potato_y
6 Nausea_n  Vomit_n     Abdo_y Fever_y Diarrhea_y Potato_y

res.mca <- MCA(poison.active, graph=FALSE)

fviz_mca_ind(): Graph of individuals

# Default plot
fviz_mca_ind(res.mca)

# Change title and axis labels
fviz_mca_ind(res.mca) +
 labs(title = "MCA", x = "Dim.1", y ="Dim.2" )

# Change axis limits by specifying the min and max
fviz_mca_ind(res.mca) +
   xlim(-0.8, 1.5) + ylim (-1.5, 1.5)

# Use text only
fviz_mca_ind(res.mca, geom = "text")

# Use points only
fviz_mca_ind(res.mca, geom="point")

# Change the size of points
fviz_mca_ind(res.mca, geom="point", pointsize = 4)

# Change point color and theme
fviz_mca_ind(res.mca, col.ind = "blue")+
   theme_minimal()

# Reduce overplotting
fviz_mca_ind(res.mca, 
             jitter = list(width = 0.2, height = 0.2))

# Control automatically the color of individuals
# using the cos2 or the contributions
# cos2 = the quality of the individuals on the factor map
fviz_mca_ind(res.mca, col.ind="cos2")

# Gradient color
fviz_mca_ind(res.mca, col.ind="cos2") +
      scale_color_gradient2(low="white", mid="blue",
      high="red", midpoint=0.4)

# Change the theme and use only points
fviz_mca_ind(res.mca, col.ind="cos2", geom = "point") +
      scale_color_gradient2(low="white", mid="blue",
      high="red", midpoint=0.4)+ theme_minimal()

# Color by the contributions
fviz_mca_ind(res.mca, col.ind="contrib") +
      scale_color_gradient2(low="white", mid="blue",
      high="red", midpoint=1.5)

# Control the transparency of the color by the
# contributions
fviz_mca_ind(res.mca, alpha.ind="contrib") +
     theme_minimal()

# Color individuals by groups
grp <- as.factor(poison.active[, "Vomiting"])
fviz_mca_ind(res.mca, label="none", habillage=grp)

# Add ellipses
p <- fviz_mca_ind(res.mca, label="none", habillage=grp,
             addEllipses=TRUE, ellipse.level=0.95)
print(p)

# Change group colors using RColorBrewer color palettes
p + scale_color_brewer(palette="Dark2") +
   theme_minimal()

p + scale_color_brewer(palette="Paired") +
     theme_minimal()

p + scale_color_brewer(palette="Set1") +
     theme_minimal()

# Change color manually
p + scale_color_manual(values=c("#999999", "#E69F00", "#56B4E9"))

# Select and visualize individuals with cos2 >= 0.4
fviz_mca_ind(res.mca, select.ind = list(cos2 = 0.4))

# Select the top 20 according to the cos2
fviz_mca_ind(res.mca, select.ind = list(cos2 = 20))

# Select the top 20 contributing individuals
fviz_mca_ind(res.mca, select.ind = list(contrib = 20))

# Select by names
fviz_mca_ind(res.mca,
select.ind = list(name = c("44", "38", "53",  "39")))

fviz_mca_var(): Graph of variable categories

# Default plot
fviz_mca_var(res.mca)

# Change color and theme
fviz_mca_var(res.mca, col.var="steelblue")+
 theme_minimal()

# Control variable colors using their contributions
fviz_mca_var(res.mca, col.var = "contrib")+
 scale_color_gradient2(low = "white", mid = "blue",
           high = "red", midpoint = 2) +
 theme_minimal()

# Control the transparency of variables using their contributions
fviz_mca_var(res.mca, alpha.var = "contrib") +
   theme_minimal()

# Select and visualize categories with cos2 >= 0.4
fviz_mca_var(res.mca, select.var = list(cos2 = 0.4))

# Select the top 10 contributing variable categories
fviz_mca_var(res.mca, select.var = list(contrib = 10))

# Select by names
fviz_mca_var(res.mca,
 select.var= list(name = c("Courg_n", "Fever_y", "Fever_n")))

fviz_mca_biplot(): Biplot of individuals of variable categories

fviz_mca_biplot(res.mca)

# Keep only the labels for variable categories
fviz_mca_biplot(res.mca, label ="var")

# Keep only labels for individuals
fviz_mca_biplot(res.mca, label ="ind")

# Hide variable categories
fviz_mca_biplot(res.mca, invisible ="var")

# Hide individuals
fviz_mca_biplot(res.mca, invisible ="ind")

# Control automatically the color of individuals using the cos2
fviz_mca_biplot(res.mca, label ="var", col.ind="cos2") +
       theme_minimal()

# Change the color by groups, add ellipses
fviz_mca_biplot(res.mca, label="var", col.var ="blue",
   habillage=grp, addEllipses=TRUE, ellipse.level=0.95) +
   theme_minimal()

# Select the top 30 contributing individuals
# And the top 10 variables
fviz_mca_biplot(res.mca,
               select.ind = list(contrib = 30),
               select.var = list(contrib = 10))

Infos

This analysis has been performed using R software (ver. 3.2.1) and factoextra (ver. 1.0.3)

fviz_ca: Quick Correspondence Analysis data visualization using factoextra - R software and data mining

Wed, 11 Nov 2015 14:44:28 +0100

Description
Install and load factoextra
Usage
Arguments
Details
Value
Examples
Infos

Description

Graph of column/row variables from the output of Correspondence Analysis (CA).

The following functions, from factoextra package are use:

fviz_ca_row(): Graph of row variables
fviz_ca_col(): Graph of column variables
fviz_ca_biplot(): Biplot of row and column variables
fviz_ca(): An alias of fviz_ca_biplot()

These functions are included in factoextra package.

Install and load factoextra

The package devtools is required for the installation as factoextra is hosted on github.

# install.packages("devtools")
library("devtools")
install_github("kassambara/factoextra")

Load factoextra :

library("factoextra")

Usage

# Graph of row variables
fviz_ca_row(X, axes = c(1, 2), shape.row = 19,
  geom = c("point", "text"), label = "all", 
  invisible = "none", labelsize = 4, pointsize = 2,
  col.row = "blue", col.row.sup = "darkblue", alpha.row = 1,
  select.row = list(name = NULL, cos2 = NULL, contrib = NULL),
  map = "symmetric",
  jitter = list(what = "label", width = NULL, height = NULL), ...)

# Graph of column variables
fviz_ca_col(X, axes = c(1, 2), shape.col = 17,
  geom = c("point", "text"), label = "all",
  invisible = "none", labelsize = 4, pointsize = 2,
  col.col = "red", col.col.sup = "darkred", alpha.col = 1,
  select.col = list(name = NULL, cos2 = NULL, contrib = NULL),
  map = "symmetric",
 jitter = list(what = "label", width = NULL, height = NULL), ...)

