Package {factoextra}

Type:	Package
Title:	Extract and Visualize the Results of Multivariate Data Analyses
Version:	2.2.0
Date:	2026-07-24
Description:	Provides easy-to-use functions to extract and visualize the output of multivariate data analyses, including 'PCA' (Principal Component Analysis), 'CA' (Correspondence Analysis), 'MCA' (Multiple Correspondence Analysis), 'FAMD' (Factor Analysis of Mixed Data), 'MFA' (Multiple Factor Analysis), and 'HMFA' (Hierarchical Multiple Factor Analysis) from different R packages. It standardizes coordinates, squared cosines, contributions, and eigenvalues from several analysis backends and produces 'ggplot2'-based factor maps, scree plots, contribution plots, clustering diagnostics, dendrograms, and silhouette plots. It also visualizes two-dimensional 'UMAP' and t-SNE embeddings and adapts precomputed or 'tidymodels' principal-component results for the same plotting interface.
License:	GPL-2
LazyData:	true
LazyDataCompression:	xz
Encoding:	UTF-8
Depends:	R (≥ 4.1.0), ggplot2 (≥ 3.5.2)
Imports:	cluster (≥ 2.1.8.2), dendextend (≥ 1.19.1), FactoMineR (≥ 2.13), ggpubr (≥ 0.6.3), grid, rlang (≥ 1.1.7), stats, ggrepel (≥ 0.9.5)
Suggests:	ade4, ca, hardhat, igraph, MASS, knitr, mclust, parsnip, recipes, rmarkdown, Rtsne, testthat (≥ 3.0.0), umap, uwot, workflows
VignetteBuilder:	knitr
URL:	https://github.com/kassambara/factoextra, https://rpkgs.datanovia.com/factoextra/
BugReports:	https://github.com/kassambara/factoextra/issues
Collate:	'fviz_add.R' 'eigenvalue.R' 'utilities.R' 'as_factoextra.R' 'cluster_utilities.R' 'decathlon2.R' 'print.factoextra.R' 'get_hmfa.R' 'fviz_hmfa.R' 'get_mfa.R' 'fviz_mfa.R' 'deprecated.R' 'dist.R' 'fviz_dend.R' 'hcut.R' 'get_pca.R' 'fviz_cluster.R' 'eclust.R' 'facto_summarize.R' 'fviz.R' 'fviz_ca.R' 'fviz_contrib.R' 'fviz_cos2.R' 'fviz_ellipses.R' 'fviz_famd.R' 'get_mca.R' 'fviz_mca.R' 'fviz_mclust.R' 'fviz_nbclust.R' 'fviz_pca.R' 'fviz_silhouette.R' 'fviz_umap.R' 'get_ca.R' 'get_clust_tendency.R' 'get_famd.R' 'hkmeans.R' 'housetasks.R' 'multishapes.R' 'poison.R' 'theme_palette.R' 'zzz.R'
RoxygenNote:	7.3.3
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-07-23 23:22:53 UTC; kassambara
Author:	Alboukadel Kassambara [aut, cre], Fabian Mundt [aut], Laszlo Erdey [ctb] (affiliation: Faculty of Economics and Business, University of Debrecen, Hungary, contribution: Modern compatibility fixes, tests, and maintenance updates)
Maintainer:	Alboukadel Kassambara <alboukadel.kassambara@gmail.com>
Repository:	CRAN
Date/Publication:	2026-07-24 09:00:02 UTC

Build a factoextra-ready object from pre-computed coordinates

Description

as_factoextra_pca() wraps pre-computed individual (and, optionally, variable) coordinates into an object that the fviz_pca family (fviz_pca_ind(), fviz_pca_var(), fviz_pca_biplot()), fviz_eig, fviz_contrib and fviz_cos2 can plot directly. Read more: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

It lets you apply factoextra's visualizations to the output of an eigenvalue-based dimension reduction - for example stats::cmdscale(), ape::pcoa(), vegan::rda()/cca(), a tidymodels recipe/workflow with step_pca() (see the methods below), or a custom analysis - without having to write a dedicated backend. You bring the coordinates; factoextra draws the biplot, scree plot, contributions and cos2.

The scree plot, contributions and cos2 assume real eigenvalues, so this constructor is for PCA-family results. Non-linear embeddings (UMAP, t-SNE) have no eigenvalues; plot their coordinates directly (a scree/loadings display would be meaningless for them).

Usage

as_factoextra_pca(ind.coord, ...)

## Default S3 method:
as_factoextra_pca(
  ind.coord,
  var.coord = NULL,
  eig = NULL,
  ind.cos2 = NULL,
  ind.contrib = NULL,
  var.cos2 = NULL,
  var.contrib = NULL,
  var.cor = NULL,
  scale.unit = FALSE,
  ...
)

## S3 method for class 'recipe'
as_factoextra_pca(ind.coord, ...)

## S3 method for class 'workflow'
as_factoextra_pca(ind.coord, ...)

Arguments

Details

When cos2/contrib are not supplied they are computed from the coordinates:

• contrib = 100 * coord^2 / colSums(coord^2) - the exact contribution of each element to each dimension.

