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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: 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. The figure below shows methods, which outputs can be visualized using the factoextra package. The official online documentation is available at: http://www.sthda.com/english/rpkgs/factoextra. Why using factoextra?The factoextra R package can handle the results of PCA, CA, MCA, MFA, FAMD and HMFA from several packages, for extracting and visualizing the most important information contained in your data. After PCA, CA, MCA, MFA, FAMD and HMFA, the most important row/column elements can be highlighted using : their cos2 values corresponding to their quality of representation on the factor maptheir 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 FactoMineRThe FactoMineR package can be installed and loaded as follow: # Install install.packages("FactoMineR") # Load library("FactoMineR")Installing and loading factoextrafactoextra can be installed from CRAN as follow:install.packages("factoextra")Or, install the latest version from Githubif(!require(devtools)) install.packages("devtools") devtools::install_github("kassambara/factoextra")Load factoextra as follow :library("factoextra") #> Loading required package: ggplot2 #> Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBaMain functions in the factoextra packageSee the online documentation (http://www.sthda.com/english/rpkgs/factoextra) for a complete list. Visualizing dimension reduction analysis outputsExtracting data from dimension reduction analysis outputsClustering analysis and visualizationDimension reduction and factoextraAs 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 analysisData: 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 datalibrary("factoextra") data("decathlon2") df Dim.1 4.1242133 41.242133 41.24213 #> Dim.2 1.8385309 18.385309 59.62744 #> Dim.3 1.2391403 12.391403 72.01885 #> Dim.4 0.8194402 8.194402 80.21325 #> Dim.5 0.7015528 7.015528 87.22878 #> Dim.6 0.4228828 4.228828 91.45760 #> Dim.7 0.3025817 3.025817 94.48342 #> Dim.8 0.2744700 2.744700 97.22812 #> Dim.9 0.1552169 1.552169 98.78029 #> Dim.10 0.1219710 1.219710 100.00000 # Visualize eigenvalues/variances fviz_screeplot(res.pca, addlabels = TRUE, ylim = c(0, 50))4.Extract and visualize results for variables: # Extract the results for variables var Principal Component Analysis Results for variables #> =================================================== #> Name Description #> 1 "$coord" "Coordinates for the variables" #> 2 "$cor" "Correlations between variables and dimensions" #> 3 "$cos2" "Cos2 for the variables" #> 4 "$contrib" "contributions of the variables" # Coordinates of variables head(var$coord) #> Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 #> X100m -0.8506257 -0.17939806 0.3015564 0.03357320 -0.1944440 #> Long.jump 0.7941806 0.28085695 -0.1905465 -0.11538956 0.2331567 #> Shot.put 0.7339127 0.08540412 0.5175978 0.12846837 -0.2488129 #> High.jump 0.6100840 -0.46521415 0.3300852 0.14455012 0.4027002 #> X400m -0.7016034 0.29017826 0.2835329 0.43082552 0.1039085 #> X110m.hurdle -0.7641252 -0.02474081 0.4488873 -0.01689589 0.2242200 # Contribution of variables head(var$contrib) #> Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 #> X100m 17.544293 1.7505098 7.338659 0.13755240 5.389252 #> Long.jump 15.293168 4.2904162 2.930094 1.62485936 7.748815 #> Shot.put 13.060137 0.3967224 21.620432 2.01407269 8.824401 #> High.jump 9.024811 11.7715838 8.792888 2.54987951 23.115504 #> X400m 11.935544 4.5799296 6.487636 22.65090599 1.539012 #> X110m.hurdle 14.157544 0.0332933 16.261261 0.03483735 7.166193 # Graph of variables: default plot fviz_pca_var(res.pca, col.var = "black")It's possible to control variable colors using their contributions ("contrib") to the principal axes: # Control variable colors using their contributions fviz_pca_var(res.pca, col.var="contrib", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), repel = TRUE # Avoid text overlapping )Variable contributions to the principal axes:# Contributions of variables to PC1 fviz_contrib(res.pca, choice = "var", axes = 1, top = 10) # Contributions of variables to PC2 fviz_contrib(res.pca, choice = "var", axes = 2, top = 10)Extract and visualize results for individuals:# Extract the results for individuals ind Principal Component Analysis Results for individuals #> =================================================== #> Name Description #> 1 "$coord" "Coordinates for the individuals" #> 2 "$cos2" "Cos2 for the individuals" #> 3 "$contrib" "contributions of the individuals" # Coordinates of individuals head(ind$coord) #> Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 #> SEBRLE 0.1955047 1.5890567 0.6424912 0.08389652 1.16829387 #> CLAY 0.8078795 2.4748137 -1.3873827 1.29838232 -0.82498206 #> BERNARD -1.3591340 1.6480950 0.2005584 -1.96409420 0.08419345 #> YURKOV -0.8889532 -0.4426067 2.5295843 0.71290837 0.40782264 #> ZSIVOCZKY -0.1081216 -2.0688377 -1.3342591 -0.10152796 -0.20145217 #> McMULLEN 0.1212195 -1.0139102 -0.8625170 1.34164291 1.62151286 # Graph of individuals # 1. Use repel = TRUE to avoid overplotting # 2. Control automatically the color of individuals using the cos2 # cos2 = the quality of the individuals on the factor map # Use points only # 3. Use gradient color fviz_pca_ind(res.pca, col.ind = "cos2", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), repel = TRUE # Avoid text overlapping (slow if many points) )# Biplot of individuals and variables fviz_pca_biplot(res.pca, repel = TRUE)Color individuals by groups:# Compute PCA on the iris data set # The variable Species (index = 5) is removed # before PCA analysis iris.pca |
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