# Biplot of row and column  variables
fviz_ca_biplot(X, axes = c(1, 2), shape.row = 19, shape.col = 17,
  geom = c("point", "text"), label = "all", invisible = "none",
  labelsize = 4, pointsize = 2, col.col = "red",
  col.col.sup = "darkred", alpha.col = 1, col.row = "blue",
  col.row.sup = "darkblue", alpha.row = 1,
  select.col = list(name = NULL, cos2 = NULL, contrib = NULL),
  select.row = list(name = NULL, cos2 = NULL, contrib = NULL),
  map = "symmetric", arrows = c(FALSE, FALSE),
  jitter = list(what = "label", width = NULL, height = NULL), ...)


# An alias of fviz_ca_biplot()
fviz_ca(X, ...)

Arguments

Argument	Description
X	an object of class CA [FactoMineR], ca [ca], coa [ade4]; correspondence [MASS].
axes	a numeric vector of length 2 specifying the dimensions to be plotted.
shape.row,shape.col	the point shapes to be used for row/column variables. Default values are 19 for rows and 17 for columns.
geom	a text specifying the geometry to be used for the graph. Allowed values are the combination of c(“point”, “arrow”, “text”). Use “point” (to show only points); “text” to show only labels; c(“point”, “text”) or c(“arrow”, “text”) to show both types.
label	a character vector specifying the elements to be labelled. Default value is “all”. Allowed values are “none” or the combination of c(“row”, “row.sup”, “col”, “col.sup”). Use “col” to label only active column variables; “col.sup” to label only supplementary columns; etc
invisible	a character value specifying the elements to be hidden on the plot. Default value is “none”. Allowed values are the combination of c(“row”, “row.sup”, “col”, col.sup“).
labelsize	font size for the labels.
pointsize	the size of points.
map	character string specifying the map type. Allowed options include: “symmetric”, “rowprincipal”, “colprincipal”, “symbiplot”, “rowgab”, “colgab”, “rowgreen” and “colgreen”. See details
jitter	a parameter used to jitter the points in order to reduce overplotting. It's a list containing the objects what, width and height (Ex.; jitter = list(what, width, height)). what: the element to be jittered. Possible values are "point" or "p"; "label" or "l"; "both" or "b". width: degree of jitter in x direction (ex: 0.2). height: degree of jitter in y direction (ex: 0.2).
col.col,col.row	color for column/row points. The default values are “red” and “blue”, respectively. Allowed values include also : “cos2”, “contrib”, “coord”, “x” or “y”. In this case, the colors for row/column variables are automatically controlled by their qualities (“cos2”), contributions (“contrib”), coordinates (x^2 + y^2, “coord”), x values(“x”) or y values(“y”)
col.col.sup,col.row.sup	colors for the supplementary column and row points, respectively.
alpha.col,alpha.row	controls the transparency of colors. The value can variate from 0 (total transparency) to 1 (no transparency). Default value is 1. Allowed values include also : "cos2", "contrib", "coord", "x" or "y" as for the arguments col.col and col.row..
select.col,select.row	a selection of columns/rows to be drawn. Allowed values are NULL or a list containing the arguments name, cos2 or contrib: name: is a character vector containing columns/rows to be drawn cos2: if cos2 is in [0, 1], ex: 0.6, then columns/rows with a cos2 > 0.6 are drawn. if cos2 > 1, ex: 5, then the top 5 columns/rows with the highest cos2 are drawn. contrib: if contrib > 1, ex: 5, then the top 5 columns/rows with the highest cos2 are drawn
arrows	Vector of two logicals specifying if the plot should contain points (FALSE, default) or arrows (TRUE). First value sets the rows and the second value sets the columns.
…	Optional arguments.

Details

The default plot of CA is a “symmetric” plot in which both rows and columns are in principal coordinates. In this situation, it’s not possible to interpret the distance between row points and column points. To overcome this problem, the simplest way is to make an asymmetric plot. This means that, the column profiles must be presented in row space or vice-versa. The allowed options for the argument map are:

“rowprincipal” or “colprincipal”: asymmetric plots with either rows in principal coordinates and columns in standard coordinates, or vice versa. These plots preserve row metric or column metric respectively.
“symbiplot”: Both rows and columns are scaled to have variances equal to the singular values (square roots of eigenvalues), which gives a symmetric biplot but does not preserve row or column metrics.
“rowgab” or “colgab”: Asymmetric maps, proposed by Gabriel & Odoroff (1990), with rows (respectively, columns) in principal coordinates and columns (respectively, rows) in standard coordinates multiplied by the mass of the corresponding point.
“rowgreen” or “colgreen”: The so-called contribution biplots showing visually the most contributing points (Greenacre 2006b). These are similar to “rowgab” and “colgab” except that the points in standard coordinates are multiplied by the square root of the corresponding masses, giving reconstructions of the standardized residuals.

Value

A ggplot2 plot

Examples

Correspondence Analysis

Correspondence Analysis (CA) is performed using the function CA() [in FactoMineR] and housetasks data [in factoextra]:

# Install and load FactoMineR to compute CA
# install.packages("FactoMineR")
library("FactoMineR")
data(housetasks)
head(housetasks)

           Wife Alternating Husband Jointly
Laundry     156          14       2       4
Main_meal   124          20       5       4
Dinner       77          11       7      13
Breakfeast   82          36      15       7
Tidying      53          11       1      57
Dishes       32          24       4      53

res.ca <- CA(housetasks, graph=FALSE)

fviz_ca_row(): Graph of row variables

# Default plot
fviz_ca_row(res.ca)

# Change title and axis labels
fviz_ca_row(res.ca) +
 labs(title = "CA", x = "Dim.1", y ="Dim.2" )

# Change axis limits by specifying the min and max
fviz_ca_row(res.ca) +
   xlim(-1.3, 1.7) + ylim (-1.5, 1)

# Use text only
fviz_ca_row(res.ca, geom = "text")

# Use points only
fviz_ca_row(res.ca, geom="point")

# Change the size of points
fviz_ca_row(res.ca, geom="point", pointsize = 4)

# Change point color and theme
fviz_ca_row(res.ca, col.row = "violet")+
   theme_minimal()

# Control automatically the color of row points
# using the cos2 or the contributions
# cos2 = the quality of the rows on the factor map
fviz_ca_row(res.ca, col.row="cos2")

# Gradient color
fviz_ca_row(res.ca, col.row="cos2") +
      scale_color_gradient2(low="white", mid="blue",
      high="red", midpoint=0.5)

# Change the theme and use only points
fviz_ca_row(res.ca, col.row="cos2", geom = "point") +
      scale_color_gradient2(low="white", mid="blue",
      high="red", midpoint=0.4)+ theme_minimal()

# Color by the contributions
fviz_ca_row(res.ca, col.row="contrib") +
      scale_color_gradient2(low="white", mid="blue",
      high="red", midpoint=10)

# Control the transparency of the color by the
# contributions
fviz_ca_row(res.ca, alpha.row="contrib") +
     theme_minimal()