• cos2 = coord^2 / rowSums(coord^2) - the quality of representation within the supplied dimensions. This equals the true cos2 only when all components are provided; with a truncated set of dimensions it is the quality restricted to that sub-space. Pass ind.cos2/var.cos2 explicitly if you have the exact values.

tidymodels (recipe / workflow). The recipe and workflow methods extract a PCA fitted with recipes::step_pca() through the public recipes/workflows API: the scores from the baked training data (or, for a fitted workflow, workflows::extract_mold()), the loadings from tidy(step, type = "coef"), and the full set of eigenvalues from tidy(step, type = "variance") (so the scree plot and axis percentages are honest even when num_comp keeps only a few components). Variable coordinates are loading times the square root of the eigenvalue. Exact variable-component correlations and cos2 are recovered from the full PCA inertia when every PCA input is provably centered. When those metrics cannot be recovered (for example, for a bare step_pca() with no centering or a zero-inertia variable), their entries in get_pca_var() are NULL. Scores, eigenvalues, variable coordinates and contributions are still returned, so the individual, scree, variable-arrow and biplot displays remain available; correlation/cos2-dependent displays fail with an explicit unavailable-metric error. The correlation circle is omitted and a warning explains how to recover the metrics. scale.unit is set to TRUE only when every PCA input is both centered and unit-scaled at the PCA boundary; partial scaling therefore does not draw a correlation circle. For fully normalized data, variable coordinates, correlations, cos2 and contributions, and the eigenvalue percentages match a full FactoMineR::PCA() regardless of how many components step_pca() keeps; the individual cos2 is computed over the retained components (it equals the full-space cos2 only when all components are kept). The two-dimensional plots (fviz_pca_ind(), fviz_pca_var(), fviz_pca_biplot()) need num_comp >= 2. The recipe must be prepped, and its single PCA step must be an unweighted step_pca() and must be the final recipe step. Case-weighted PCA is rejected because the adapter cannot yet propagate those weights into individual contributions. Later steps could transform the baked/mold PCA scores without updating the fitted PCA loadings or eigenvalues, so such recipes fail explicitly instead of returning internally inconsistent geometry. Non-linear embedding steps such as step_umap() have no eigenvalues and are rejected with a message. For the loadings display of a recipe PCA see also learntidymodels::plot_top_loadings().

Value

An object of class c("factoextra_pca", "list") holding the standardized ind (and var) results and eigenvalues, ready for the fviz_pca_*() functions.

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

See Also

For UMAP / t-SNE embeddings, which have no eigenvalues, use fviz_umap / fviz_tsne instead. Online tutorial: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

Examples

# 1. Bring your own coordinates: classical MDS (cmdscale) -> factoextra
d <- dist(scale(mtcars))
mds <- cmdscale(d, k = 3)
obj <- as_factoextra_pca(ind.coord = mds)
fviz_pca_ind(obj, repel = TRUE)
fviz_eig(obj)

# 2. Round-trip a prcomp result through the constructor (biplot)
pca <- prcomp(iris[, -5], scale. = TRUE)
obj2 <- as_factoextra_pca(
  ind.coord = pca$x,
  var.coord = sweep(pca$rotation, 2, pca$sdev, "*"),
  eig       = pca$sdev^2,
  scale.unit = TRUE
)
fviz_pca_biplot(obj2, label = "var", col.ind = "steelblue")

# 3. A tidymodels recipe PCA (step_pca) -> factoextra biplot + honest scree
if (requireNamespace("recipes", quietly = TRUE)) {
  library(recipes)
  rec <- recipe(~ ., data = iris[, 1:4]) |>
    step_normalize(all_numeric_predictors()) |>
    step_pca(all_numeric_predictors(), num_comp = 4)
  obj3 <- as_factoextra_pca(prep(rec))
  fviz_pca_biplot(obj3, label = "var")
  fviz_eig(obj3, addlabels = TRUE)
}

Clean up stale package lock files

Description

Removes stale lock directories that can prevent package installation.

Lock files are created during package installation and should be automatically removed when installation completes. If installation is interrupted (e.g., by closing R or a crash), these lock files may remain and block future installations.

Usage

clean_lock_files(package = "factoextra", lib = .libPaths()[1], ask = TRUE)

Arguments

Value

Invisibly returns TRUE only when every discovered lock directory is removed. Returns FALSE when no lock directories are found, removal is declined, or any removal fails.

Examples

# Use a temporary library so the example cannot affect installed packages.
example_lib <- tempfile("factoextra-lock-example-")
example_lock <- file.path(example_lib, "00LOCK-factoextra")
dir.create(example_lock, recursive = TRUE)
clean_locks <- getFromNamespace("clean_lock_files", "factoextra")
clean_locks(lib = example_lib, ask = FALSE)
stopifnot(!dir.exists(example_lock))
unlink(example_lib, recursive = TRUE)

Athletes' performance in decathlon

Description

Athletes' performance during two sporting meetings

Usage

data("decathlon2")

Format

A data frame with 27 observations on the following 13 variables.

X100m

a numeric vector

Long.jump

a numeric vector

Shot.put

a numeric vector

High.jump

a numeric vector

X400m

a numeric vector

X110m.hurdle

a numeric vector

Discus

a numeric vector

Pole.vault

a numeric vector

Javeline

a numeric vector

X1500m

a numeric vector

Rank

a numeric vector corresponding to the rank

Points

a numeric vector specifying the point obtained

Competition

a factor with levels Decastar OlympicG

Source

This data is a subset of decathlon data in FactoMineR package.

Examples

data(decathlon2)
decathlon.active <- decathlon2[1:23, 1:10]
res.pca <- prcomp(decathlon.active, scale = TRUE)
fviz_pca_biplot(res.pca)

Deprecated Functions

Description

Deprecated functions. Will be removed in a future version.

• get_mfa_quanti_var(). Deprecated. Use get_mfa_var(res.mfa, "quanti.var") instead.

• get_mfa_quali_var(). Deprecated. Use get_mfa_var(res.mfa, "quali.var") instead.

• get_mfa_group(). Deprecated. Use get_mfa_var(res.mfa, "group") instead.

• fviz_mfa_ind_starplot(): Star graph of individuals (draws partial points). Deprecated. Use fviz_mfa_ind(res.mfa, partial = "all") instead.

• fviz_mfa_quanti_var(): Graph of quantitative variables. Deprecated. Use fviz_mfa(X, "quanti.var") instead.

• fviz_mfa_quali_var(): Graph of qualitative variables. Deprecated. Use fviz_mfa(X, "quali.var") instead.

• get_hmfa_quanti_var(). Deprecated. Use get_hmfa_var(res.hmfa, "quanti.var") instead.

• get_hmfa_quali_var(). Deprecated. Use get_hmfa_var(res.hmfa, "quali.var") instead.

• get_hmfa_group(). Deprecated. Use get_hmfa_var(res.hmfa, "group") instead.

• fviz_hmfa_ind_starplot(): Graph of partial individuals. Deprecated. Use fviz_hmfa_ind(X, partial = "all") instead.

• fviz_hmfa_quanti_var(): Graph of quantitative variables. Deprecated. Use fviz_hmfa_var(X, "quanti.var") instead.

• fviz_hmfa_quali_var(): Graph of qualitative variables. Deprecated. Use fviz_hmfa_var(X, "quali.var") instead.

• fviz_hmfa_group(): Graph of the groups representation. Deprecated. Use fviz_hmfa_var(X, "group") instead.

Usage

get_mfa_quanti_var(res.mfa)

get_mfa_quali_var(res.mfa)

get_mfa_group(res.mfa)

fviz_mfa_ind_starplot(X, ...)

fviz_mfa_group(X, ...)

fviz_mfa_quanti_var(X, ...)

fviz_mfa_quali_var(X, ...)

get_hmfa_quanti_var(res.hmfa)

get_hmfa_quali_var(res.hmfa)

get_hmfa_group(res.hmfa)

fviz_hmfa_quanti_var(X, ...)

fviz_hmfa_quali_var(X, ...)

fviz_hmfa_ind_starplot(X, ...)

fviz_hmfa_group(X, ...)

Arguments

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

Enhanced Distance Matrix Computation and Visualization

Description

Clustering methods classify data samples into groups of similar objects. This process requires some methods for measuring the distance or the (dis)similarity between the observations. Read more: Clustering Distance Measures in R.

• get_dist(): Computes a distance matrix between the rows of a data matrix. Compared to the standard dist() function, it supports correlation-based distance measures including "pearson", "kendall" and "spearman" methods.

• fviz_dist(): Visualizes a distance matrix

When stand = TRUE, scaling that produces non-finite values is rejected. fviz_dist() also validates that supplied distance objects contain only finite values before plotting.

Usage

get_dist(x, method = "euclidean", stand = FALSE, ...)

fviz_dist(
  dist.obj,
  order = TRUE,
  show_labels = TRUE,
  lab_size = NULL,
  gradient = list(low = "red", mid = "white", high = "blue")
)

Arguments

Value

• get_dist(): returns an object of class "dist".

• fviz_dist(): returns a ggplot2

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

See Also

dist. Online tutorial: Clustering Distance Measures in R.

Examples

data(USArrests)
res.dist <- get_dist(USArrests, stand = TRUE, method = "pearson")

fviz_dist(res.dist, 
   gradient = list(low = "#00AFBB", mid = "white", high = "#FC4E07"))

Visual enhancement of clustering analysis

Description

Provides a convenient workflow for clustering analyses and ggplot2-based data visualization. When k = NULL, the gap statistic selects the number of clusters. Hierarchical backends may validly return k = 1; in that case eclust() returns a one-cluster result without silhouette information. Read more: Enhanced Cluster Analysis in R with factoextra's eclust().

Usage

eclust(
  x,
  FUNcluster = c("kmeans", "pam", "clara", "fanny", "hclust", "agnes", "diana",
    "hkmeans"),
  k = NULL,
  k.max = 10,
  stand = FALSE,
  graph = TRUE,
  hc_metric = "euclidean",
  hc_method = "ward.D2",
  gap_maxSE = list(method = "firstSEmax", SE.factor = 1),
  nboot = 100,
  verbose = interactive(),
  seed = 123,
  ...
)

Arguments

Value

Returns an object of class "eclust" containing the result of the standard function used (e.g., kmeans, pam, hclust, agnes, diana, etc.).

It also includes:

• cluster: the cluster assignment of observations after cutting the tree

• nbclust: the number of clusters

• silinfo: the silhouette information of observations, when available for solutions with at least two clusters, including $widths (silhouette width values of each observation), $clus.avg.widths (average silhouette width of each cluster) and $avg.width (average width of all clusters)

• size: the size of clusters

• data: a matrix containing the original or the standardized data (if stand = TRUE)

The "eclust" class has methods for fviz_silhouette(), fviz_dend(), and fviz_cluster().

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

See Also

fviz_silhouette, fviz_dend, fviz_cluster. Online tutorials: Enhanced Cluster Analysis in R with factoextra's eclust() and Choosing the Best Clustering Algorithm in R.