# Select and visualize rows with cos2 > 0.5
fviz_ca_row(res.ca, select.row = list(cos2 = 0.5))

# Select the top 7 according to the cos2
fviz_ca_row(res.ca, select.row = list(cos2 = 7))

# Select the top 7 contributing rows
fviz_ca_row(res.ca, select.row = list(contrib = 7))

# Select by names
fviz_ca_row(res.ca,
select.row = list(name = c("Breakfeast", "Repairs", "Holidays")))

fviz_ca_col(): Graph of column categories

# Default plot
fviz_ca_col(res.ca)

# Change color and theme
fviz_ca_col(res.ca, col.col="steelblue")+
 theme_minimal()

# Control colors using their contributions
fviz_ca_col(res.ca, col.col = "contrib")+
 scale_color_gradient2(low = "white", mid = "blue",
           high = "red", midpoint = 25) +
 theme_minimal()

# Control the transparency of variables using their contributions
fviz_ca_col(res.ca, alpha.col = "contrib") +
   theme_minimal()

# Select and visualize columns with cos2 >= 0.4
fviz_ca_col(res.ca, select.col = list(cos2 = 0.4))

# Select the top 3 contributing columns
fviz_ca_col(res.ca, select.col = list(contrib = 3))

# Select by names
fviz_ca_col(res.ca,
 select.col= list(name = c("Wife", "Husband", "Jointly")))

fviz_ca_biplot(): Biplot of rows and columns

# Symetric Biplot of rows and columns
fviz_ca_biplot(res.ca)

# Asymetric biplot, use arrows for columns
fviz_ca_biplot(res.ca, map ="rowprincipal",
 arrow = c(FALSE, TRUE))

# Keep only the labels for row points
fviz_ca_biplot(res.ca, label ="row")

# Keep only labels for column points
fviz_ca_biplot(res.ca, label ="col")

# Hide row points
fviz_ca_biplot(res.ca, invisible ="row")

# Hide column points
fviz_ca_biplot(res.ca, invisible ="col")

# Control automatically the color of rows using the cos2
fviz_ca_biplot(res.ca, col.row="cos2") +
       theme_minimal()

# Select the top 7 contributing rows
# And the top 3 columns
fviz_ca_biplot(res.ca,
               select.row = list(contrib = 7),
               select.col = list(contrib = 3))

Infos

This analysis has been performed using R software (ver. 3.2.1) and factoextra (ver. 1.0.3)

facto_summarize - Subset and summarize the output of factor analyses - R software and data mining

Wed, 11 Nov 2015 13:02:54 +0100

Description
Install and load factoextra
Usage
Arguments
Details
Value
Examples
Infos

Description

Subset and summarize the results of Principal Component Analysis (PCA), Correspondence Analysis (CA) and Multiple Correspondence Analysis (MCA) functions from several packages.

The function facto_summarize() [in factoextra package] is used.

Install and load factoextra

The package devtools is required for the installation as factoextra is hosted on github.

# install.packages("devtools")
devtools::install_github("kassambara/factoextra")

Load factoextra :

library("factoextra")

Usage

facto_summarize(X, element, result = c("coord", "cos2", "contrib"),
                axes = 1:2, select = NULL)

Arguments

Argument	Description
X	an object of class PCA, CA and MCA [FactoMineR]; prcomp and princomp [stats]; dudi, pca, coa and acm [ade4]; ca [ca package].
element	allowed values are “row” and “col” for CA; “var” and “ind” for PCA or MCA.
result	the result to be extracted for the element. Possible values are the combination of c(“cos2”, “contrib”, “coord”).
axes	a numeric vector specifying the axes of interest. Default values are 1:2 for axes 1 and 2.
select	a selection of variables. Allowed values are NULL or a list containing the arguments name, cos2 or contrib. Default is list(name = NULL, cos2 = NULL, contrib = NULL): name: is a character vector containing variable names to be selected cos2: if cos2 is in [0, 1], ex: 0.6, then variables with a cos2 > 0.6 are selected. if cos2 > 1, ex: 5, then the top 5 variables with the highest cos2 are selected contrib: if contrib > 1, ex: 5, then the top 5 variables with the highest contrib are selected.

Details

If length(axes) > 1, then the columns contrib and cos2 correspond to the total contributions and total cos2 of the axes. In this case, the column coord is calculated as x^2 + y^2 + …+; x, y, … are the coordinates of the points on the specified axes.

Value

A data frame containing the (total) coord, cos2 and the contribution for the axes.

Examples

Principal component analysis

A principal component analysis (PCA) is performed using the built-in R function prcomp() and the decathlon2 [in factoextra] data

data(decathlon2)
decathlon2.active <- decathlon2[1:23, 1:10]
res.pca <- prcomp(decathlon2.active,  scale = TRUE)
# Summarize variables on axes 1:2
facto_summarize(res.pca, "var", axes = 1:2)[,-1]

                    Dim.1       Dim.2     coord      cos2  contrib
X100m        -0.850625692  0.17939806 0.7557477 0.7557477 75.57477
Long.jump     0.794180641 -0.28085695 0.7096035 0.7096035 70.96035
Shot.put      0.733912733 -0.08540412 0.5459218 0.5459218 54.59218
High.jump     0.610083985  0.46521415 0.5886267 0.5886267 58.86267
X400m        -0.701603377 -0.29017826 0.5764507 0.5764507 57.64507
X110m.hurdle -0.764125197  0.02474081 0.5844994 0.5844994 58.44994
Discus        0.743209016 -0.04966086 0.5548258 0.5548258 55.48258
Pole.vault   -0.217268042 -0.80745110 0.6991827 0.6991827 69.91827
Javeline      0.428226639 -0.38610928 0.3324584 0.3324584 33.24584
X1500m        0.004278487 -0.78448019 0.6154275 0.6154275 61.54275

# Select the top 5 contributing variables
facto_summarize(res.pca, "var", axes = 1:2,
           select = list(contrib = 5))[,-1]

                  Dim.1      Dim.2     coord      cos2  contrib
X100m      -0.850625692  0.1793981 0.7557477 0.7557477 75.57477
Long.jump   0.794180641 -0.2808570 0.7096035 0.7096035 70.96035
Pole.vault -0.217268042 -0.8074511 0.6991827 0.6991827 69.91827
X1500m      0.004278487 -0.7844802 0.6154275 0.6154275 61.54275
High.jump   0.610083985  0.4652142 0.5886267 0.5886267 58.86267

# Select variables with cos2 >= 0.6
facto_summarize(res.pca, "var", axes = 1:2,
           select = list(cos2 = 0.6))[,-1]

                  Dim.1      Dim.2     coord      cos2  contrib
X100m      -0.850625692  0.1793981 0.7557477 0.7557477 75.57477
Long.jump   0.794180641 -0.2808570 0.7096035 0.7096035 70.96035
Pole.vault -0.217268042 -0.8074511 0.6991827 0.6991827 69.91827
X1500m      0.004278487 -0.7844802 0.6154275 0.6154275 61.54275