Examples

# Load and scale data
data("USArrests")
df <- scale(USArrests)

# Enhanced k-means clustering
# nboot >= 500 is recommended
res.km <- eclust(df, "kmeans", nboot = 2)
# Silhouette plot
fviz_silhouette(res.km)
# Optimal number of clusters using gap statistics
res.km$nbclust
# Print result
 res.km
 
## Not run: 
# Enhanced hierarchical clustering
res.hc <- eclust(df, "hclust", nboot = 2) # compute hclust
fviz_dend(res.hc) # dendrogram
if (res.hc$nbclust > 1) fviz_silhouette(res.hc) # silhouette plot

## End(Not run)
 

Extract and visualize the eigenvalues/variances of dimensions

Description

Eigenvalues correspond to the amount of the variation explained by each principal component (PC).

• get_eig(): Extract the eigenvalues/variances of the principal dimensions

• fviz_eig(): Plot the eigenvalues/variances against the number of dimensions

• get_eigenvalue(): an alias of get_eig()

• fviz_screeplot(): an alias of fviz_eig()

These functions support the results of Principal Component Analysis (PCA), Correspondence Analysis (CA), Multiple Correspondence Analysis (MCA), Factor Analysis of Mixed Data (FAMD), Multiple Factor Analysis (MFA) and Hierarchical Multiple Factor Analysis (HMFA) functions. fviz_eig() validates ncp, parallel.iter, and parallel.seed before plotting, accepting integer-like numeric values while still rejecting fractional inputs.

Recent versions of FactoMineR::PCA() may retain only the number of eigenvalues requested through its ncp argument. When the stored eigenvalues do not account for the result's recorded total inertia, fviz_eig() warns that the scree plot is incomplete. Refit the PCA with a sufficiently large ncp to plot the complete spectrum. get_eig() continues to return the eigenvalues stored in the object.

Read more: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

Usage

get_eig(X)

get_eigenvalue(X)

fviz_eig(
  X,
  choice = c("variance", "eigenvalue"),
  geom = c("bar", "line"),
  barfill = "steelblue",
  barcolor = "steelblue",
  linecolor = "black",
  ncp = 10,
  addlabels = FALSE,
  hjust = 0,
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  ggtheme = theme_minimal(),
  parallel = FALSE,
  parallel.color = "red",
  parallel.lty = "dashed",
  parallel.iter = 100,
  parallel.seed = NULL,
  ...
)

fviz_screeplot(...)

Arguments

Value

• get_eig() (or get_eigenvalue()): returns a data.frame containing 3 columns: the eigenvalues, the percentage of variance and the cumulative percentage of variance retained by each dimension.

• fviz_eig() (or fviz_screeplot()): returns a ggplot2

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

See Also

fviz_pca, fviz_ca, fviz_mca, fviz_mfa, fviz_hmfa. Online tutorial: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

Examples

# Principal Component Analysis
# ++++++++++++++++++++++++++
data(iris)
res.pca <- prcomp(iris[, -5],  scale = TRUE)

# Extract eigenvalues/variances
get_eig(res.pca)

# Default plot
fviz_eig(res.pca, addlabels = TRUE, ylim = c(0, 85))
  
# Scree plot - Eigenvalues
fviz_eig(res.pca, choice = "eigenvalue", addlabels=TRUE)

# Use only bar  or line plot: geom = "bar" or geom = "line"
fviz_eig(res.pca, geom="line")

# Parallel analysis (Horn's method) to determine the number of components
# Retain components whose eigenvalues exceed their component-specific points
fviz_eig(res.pca, choice = "eigenvalue", parallel = TRUE,
         addlabels = TRUE, parallel.color = "red",
         parallel.iter = 10, parallel.seed = 123)

## Not run:          
# Correspondence Analysis
# +++++++++++++++++++++++++++++++++
library(FactoMineR)
data(housetasks)
res.ca <- CA(housetasks, graph = FALSE)
get_eig(res.ca)
fviz_eig(res.ca, linecolor = "#FC4E07",
   barcolor = "#00AFBB", barfill = "#00AFBB")

# Multiple Correspondence Analysis
# +++++++++++++++++++++++++++++++++
library(FactoMineR)
data(poison)
res.mca <- MCA(poison, quanti.sup = 1:2, 
              quali.sup = 3:4, graph=FALSE)
get_eig(res.mca)
fviz_eig(res.mca, linecolor = "#FC4E07",
   barcolor = "#2E9FDF", barfill = "#2E9FDF")

## End(Not run)

Subset and summarize the output of factor analyses

Description

Subset and summarize the results of Principal Component Analysis (PCA), Correspondence Analysis (CA), Multiple Correspondence Analysis (MCA), Factor Analysis of Mixed Data (FAMD), Multiple Factor Analysis (MFA) and Hierarchical Multiple Factor Analysis (HMFA) functions from several packages. Axis indices are validated before extraction, and MCA quantitative supplementary summaries inherit the package-level error raised when that result is unavailable.

Usage

facto_summarize(
  X,
  element,
  node.level = 1,
  group.names,
  result = c("coord", "cos2", "contrib"),
  axes = 1:2,
  select = NULL
)

Arguments

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 requested coordinates and the cos2 and contribution metrics aggregated over the requested axes.