# Select by names
facto_summarize(res.pca, "var", axes = 1:2,
     select = list(name = c("X100m", "Discus", "Javeline")))[,-1]

              Dim.1       Dim.2     coord      cos2  contrib
X100m    -0.8506257  0.17939806 0.7557477 0.7557477 75.57477
Discus    0.7432090 -0.04966086 0.5548258 0.5548258 55.48258
Javeline  0.4282266 -0.38610928 0.3324584 0.3324584 33.24584

# Summarize individuals on axes 1:2
facto_summarize(res.pca, "ind", axes = 1:2)[,-1]

                 Dim.1      Dim.2      coord      cos2   contrib
SEBRLE       0.1912074 -1.5541282  2.4518746 0.5050034 10.660324
CLAY         0.7901217 -2.4204156  6.4827039 0.5057178 28.185669
BERNARD     -1.3292592 -1.6118687  4.3650507 0.4871654 18.978481
YURKOV      -0.8694134  0.4328779  0.9432630 0.1199355  4.101143
ZSIVOCZKY   -0.1057450  2.0233632  4.1051806 0.5779938 17.848611
McMULLEN     0.1185550  0.9916237  0.9973729 0.1543704  4.336404
MARTINEAU   -2.3923532  1.2849234  7.3743818 0.5205607 32.062530
HERNU       -1.8910497 -1.1784614  4.9648401 0.5543447 21.586261
BARRAS      -1.7744575  0.4125321  3.3188820 0.6495490 14.429922
NOOL        -2.7770058  1.5726757 10.1850700 0.6469840 44.282913
BOURGUIGNON -4.4137335 -1.2635770 21.0776704 0.9301572 91.642045
Sebrle       3.4514485 -1.2169193 13.3933893 0.7593400 58.232127
Clay         3.3162243 -1.6232908 13.6324164 0.8523470 59.271375
Karpov       4.0703560  0.7983510 17.2051623 0.8138146 74.805053
Macey        1.8484623  2.0638828  7.6764252 0.8165181 33.375762
Warners      1.3873514 -0.2819083  2.0042163 0.2662078  8.713984
Zsivoczky    0.4715533  0.9267436  1.0812163 0.2190667  4.700940
Hernu        0.2763118  1.1657260  1.4352654 0.4666709  6.240284
Bernard      1.3672590  1.4780354  4.0539857 0.6274807 17.626025
Schwarzl    -0.7102777 -0.6584251  0.9380181 0.2170229  4.078340
Pogorelov   -0.2143524 -0.8610557  0.7873639 0.1337231  3.423321
Schoenbeck  -0.4953166 -1.3000530  1.9354762 0.5291161  8.415114
Barras      -0.3158867  0.8193681  0.7711485 0.1466237  3.352820

Correspondence Analysis

The function CA() in FactoMineR package is used:

# Install and load FactoMineR to compute CA
# install.packages("FactoMineR")
library("FactoMineR")
data("housetasks")
res.ca <- CA(housetasks, graph = FALSE)
# Summarize row variables on axes 1:2
facto_summarize(res.ca, "row", axes = 1:2)[,-1]

                Dim.1      Dim.2     coord      cos2   contrib
Laundry    -0.9918368  0.4953220 1.2290841 0.9245395 12.403601
Main_meal  -0.8755855  0.4901092 1.0068569 0.9739621  8.833091
Dinner     -0.6925740  0.3081043 0.5745869 0.9303433  3.558222
Breakfeast -0.5086002  0.4528038 0.4637054 0.9051733  3.722406
Tidying    -0.3938084 -0.4343444 0.3437401 0.9748275  2.404604
Dishes     -0.1889641 -0.4419662 0.2310416 0.7642703  1.497001
Shopping   -0.1176813 -0.4033171 0.1765136 0.8113088  1.214543
Official    0.2266324  0.2536132 0.1156819 0.1194711  0.636781
Driving     0.7417696  0.6534143 0.9771724 0.7672477  7.788243
Finances    0.2707669 -0.6178684 0.4550760 0.9973464  2.948600
Insurance   0.6470759 -0.4737832 0.6431778 0.8848140  5.126245
Repairs     1.5287787  0.8642647 3.0841176 0.9326072 29.178865
Holidays    0.2524863 -1.4350066 2.1229933 0.9921522 19.477003

# Summarize column variables on axes 1:2
facto_summarize(res.ca, "col", axes = 1:2)[,-1]

                  Dim.1      Dim.2      coord      cos2  contrib
Wife        -0.83762154  0.3652207 0.83499601 0.9543242 28.72693
Alternating -0.06218462  0.2915938 0.08889388 0.1098815  1.29467
Husband      1.16091847  0.6019199 1.71003929 0.9795683 37.35808
Jointly      0.14942609 -1.0265791 1.07619274 0.9979998 31.40952

Multiple Correspondence Analysis

The function MCA() in FactoMineR package is used:

library(FactoMineR)
data(poison)
res.mca <- MCA(poison, quanti.sup = 1:2,
              quali.sup = 3:4, graph=FALSE)
# Summarize variables on axes 1:2
res <- facto_summarize(res.mca, "var", axes = 1:2)
head(res)

             name      Dim.1       Dim.2      coord      cos2   contrib
Nausea_n Nausea_n  0.2673909  0.12139029 0.08623348 0.3090033 0.6128991
Nausea_y Nausea_y -0.9581506 -0.43498187 1.10726185 0.3090033 2.1962218
Vomit_n   Vomit_n  0.4790279 -0.40919465 0.39690803 0.5953620 2.1649529
Vomit_y   Vomit_y -0.7185419  0.61379197 0.89304306 0.5953620 3.2474293
Abdo_n     Abdo_n  1.3180221 -0.03574501 1.73845988 0.8457372 5.1722773
Abdo_y     Abdo_y -0.6411999  0.01738946 0.41143974 0.8457372 2.5162430

# Summarize individuals on axes 1:2
res <- facto_summarize(res.mca, "ind", axes = 1:2)
head(res)

  name      Dim.1       Dim.2     coord       cos2   contrib
1    1 -0.4525811 -0.26415072 0.2746052 0.46457063 0.4992822
2    2  0.8361700 -0.03193457 0.7002000 0.55670644 1.2730909
3    3 -0.4481892  0.13538726 0.2192032 0.59815656 0.3985513
4    4  0.8803694 -0.08536230 0.7823370 0.75476958 1.4224310
5    5 -0.4481892  0.13538726 0.2192032 0.59815656 0.3985513
6    6 -0.3594324 -0.43604390 0.3193260 0.06143111 0.5805927

Infos

This analysis has been performed using R software (ver. 3.1.2) and factoextra (ver. 1.0.2)

factoextra: Reduce overplotting of points and labels - R software and data mining

Wed, 08 Jul 2015 22:05:08 +0200

Install required packages
Load FactoMineR and factoextra
Multiple Correspondence Analysis (MCA)
Simple Correspondence Analysis (CA)
Principal Componet Analysis (PCA)
Infos

To reduce overplotting, the argument jitter is used in the functions fviz_pca_xx(), fviz_ca_xx() and fviz_mca_xx() available in the R package factoextra.

The argument jitter is a list containing the parameters what, width and height (i.e jitter = list(what, width, height)):

what: the element to be jittered. Possible values are “point” or “p”; “label” or “l”; “both” or “b”.
width: degree of jitter in x direction
height: degree of jitter in y direction

Some examples of usage are described in the next sections.

Install required packages

FactoMineR: for computing PCA (Principal Component Analysis), CA (Correspondence Analysis) and MCA (Multiple Correspondence Analysis)
factoextra: for the visualization of FactoMineR results

FactoMineR and factoextra R packages can be installed as follow :

install.packages("FactoMineR")

# install.packages("devtools")
devtools::install_github("kassambara/factoextra")

Note that, for factoextra a version >= 1.0.3 is required for using the argument jitter. If it’s already installed on your computer, you should re-install it to have the most updated version.

Load FactoMineR and factoextra

library("FactoMineR")
library("factoextra")

Multiple Correspondence Analysis (MCA)

# Load data
data(poison)
poison.active <- poison[1:55, 5:15]
# Compute MCA
res.mca <- MCA(poison.active, graph = FALSE)
# Default plot
fviz_mca_ind(res.mca)

# Use jitter to reduce overplotting.
# Only labels are jittered
fviz_mca_ind(res.mca, jitter = list(what = "label",
                                    width = 0.1, height = 0.15))

# Jitter both points and labels
fviz_mca_ind(res.mca, jitter = list(what = "both", 
                                    width = 0.1, height = 0.15))

Simple Correspondence Analysis (CA)

# Load data
data("housetasks")
# Compute CA
res.ca <- CA(housetasks, graph = FALSE)
# Default biplot
fviz_ca_biplot(res.ca)

# Jitter in y direction
fviz_ca_biplot(res.ca, jitter = list(what = "label", 
                                     width = 0.4, height = 0.3))

Principal Componet Analysis (PCA)

# Load data
data(decathlon2)
decathlon2.active <- decathlon2[1:23, 1:10]
# Compute PCA
res.pca <- PCA(decathlon2.active, graph = FALSE)
# Default biplot
fviz_pca_ind(res.pca)

# Use jitter in x and y direction
fviz_pca_ind(res.pca, jitter = list(what = "label", 
                                    width = 0.6, height = 0.6))

Infos

This analysis has been performed using R software (ver. 3.2.1), FactoMineR (ver. 1.30) and factoextra (ver. 1.0.2)

Explore the outputs of a principal component analysis - R software and data mining

Mon, 25 May 2015 08:42:28 +0200

Description
Install and load factoextra
Usage
Arguments
Examples
Infos

Description

The functions get_eig(), get_pca_ind() and get_pca_var() can be used to explore the outputs of several PCA functions : the function PCA() from FactoMineR package; prcomp() and princomp() from stats package; dudi.pca() from ade4 package.

These 3 functions are included in the R package factoextra.

Install and load factoextra

The package devtools is required for the installation as factoextra is hosted on github.

# install.packages("devtools")
library("devtools")
install_github("kassambara/factoextra")

Load factoextra :

library("factoextra")

Usage

get_eig(X)

get_pca_var(res.pca)

get_pca_ind(res.pca)

Arguments

X, res.pca : an object of class PCA (FactoMineR); prcomp and princomp (stats); dudi and pca (ade4).

Examples

Principal component analysis

A principal component analysis (PCA) is performed using the built-in R function prcomp() and iris data :

data(iris)
head(iris)

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

# The variable Species (index = 5) is removed
# before PCA analysis
res.pca <- prcomp(iris[, -5],  scale = TRUE)

Extract the eigenvalues/variances

eig <- get_eig(res.pca)
eig

      eigenvalue variance.percent cumulative.variance.percent
Dim.1 2.91849782       72.9624454                    72.96245
Dim.2 0.91403047       22.8507618                    95.81321
Dim.3 0.14675688        3.6689219                    99.48213
Dim.4 0.02071484        0.5178709                   100.00000

Extract the results for variables

The function get_pca_var() provides a list of matrices containing all the results for the active variables (coordinates, correlation between variables and axes, square cosine and contributions)

var <- get_pca_var(res.pca)
names(var)

[1] "coord"   "cor"     "cos2"    "contrib"

# Coordinates of variables
head(var$coord)

                  Dim.1       Dim.2       Dim.3       Dim.4
Sepal.Length  0.8901688 -0.36082989  0.27565767  0.03760602
Sepal.Width  -0.4601427 -0.88271627 -0.09361987 -0.01777631
Petal.Length  0.9915552 -0.02341519 -0.05444699 -0.11534978
Petal.Width   0.9649790 -0.06399985 -0.24298265  0.07535950

# Cos2 of variables
head(var$cos2)

                 Dim.1       Dim.2       Dim.3        Dim.4
Sepal.Length 0.7924004 0.130198208 0.075987149 0.0014142127
Sepal.Width  0.2117313 0.779188012 0.008764681 0.0003159971
Petal.Length 0.9831817 0.000548271 0.002964475 0.0133055723
Petal.Width  0.9311844 0.004095980 0.059040571 0.0056790544

# Contribution of variables
head(var$contrib)

                 Dim.1       Dim.2     Dim.3     Dim.4
Sepal.Length 27.150969 14.24440565 51.777574  6.827052
Sepal.Width   7.254804 85.24748749  5.972245  1.525463
Petal.Length 33.687936  0.05998389  2.019990 64.232089
Petal.Width  31.906291  0.44812296 40.230191 27.415396

Extract the results for individuals

The function get_pca_ind() provides a list of matrices containing all the results for the active individuals (coordinates, correlation between variables and axes, square cosine and contributions)

ind <- get_pca_ind(res.pca)
names(ind)

[1] "coord"   "cos2"    "contrib"

# Coordinates of individuals
head(ind$coord)

      Dim.1      Dim.2       Dim.3        Dim.4
1 -2.257141 -0.4784238  0.12727962  0.024087508
2 -2.074013  0.6718827  0.23382552  0.102662845
3 -2.356335  0.3407664 -0.04405390  0.028282305
4 -2.291707  0.5953999 -0.09098530 -0.065735340
5 -2.381863 -0.6446757 -0.01568565 -0.035802870
6 -2.068701 -1.4842053 -0.02687825  0.006586116

# Cos2 of individuals
head(ind$cos2)

      Dim.1      Dim.2        Dim.3        Dim.4
1 0.9539975 0.04286032 0.0030335249 1.086460e-04
2 0.8927725 0.09369248 0.0113475382 2.187482e-03
3 0.9790410 0.02047578 0.0003422122 1.410446e-04
4 0.9346682 0.06308947 0.0014732682 7.690193e-04
5 0.9315095 0.06823959 0.0000403979 2.104697e-04
6 0.6600989 0.33978301 0.0001114335 6.690714e-06