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

Examples

# Principal component analysis
# +++++++++++++++++++++++++++++
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]
# Select the top 5 contributing variables
facto_summarize(res.pca, "var", axes = 1:2,
           select = list(contrib = 5))[,-1]
# Select variables with cos2 >= 0.6
facto_summarize(res.pca, "var", axes = 1:2,
           select = list(cos2 = 0.6))[,-1]
# Select by names
facto_summarize(res.pca, "var", axes = 1:2,
     select = list(name = c("X100m", "Discus", "Javeline")))[,-1]
           
# Summarize individuals on axes 1:2
facto_summarize(res.pca, "ind", axes = 1:2)[,-1]

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

# Multiple Correspondence Analysis
# +++++++++++++++++++++++++++++++++
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)
# Summarize individuals on axes 1:2
res <- facto_summarize(res.mca, "ind", axes = 1:2)
head(res)
# Summarize quantitative supplementary variables on axes 1:2
res <- facto_summarize(res.mca, "quanti.sup", axes = 1:2)
head(res)

# Multiple factor Analysis
# +++++++++++++++++++++++++++++++++
library(FactoMineR)
data(poison)
res.mfa <- MFA(poison, group=c(2,2,5,6), type=c("s","n","n","n"),
               name.group=c("desc","desc2","symptom","eat"),
               num.group.sup=1:2, graph=FALSE)
# Summarize categorical variables on axes 1:2
res <- facto_summarize(res.mfa, "quali.var", axes = 1:2)
head(res)
# Summarize individuals on axes 1:2
res <- facto_summarize(res.mfa, "ind", axes = 1:2)
head(res)

Colorblind-safe color palette for factoextra plots

Description

Returns a colorblind-safe categorical color palette as a character vector of hex codes, to pass explicitly to the palette argument of the fviz_*() functions (e.g. fviz_cluster(res, palette = factoextra_palette("okabe"))). The default is the Okabe-Ito color-universal-design palette, which stays distinguishable under the common forms of color-vision deficiency.

The palette is returned as a plain color vector (not a ggplot2 scale), for the existing palette argument. Use it for discrete group coloring (habillage, a factor col.ind, or clusters), where it also tints the matching ellipse fills. For a continuous metric (e.g. col.ind = "cos2") use gradient.cols instead — a categorical palette does not apply there. It introduces no global option and no hidden state. The colors are ordered so the highest-contrast hues come first; yellow, the palest on a white background, is placed late, so plots with a few groups stay crisp.

Read more: ggplot2 Colours in R: Change Colours by Group.

Usage

factoextra_palette(palette = "okabe", n = NULL)

Arguments

Details

The Okabe-Ito colors are those of grDevices::palette.colors( palette = "Okabe-Ito") (here reordered so the vivid hues lead, with grey and black last). They were designed by Masataka Okabe and Kei Ito as a color-universal-design set, and popularized for figures by Wong (2011).

Value

A character vector of hex color codes.

References

Okabe, M. and Ito, K. (2008). Color Universal Design (CUD): How to make figures and presentations that are friendly to colorblind people. https://jfly.uni-koeln.de/color/.

Wong, B. (2011). Points of view: Color blindness. Nature Methods, 8(6), 441. doi:10.1038/nmeth.1618.

See Also

theme_factoextra. Online tutorial: ggplot2 Colours in R: Change Colours by Group.

Examples

# A colorblind-safe categorical palette
factoextra_palette("okabe")
factoextra_palette("okabe", n = 3)


# Publication-grade recipe: colorblind-safe groups + a clean theme
data(iris)
km <- kmeans(scale(iris[, 1:4]), 3, nstart = 25)
fviz_cluster(km, data = iris[, 1:4],
             palette = factoextra_palette("okabe"),
             ggtheme = theme_factoextra())

Map FactoMineR category labels to legacy naming patterns

Description

Map FactoMineR category labels to legacy naming patterns

Usage

factominer_category_map(X, element = c("quali.var", "quali.sup", "var"))

Arguments

Value

A data.frame with current labels, variable names, levels, and legacy naming patterns.

Examples

if (requireNamespace("FactoMineR", quietly = TRUE)) {
  data(poison)
  res.mca <- FactoMineR::MCA(poison, quanti.sup = 1:2, quali.sup = 3:4, graph = FALSE)
  head(factominer_category_map(res.mca, element = "var"))
}

Visualizing Multivariate Analysis Outputs

Description

Generic function to create a scatter plot of multivariate analysis outputs, including PCA, CA, MCA and MFA.

Usage

fviz(
  X,
  element,
  axes = c(1, 2),
  geom = "auto",
  label = "all",
  invisible = "none",
  labelsize = 4,
  pointsize = 1.5,
  pointshape = 19,
  arrowsize = 0.5,
  arrow.linetype = "solid",
  habillage = "none",
  addEllipses = FALSE,
  ellipse.level = 0.95,
  ellipse.type = "norm",
  ellipse.alpha = 0.1,
  mean.point = TRUE,
  color = "black",
  fill = "white",
  alpha = 1,
  gradient.cols = NULL,
  col.row.sup = "darkblue",
  col.col.sup = "darkred",
  select = list(name = NULL, cos2 = NULL, contrib = NULL),
  title = NULL,
  axes.linetype = "dashed",
  repel = FALSE,
  col.circle = "grey70",
  circlesize = 0.5,
  add.circle = NULL,
  rotate.labels = FALSE,
  ggtheme = theme_minimal(),
  ggp = NULL,
  font.family = "",
  max.points = NULL,
  sample.seed = 123,
  ...
)