# Contribution of individuals
head(ind$contrib)

      Dim.1      Dim.2       Dim.3       Dim.4
1 1.1637691 0.16694510 0.073591567 0.018672867
2 0.9825900 0.32925696 0.248367113 0.339198420
3 1.2683043 0.08469576 0.008816151 0.025742863
4 1.1996857 0.25856249 0.037605617 0.139067312
5 1.2959338 0.30313118 0.001117674 0.041253702
6 0.9775628 1.60670454 0.003281801 0.001396002

Infos

This analysis has been performed using R software (ver. 3.1.2) and factoextra (ver. 1.0.2)

get_pca: Extract the results for individuals/variables in Principal Component Analysis - R software and data mining

Sat, 23 May 2015 10:08:22 +0200

Description
Install and load factoextra
Usage
Arguments
Value
Examples
Infos

Description

Extract all the results (coordinates, squared cosine, contributions) for the active individuals/variables from Principal Component Analysis (PCA) outputs.

get_pca(): Extract the results for variables and individuals
get_pca_ind(): Extract the results for individuals only
get_pca_var(): Extract the results for variables only

These functions are included in factoextra package.

Install and load factoextra

The package devtools is required for the installation as factoextra is hosted on github.

# install.packages("devtools")
library("devtools")
install_github("kassambara/factoextra")

Load factoextra :

library("factoextra")

Usage

# Extract the results for variables and individuals
get_pca(res.pca, element = c("var", "ind"))

# Extract the results for individuals only
get_pca_ind(res.pca, ...)

# Extract the results for variables only
get_pca_var(res.pca)

Arguments

Argument	Description
res.pca	an object of class PCA [FactoMineR]; prcomp and princomp [stats]; pca, dudi [adea4].
element	the element to subset from the output. Allowed values are “var” (for active variables) or “ind” (for active individuals).
…	not used

Value

A list of matrices containing all the results for the active individuals/variables including:

coord: coordinates for the individuals/variables
cos2: cos2 for the individuals/variables
contrib: contributions of the individuals/variables

Examples

Principal component analysis

A principal component analysis (PCA) is performed using the built-in R function prcomp() and iris data:

data(iris)
head(iris)

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

# The variable Species (index = 5) is removed
# before PCA analysis
res.pca <- prcomp(iris[, -5],  scale = TRUE)

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
Sepal.Length  0.8901688 -0.36082989  0.27565767  0.03760602
Sepal.Width  -0.4601427 -0.88271627 -0.09361987 -0.01777631
Petal.Length  0.9915552 -0.02341519 -0.05444699 -0.11534978
Petal.Width   0.9649790 -0.06399985 -0.24298265  0.07535950

# Cos2 of variables
head(var$cos2)

                 Dim.1       Dim.2       Dim.3        Dim.4
Sepal.Length 0.7924004 0.130198208 0.075987149 0.0014142127
Sepal.Width  0.2117313 0.779188012 0.008764681 0.0003159971
Petal.Length 0.9831817 0.000548271 0.002964475 0.0133055723
Petal.Width  0.9311844 0.004095980 0.059040571 0.0056790544

# Contribution of variables
head(var$contrib)

                 Dim.1       Dim.2     Dim.3     Dim.4
Sepal.Length 27.150969 14.24440565 51.777574  6.827052
Sepal.Width   7.254804 85.24748749  5.972245  1.525463
Petal.Length 33.687936  0.05998389  2.019990 64.232089
Petal.Width  31.906291  0.44812296 40.230191 27.415396

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
1 -2.257141 -0.4784238  0.12727962  0.024087508
2 -2.074013  0.6718827  0.23382552  0.102662845
3 -2.356335  0.3407664 -0.04405390  0.028282305
4 -2.291707  0.5953999 -0.09098530 -0.065735340
5 -2.381863 -0.6446757 -0.01568565 -0.035802870
6 -2.068701 -1.4842053 -0.02687825  0.006586116

# Cos2 of individuals
head(ind$cos2)

      Dim.1      Dim.2        Dim.3        Dim.4
1 0.9539975 0.04286032 0.0030335249 1.086460e-04
2 0.8927725 0.09369248 0.0113475382 2.187482e-03
3 0.9790410 0.02047578 0.0003422122 1.410446e-04
4 0.9346682 0.06308947 0.0014732682 7.690193e-04
5 0.9315095 0.06823959 0.0000403979 2.104697e-04
6 0.6600989 0.33978301 0.0001114335 6.690714e-06

# Contribution of individuals
head(ind$contrib)

      Dim.1      Dim.2       Dim.3       Dim.4
1 1.1637691 0.16694510 0.073591567 0.018672867
2 0.9825900 0.32925696 0.248367113 0.339198420
3 1.2683043 0.08469576 0.008816151 0.025742863
4 1.1996857 0.25856249 0.037605617 0.139067312
5 1.2959338 0.30313118 0.001117674 0.041253702
6 0.9775628 1.60670454 0.003281801 0.001396002

get_pca

# You can also use the function get_pca()
get_pca(res.pca, "ind") # Results for individuals

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"

get_pca(res.pca, "var") # Results for variable categories

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"

Infos

This analysis has been performed using R software (ver. 3.1.2) and factoextra (ver. 1.0.2)

get_mca: Extract the results for individuals/variables in Multiple Correspondence Analysis

Sat, 23 May 2015 10:03:52 +0200

Description
Install and load factoextra
Usage
Arguments
Value
Examples
Infos

Description

Extract all the results (coordinates, squared cosine and contributions) for the active individuals/variable categories from Multiple Correspondence Analysis (MCA) outputs.

get_mca(): Extract the results for variables and individuals
get_mca_ind(): Extract the results for individuals only
get_mca_var(): Extract the results for variables only

These functions are included in factoextra package.

Install and load factoextra

The package devtools is required for the installation as factoextra is hosted on github.

# install.packages("devtools")
library("devtools")
install_github("kassambara/factoextra")

Load factoextra :

library("factoextra")

Usage

# Extract the results for variables and individuals
get_mca(res.mca, element = c("var", "ind"))

# Extract the results for individuals only
get_mca_var(res.mca)

# Extract the results for variables only
get_mca_ind(res.mca)

Arguments

Argument	Description
res.mca	an object of class MCA [FactoMineR], acm [ade4].
element	the element to subset from the output. Allowed values are “var” (for active variables) or “ind” (for active individuals).