Arguments

Value

a ggplot

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

Examples

# Principal component analysis
# +++++++++++++++++++++++++++++
data(decathlon2)
decathlon2.active <- decathlon2[1:23, 1:10]
res.pca <- prcomp(decathlon2.active,  scale = TRUE)
fviz(res.pca, "ind") # Individuals plot
fviz(res.pca, "var") # Variables plot

# Correspondence Analysis
# ++++++++++++++++++++++++++
# Install and load FactoMineR to compute CA
# install.packages("FactoMineR")
library("FactoMineR")
data("housetasks")
res.ca <- CA(housetasks, graph = FALSE)
fviz(res.ca, "row") # Rows plot
fviz(res.ca, "col") # Columns plot

# Multiple Correspondence Analysis
# +++++++++++++++++++++++++++++++++
library(FactoMineR)
data(poison)
res.mca <- MCA(poison, quanti.sup = 1:2, 
              quali.sup = 3:4, graph=FALSE)
              
fviz(res.mca, "ind") # Individuals plot
fviz(res.mca, "var") # Variables plot

 

Add supplementary data to a plot

Description

Add supplementary data to a plot

Usage

fviz_add(
  ggp,
  df,
  axes = c(1, 2),
  geom = c("point", "arrow"),
  color = "blue",
  addlabel = TRUE,
  labelsize = 4,
  pointsize = 2,
  shape = 19,
  linetype = "dashed",
  repel = FALSE,
  font.family = "",
  ...
)

Arguments

Value

a ggplot2 plot

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

Examples

# Principal component analysis
data(decathlon2)
decathlon2.active <- decathlon2[1:23, 1:10]
res.pca <- prcomp(decathlon2.active,  scale = TRUE)

# Visualize variables
p <- fviz_pca_var(res.pca)
print(p)

# Add supplementary variables
coord <- data.frame(PC1 = c(-0.7, 0.9), PC2 = c(0.25, -0.07))
rownames(coord) <- c("Rank", "Points")
print(coord)
fviz_add(p, coord, color ="blue", geom="arrow") 
 
 

Visualize Correspondence Analysis

Description

Correspondence analysis (CA) is an extension of Principal Component Analysis (PCA) suited to analyze frequencies formed by two categorical variables. fviz_ca() provides ggplot2-based elegant visualization of CA outputs from the R functions: CA [in FactoMineR], ca [in ca], coa [in ade4], correspondence [in MASS] and expoOutput/epCA [in ExPosition]. Read more: Correspondence Analysis (CA) in R: Contingency Tables, Biplot & Interpretation.

• 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()

Usage

fviz_ca_row(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  geom.row = geom,
  shape.row = 19,
  col.row = "blue",
  alpha.row = 1,
  col.row.sup = "darkblue",
  select.row = list(name = NULL, cos2 = NULL, contrib = NULL),
  map = "symmetric",
  repel = FALSE,
  ...
)

fviz_ca_col(
  X,
  axes = c(1, 2),
  shape.col = 17,
  geom = c("point", "text"),
  geom.col = geom,
  col.col = "red",
  col.col.sup = "darkred",
  alpha.col = 1,
  select.col = list(name = NULL, cos2 = NULL, contrib = NULL),
  map = "symmetric",
  repel = FALSE,
  ...
)

fviz_ca_biplot(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  geom.row = geom,
  geom.col = geom,
  label = "all",
  invisible = "none",
  arrows = c(FALSE, FALSE),
  repel = FALSE,
  title = "CA - Biplot",
  ...
)

fviz_ca(X, ...)

Arguments

Details

The default plot of (M)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 ggplot

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

See Also

get_ca, fviz_pca, fviz_mca. Online tutorial: Correspondence Analysis (CA) in R: Contingency Tables, Biplot & Interpretation.

Examples

# Correspondence Analysis
# ++++++++++++++++++++++++++++++
# Install and load FactoMineR to compute CA
# install.packages("FactoMineR")

library("FactoMineR")
data(housetasks)
head(housetasks)
res.ca <- CA(housetasks, graph=FALSE)

# Biplot of rows and columns
# ++++++++++++++++++++++++++
# Symmetric biplot of rows and columns
fviz_ca_biplot(res.ca)

# Asymmetric biplot, use arrows for columns
fviz_ca_biplot(res.ca, map ="rowprincipal",
 arrows = 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")

       
# 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))

# Graph of row variables
# +++++++++++++++++++++
   
# Control automatically the color of row points
   # using the "cos2" or the contributions "contrib"
   # cos2 = the quality of the rows on the factor map
   # Change gradient color
   # Use repel = TRUE to avoid overplotting (slow if many points)
fviz_ca_row(res.ca, col.row = "cos2",
   gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
   repel = TRUE)

# You can also control the transparency 
# of the color by the "cos2" or "contrib"
fviz_ca_row(res.ca, alpha.row="contrib") 
      
# Select and visualize some rows with select.row argument.
 # - Rows with cos2 >= 0.5: select.row = list(cos2 = 0.5)
 # - Top 7 rows according to the cos2: select.row = list(cos2 = 7)
 # - Top 7 contributing rows: select.row = list(contrib = 7)
 # - Select rows by names: select.row = list(name = c("Breakfeast", "Repairs", "Holidays"))
 
 # Example: Select the top 7 contributing rows
fviz_ca_row(res.ca, select.row = list(contrib = 7))

 
# Graph of column points
# ++++++++++++++++++++++++++++

 
# Control colors using their contributions
fviz_ca_col(res.ca, col.col = "contrib",
   gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"))
       
# Select columns with select.col argument
   # You can select by contrib, cos2 and name 
   # as previously described for ind
# Select the top 3 contributing columns
fviz_ca_col(res.ca, select.col = list(contrib = 3))
    
    
 

Visualize Clustering Results

Description

Provides ggplot2-based elegant visualization of partitioning methods including kmeans [stats package]; pam, clara and fanny [cluster package]; dbscan [fpc package]; Mclust [mclust package]; HCPC [FactoMineR]; hkmeans [factoextra]. Observations are represented by points in the plot, using principal components if ncol(data) > 2. An ellipse is drawn around each cluster. When stand = TRUE, the plotting data must remain finite after scaling.

Read more: K-Means Clustering in R: Algorithm, Visualization & Interpretation.

Usage

fviz_cluster(
  object,
  data = NULL,
  choose.vars = NULL,
  stand = TRUE,
  axes = c(1, 2),
  geom = c("point", "text"),
  repel = FALSE,
  show.clust.cent = TRUE,
  ellipse = TRUE,
  ellipse.type = "convex",
  ellipse.level = 0.95,
  ellipse.alpha = 0.2,
  shape = NULL,
  pointsize = 1.5,
  labelsize = 12,
  main = "Cluster plot",
  xlab = NULL,
  ylab = NULL,
  outlier.color = "black",
  outlier.shape = 19,
  outlier.pointsize = pointsize,
  outlier.labelsize = labelsize,
  ggtheme = theme_grey(),
  max.points = NULL,
  sample.seed = 123,
  ...
)

Arguments

Value

a ggplot2 object.

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

See Also

fviz_silhouette, hcut, hkmeans, eclust, fviz_dend. Online tutorial: K-Means Clustering in R: Algorithm, Visualization & Interpretation.

Examples

set.seed(123)

# Data preparation
# +++++++++++++++
data("iris")
head(iris)
# Remove species column (5) and scale the data
iris.scaled <- scale(iris[, -5])

# K-means clustering
# +++++++++++++++++++++
km.res <- kmeans(iris.scaled, 3, nstart = 10)

# Visualize kmeans clustering
# use repel = TRUE to avoid overplotting
fviz_cluster(km.res, iris[, -5], ellipse.type = "norm")


# Change the color palette and theme
fviz_cluster(km.res, iris[, -5],
   palette = "Set2", ggtheme = theme_minimal())

 ## Not run: 
# Show points only
fviz_cluster(km.res, iris[, -5], geom = "point")
# Show text only
fviz_cluster(km.res, iris[, -5], geom = "text")

# PAM clustering
# ++++++++++++++++++++
requireNamespace("cluster", quietly = TRUE)
pam.res <- cluster::pam(iris.scaled, 3)
 # Visualize pam clustering
fviz_cluster(pam.res, geom = "point", ellipse.type = "norm")

# Hierarchical clustering
# ++++++++++++++++++++++++
# Use hcut(), which computes hclust and cuts the tree
hc.cut <- hcut(iris.scaled, k = 3, hc_method = "complete")
# Visualize dendrogram
fviz_dend(hc.cut, show_labels = FALSE, rect = TRUE)
# Visualize cluster
fviz_cluster(hc.cut, ellipse.type = "convex")


## End(Not run)

Visualize the contributions of row/column elements

Description

This function can be used to visualize the contribution of rows/columns from the results of Principal Component Analysis (PCA), Correspondence Analysis (CA), Multiple Correspondence Analysis (MCA), Factor Analysis of Mixed Data (FAMD), and Multiple Factor Analysis (MFA) functions.

Read more: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

Usage

fviz_contrib(
  X,
  choice = c("row", "col", "var", "ind", "quanti.var", "quali.var", "group",
    "partial.axes"),
  axes = 1,
  fill = "steelblue",
  color = "steelblue",
  sort.val = c("desc", "asc", "none"),
  top = Inf,
  xtickslab.rt = 45,
  ggtheme = theme_minimal(),
  display = c("bar", "heatmap"),
  ...
)

fviz_pca_contrib(
  X,
  choice = c("var", "ind"),
  axes = 1,
  fill = "steelblue",
  color = "steelblue",
  sortcontrib = c("desc", "asc", "none"),
  top = Inf,
  ...
)

Arguments

Details

The function fviz_contrib() creates a barplot of row/column contributions. A reference dashed line is also shown on the barplot. This reference line corresponds to the expected value if the contribution were uniform.

For a given dimension, any row/column with a contribution above the reference line could be considered as important in contributing to the dimension.

Value

a ggplot2 plot

Functions

• fviz_pca_contrib(): deprecated function. Use fviz_contrib()

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

See Also

fviz_cos2, get_pca. Online tutorial: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

Examples

# Principal component analysis
# ++++++++++++++++++++++++++
data(decathlon2)
decathlon2.active <- decathlon2[1:23, 1:10]
res.pca <- prcomp(decathlon2.active,  scale = TRUE)

# variable contributions on axis 1
fviz_contrib(res.pca, choice="var", axes = 1, top = 10 )

# Change theme and color
fviz_contrib(res.pca, choice="var", axes = 1,
         fill = "lightgray", color = "black") +
         theme_minimal() +
         theme(axis.text.x = element_text(angle=45))

# Variable contributions on axis 2
fviz_contrib(res.pca, choice="var", axes = 2)
# Variable contributions on axes 1 + 2
fviz_contrib(res.pca, choice="var", axes = 1:2)