Value

A list of matrices containing all the results for the active individuals/variables including:

coord: coordinates for the individuals/variables
cos2: cos2 for the individuals/variables
contrib: contributions of the individuals/variables

Examples

Multiple Correspondence Analysis

A Multiple Correspondence Analysis (MCA) is performed using the function MCA() [in FactoMineR] and poison data [in FactoMineR]:

# Multiple Correspondence Analysis
# ++++++++++++++++++++++++++++++
# Install and load FactoMineR to compute MCA
# install.packages("FactoMineR")
library("FactoMineR")
data(poison)
poison.active <- poison[1:55, 5:15]
head(poison.active[, 1:6])

    Nausea Vomiting Abdominals   Fever   Diarrhae   Potato
1 Nausea_y  Vomit_n     Abdo_y Fever_y Diarrhea_y Potato_y
2 Nausea_n  Vomit_n     Abdo_n Fever_n Diarrhea_n Potato_y
3 Nausea_n  Vomit_y     Abdo_y Fever_y Diarrhea_y Potato_y
4 Nausea_n  Vomit_n     Abdo_n Fever_n Diarrhea_n Potato_y
5 Nausea_n  Vomit_y     Abdo_y Fever_y Diarrhea_y Potato_y
6 Nausea_n  Vomit_n     Abdo_y Fever_y Diarrhea_y Potato_y

res.mca <- MCA(poison.active, graph=FALSE)

Extract the results for variables

# Extract the results for variable categories
var <- get_mca_var(res.mca)
print(var)

Multiple Correspondence Analysis Results for variables
 ===================================================
  Name       Description                  
1 "$coord"   "Coordinates for categories" 
2 "$cos2"    "Cos2 for categories"        
3 "$contrib" "contributions of categories"

head(var$coord) # coordinates of variables

              Dim 1       Dim 2        Dim 3       Dim 4       Dim 5
Nausea_n  0.2673909  0.12139029 -0.265583253  0.03376130  0.07370500
Nausea_y -0.9581506 -0.43498187  0.951673323 -0.12097801 -0.26410958
Vomit_n   0.4790279 -0.40919465  0.084492799  0.27361142  0.05245250
Vomit_y  -0.7185419  0.61379197 -0.126739198 -0.41041713 -0.07867876
Abdo_n    1.3180221 -0.03574501 -0.005094243 -0.15360951 -0.06986987
Abdo_y   -0.6411999  0.01738946  0.002478280  0.07472895  0.03399075

head(var$cos2) # cos2 of variables

             Dim 1        Dim 2        Dim 3       Dim 4       Dim 5
Nausea_n 0.2562007 0.0528025759 2.527485e-01 0.004084375 0.019466197
Nausea_y 0.2562007 0.0528025759 2.527485e-01 0.004084375 0.019466197
Vomit_n  0.3442016 0.2511603912 1.070855e-02 0.112294813 0.004126898
Vomit_y  0.3442016 0.2511603912 1.070855e-02 0.112294813 0.004126898
Abdo_n   0.8451157 0.0006215864 1.262496e-05 0.011479077 0.002374929
Abdo_y   0.8451157 0.0006215864 1.262496e-05 0.011479077 0.002374929

head(var$contrib) # contributions of variables

             Dim 1       Dim 2        Dim 3      Dim 4      Dim 5
Nausea_n  1.515869  0.81100008 4.670018e+00 0.08449397 0.48977906
Nausea_y  5.431862  2.90608363 1.673423e+01 0.30277007 1.75504164
Vomit_n   3.733667  7.07226253 3.627455e-01 4.25893721 0.19036376
Vomit_y   5.600500 10.60839380 5.441183e-01 6.38840581 0.28554563
Abdo_n   15.417637  0.02943661 7.192511e-04 0.73219636 0.18424268
Abdo_y    7.500472  0.01432051 3.499060e-04 0.35620363 0.08963157

Extract the results for individuals

# Extract the results for individuals
ind <- get_mca_ind(res.mca)
print(ind)

Multiple Correspondence Analysis Results for individuals
 ===================================================
  Name       Description                       
1 "$coord"   "Coordinates for the individuals" 
2 "$cos2"    "Cos2 for the individuals"        
3 "$contrib" "contributions of the individuals"

head(ind$coord) # coordinates of individuals

       Dim 1       Dim 2       Dim 3       Dim 4       Dim 5
1 -0.4525811 -0.26415072  0.17151614  0.01369348 -0.11696806
2  0.8361700 -0.03193457 -0.07208249 -0.08550351  0.51978710
3 -0.4481892  0.13538726 -0.22484048 -0.14170168 -0.05004753
4  0.8803694 -0.08536230 -0.02052044 -0.07275873 -0.22935022
5 -0.4481892  0.13538726 -0.22484048 -0.14170168 -0.05004753
6 -0.3594324 -0.43604390 -1.20932223  1.72464616  0.04348157

head(ind$cos2) # cos2 of individuals

       Dim 1        Dim 2        Dim 3        Dim 4        Dim 5
1 0.34652591 0.1180447167 0.0497683175 0.0003172275 0.0231460846
2 0.55589562 0.0008108236 0.0041310808 0.0058126211 0.2148103098
3 0.54813888 0.0500176790 0.1379484860 0.0547920948 0.0068349171
4 0.74773962 0.0070299584 0.0004062504 0.0051072923 0.0507479873
5 0.54813888 0.0500176790 0.1379484860 0.0547920948 0.0068349171
6 0.02485357 0.0365775483 0.2813443706 0.5722083217 0.0003637178

head(ind$contrib) # contributions of individuals

     Dim 1      Dim 2        Dim 3        Dim 4      Dim 5
1 1.110927 0.98238297  0.498254685  0.003555817 0.31554778
2 3.792117 0.01435818  0.088003703  0.138637089 6.23134138
3 1.089470 0.25806722  0.856229950  0.380768961 0.05776914
4 4.203611 0.10259105  0.007132055  0.100387990 1.21319013
5 1.089470 0.25806722  0.856229950  0.380768961 0.05776914
6 0.700692 2.67693398 24.769968729 56.404214518 0.04360547

get_mca: Extract the results for both individuals and variables

# You can also use the function get_mca()
get_mca(res.mca, "ind") # Results for individuals

Multiple Correspondence Analysis Results for individuals
 ===================================================
  Name       Description                       
1 "$coord"   "Coordinates for the individuals" 
2 "$cos2"    "Cos2 for the individuals"        
3 "$contrib" "contributions of the individuals"

get_mca(res.mca, "var") # Results for variable categories

Multiple Correspondence Analysis Results for variables
 ===================================================
  Name       Description                  
1 "$coord"   "Coordinates for categories" 
2 "$cos2"    "Cos2 for categories"        
3 "$contrib" "contributions of categories"

Infos

This analysis has been performed using R software (ver. 3.1.2) and factoextra (ver. 1.0.2)

get_ca: Extract the results for rows/columns in Correspondence Analysis - R software and data mining

Sat, 23 May 2015 09:56:46 +0200

Description
Install and load factoextra
Usage
Arguments
Value
Examples
Infos

Description

Extract all the results (coordinates, squared cosine, contributions and inertia) for the active row/column variables from Correspondence Analysis (CA) outputs.

get_ca(): Extract the results for rows and columns
get_ca_row(): Extract the results for rows only
get_ca_col(): Extract the results for columns only

These functions are included in factoextra package.

Install and load factoextra

The package devtools is required for the installation as factoextra is hosted on github.

# install.packages("devtools")
library("devtools")
install_github("kassambara/factoextra")

Load factoextra :

library("factoextra")

Usage

# Extract the results for rows and columns
get_ca(res.ca, element = c("row", "col"))

# Extract the results for rows only
get_ca_col(res.ca)

# Extract the results for columns only
get_ca_row(res.ca)

Arguments

Argument	Description
res.ca	an object of class CA [FactoMineR], ca [ca], coa [ade4]; correspondence [MASS].
element	the element to subset from the output. Possible values are “row” or “col”.

Value

A list of matrices containing all the results for the active rows/columns including:

coord: coordinates for the rows/columns
cos2: cos2 for the rows/columns
contrib: contributions of the rows/columns

Examples

Correspondence Analysis

A Correspondence Analysis (CA) is performed using the function CA() [in FactoMineR] and housetasks data [in factoextra]:

# Install and load FactoMineR to compute CA
# install.packages("FactoMineR")
 library("FactoMineR")
 data("housetasks")
 res.ca <- CA(housetasks, graph = FALSE)

Extract the results for column variables

# Result for column variables
col <- get_ca_col(res.ca)
col # print

Correspondence Analysis - Results for columns
 ===================================================
  Name       Description                   
1 "$coord"   "Coordinates for the columns" 
2 "$cos2"    "Cos2 for the columns"        
3 "$contrib" "contributions of the columns"
4 "$inertia" "Inertia of the columns"

head(col$coord) # column coordinates

                  Dim 1      Dim 2       Dim 3
Wife        -0.83762154  0.3652207 -0.19991139
Alternating -0.06218462  0.2915938  0.84858939
Husband      1.16091847  0.6019199 -0.18885924
Jointly      0.14942609 -1.0265791 -0.04644302

head(col$cos2) # column cos2

                  Dim 1     Dim 2       Dim 3
Wife        0.801875947 0.1524482 0.045675847
Alternating 0.004779897 0.1051016 0.890118521
Husband     0.772026244 0.2075420 0.020431728
Jointly     0.020705858 0.9772939 0.002000236

head(col$contrib) # column contributions

                Dim 1     Dim 2      Dim 3
Wife        44.462018 10.312237 10.8220753
Alternating  0.103739  2.782794 82.5492464
Husband     54.233879 17.786612  6.1331792
Jointly      1.200364 69.118357  0.4954991

Extract the results for row variables

# Result for row variables
row <- get_ca_row(res.ca)
row # print

Correspondence Analysis - Results for rows
 ===================================================
  Name       Description                
1 "$coord"   "Coordinates for the rows" 
2 "$cos2"    "Cos2 for the rows"        
3 "$contrib" "contributions of the rows"
4 "$inertia" "Inertia of the rows"

head(row$coord) # row coordinates

                Dim 1      Dim 2       Dim 3
Laundry    -0.9918368  0.4953220 -0.31672897
Main_meal  -0.8755855  0.4901092 -0.16406487
Dinner     -0.6925740  0.3081043 -0.20741377
Breakfeast -0.5086002  0.4528038  0.22040453
Tidying    -0.3938084 -0.4343444 -0.09421375
Dishes     -0.1889641 -0.4419662  0.26694926

head(row$cos2) # row cos2

               Dim 1     Dim 2      Dim 3
Laundry    0.7399874 0.1845521 0.07546047
Main_meal  0.7416028 0.2323593 0.02603787
Dinner     0.7766401 0.1537032 0.06965666
Breakfeast 0.5049433 0.4002300 0.09482670
Tidying    0.4398124 0.5350151 0.02517249
Dishes     0.1181178 0.6461525 0.23572969

head(row$contrib) # row contributions

                Dim 1    Dim 2    Dim 3
Laundry    18.2867003 5.563891 7.968424
Main_meal  12.3888433 4.735523 1.858689
Dinner      5.4713982 1.321022 2.096926
Breakfeast  3.8249284 3.698613 3.069399
Tidying     1.9983518 2.965644 0.488734
Dishes      0.4261663 2.844117 3.634294

get_ca: extract the results for both rows and columns

 # You can also use the function get_ca()
 get_ca(res.ca, "row") # Results for rows

Correspondence Analysis - Results for rows
 ===================================================
  Name       Description                
1 "$coord"   "Coordinates for the rows" 
2 "$cos2"    "Cos2 for the rows"        
3 "$contrib" "contributions of the rows"
4 "$inertia" "Inertia of the rows"

 get_ca(res.ca, "col") # Results for columns

Correspondence Analysis - Results for columns
 ===================================================
  Name       Description                   
1 "$coord"   "Coordinates for the columns" 
2 "$cos2"    "Cos2 for the columns"        
3 "$contrib" "contributions of the columns"
4 "$inertia" "Inertia of the columns"

Infos

This analysis has been performed using R software (ver. 3.1.2) and factoextra (ver. 1.0.2)

Easy Guides

Factoextra R Package: Easy Multivariate Data Analyses and Elegant Visualization

Why using factoextra?

Installing FactoMineR

Installing and loading factoextra

Main functions in the factoextra package

Visualizing dimension reduction analysis outputs

Extracting data from dimension reduction analysis outputs

Clustering analysis and visualization

Dimension reduction and factoextra

Principal component analysis

Correspondence analysis

Multiple correspondence analysis

Advanced methods

Cluster analysis and factoextra

Partitioning clustering

Hierarchical clustering

Determine the optimal number of clusters

Acknoweledgment

References

Infos

fviz_pca: Quick Principal Component Analysis data visualization - R software and data mining

Description

Install and load factoextra

Usage

Arguments

Value

Examples

Principal component analysis

fviz_pca_ind(): Graph of individuals

fviz_pca_var(): Graph of variables

fviz_pca_biplot(): Biplot of individuals of variables

Infos

fviz_mca: Quick Multiple Correspondence Analysis data visualization - R software and data mining

Description

Install and load factoextra

Usage

Arguments

Details

Value

Examples

Multiple Correspondence Analysis

fviz_mca_ind(): Graph of individuals

fviz_mca_var(): Graph of variable categories

fviz_mca_biplot(): Biplot of individuals of variable categories

Infos

fviz_ca: Quick Correspondence Analysis data visualization using factoextra - R software and data mining

Description

Install and load factoextra

Usage

Arguments

Details

Value

Examples

Correspondence Analysis

fviz_ca_row(): Graph of row variables

fviz_ca_col(): Graph of column categories

fviz_ca_biplot(): Biplot of rows and columns

Infos

facto_summarize - Subset and summarize the output of factor analyses - R software and data mining

Description

Install and load factoextra

Usage

Arguments

Details

Value

Examples

Principal component analysis

Correspondence Analysis

Multiple Correspondence Analysis

Infos

factoextra: Reduce overplotting of points and labels - R software and data mining

Install required packages

Load FactoMineR and factoextra

Multiple Correspondence Analysis (MCA)

Simple Correspondence Analysis (CA)

Principal Componet Analysis (PCA)

Infos

Explore the outputs of a principal component analysis - R software and data mining

Description