# Heat-grid of contributions across several dimensions
fviz_contrib(res.pca, choice = "var", axes = 1:3, display = "heatmap")

# Contributions of individuals on axis 1
fviz_contrib(res.pca, choice="ind", axes = 1)

## Not run: 
# Correspondence Analysis
# ++++++++++++++++++++++++++
# Install and load FactoMineR to compute CA
# install.packages("FactoMineR")
library("FactoMineR")
data("housetasks")
res.ca <- CA(housetasks, graph = FALSE)

# 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
# +++++++++++++++++++++++++++++++++
library(FactoMineR)
data(poison)
res.mca <- MCA(poison, quanti.sup = 1:2,
              quali.sup = 3:4, graph=FALSE)

# Visualize individual contributions on axes 1
fviz_contrib(res.mca, choice ="ind", axes = 1)
# Visualize variable category contributions on axes 1
fviz_contrib(res.mca, choice ="var", axes = 1)

# Multiple Factor Analysis
# ++++++++++++++++++++++++
library(FactoMineR)
data(poison)
res.mfa <- MFA(poison, group=c(2,2,5,6), type=c("s","n","n","n"),
               name.group=c("desc","desc2","symptom","eat"),
               num.group.sup=1:2, graph=FALSE)

# Visualize individual contributions on axes 1
fviz_contrib(res.mfa, choice ="ind", axes = 1, top = 20)
# Visualize categorical variable category contributions on axes 1
fviz_contrib(res.mfa, choice ="quali.var", axes = 1)

## End(Not run)

 

Visualize the quality of representation of rows/columns

Description

This function can be used to visualize the quality of representation (cos2) of rows/columns from the results of Principal Component Analysis (PCA), Correspondence Analysis (CA), Multiple Correspondence Analysis (MCA), Factor Analysis of Mixed Data (FAMD), Multiple Factor Analysis (MFA) and Hierarchical Multiple Factor Analysis (HMFA) functions.

Read more: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

Usage

fviz_cos2(
  X,
  choice = c("row", "col", "var", "ind", "quanti.var", "quali.var", "group"),
  axes = 1,
  fill = "steelblue",
  color = "steelblue",
  sort.val = c("desc", "asc", "none"),
  top = Inf,
  xtickslab.rt = 45,
  ggtheme = theme_minimal(),
  display = c("bar", "heatmap"),
  ...
)

Arguments

Value

a ggplot

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

See Also

fviz_contrib, get_pca. Online tutorial: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

Examples

# Principal component analysis
# ++++++++++++++++++++++++++
data(decathlon2)
decathlon2.active <- decathlon2[1:23, 1:10]
res.pca <- prcomp(decathlon2.active,  scale = TRUE)

# variable cos2 on axis 1
fviz_cos2(res.pca, choice="var", axes = 1, top = 10 )

# Change color
fviz_cos2(res.pca, choice="var", axes = 1,
         fill = "lightgray", color = "black") 
         
# Variable cos2 on axes 1 + 2
fviz_cos2(res.pca, choice="var", axes = 1:2)

# Heat-grid of cos2 across several dimensions
fviz_cos2(res.pca, choice = "var", axes = 1:4, display = "heatmap")

# cos2 of individuals on axis 1
fviz_cos2(res.pca, choice="ind", axes = 1)

## Not run: 
# Correspondence Analysis
# ++++++++++++++++++++++++++
library("FactoMineR")
data("housetasks")
res.ca <- CA(housetasks, graph = FALSE)

# Visualize row cos2 on axes 1
fviz_cos2(res.ca, choice ="row", axes = 1)
# Visualize column cos2 on axes 1
fviz_cos2(res.ca, choice ="col", axes = 1)

# Multiple Correspondence Analysis
# +++++++++++++++++++++++++++++++++
library(FactoMineR)
data(poison)
res.mca <- MCA(poison, quanti.sup = 1:2, 
              quali.sup = 3:4, graph=FALSE)
              
# Visualize individual cos2 on axes 1
fviz_cos2(res.mca, choice ="ind", axes = 1, top = 20)
# Visualize variable category cos2 on axes 1
fviz_cos2(res.mca, choice ="var", axes = 1)

# Multiple Factor Analysis
# ++++++++++++++++++++++++
library(FactoMineR)
data(poison)
res.mfa <- MFA(poison, group=c(2,2,5,6), type=c("s","n","n","n"),
               name.group=c("desc","desc2","symptom","eat"),
               num.group.sup=1:2, graph=FALSE)
# Visualize individual cos2 on axes 1
# Select the top 20
fviz_cos2(res.mfa, choice ="ind", axes = 1, top = 20)
# Visualize categorical variable category cos2 on axes 1
fviz_cos2(res.mfa, choice ="quali.var", axes = 1)

## End(Not run)
               
 

Enhanced Visualization of Dendrogram

Description

Draws easily beautiful dendrograms using either R base plot or ggplot2. It also provides options for circular dendrograms and phylogenetic-style trees.

Read more: Visualizing Dendrograms in R: Color, Zoom & Customize; to compare two trees see Comparing Dendrograms in R: Tanglegrams & Correlation.

Usage

fviz_dend(
  x,
  k = NULL,
  h = NULL,
  k_colors = NULL,
  palette = NULL,
  show_labels = TRUE,
  color_labels_by_k = TRUE,
  match_coord_colors = FALSE,
  label_cols = NULL,
  labels_font = "plain",
  labels_track_height = NULL,
  repel = FALSE,
  lwd = 0.7,
  highlight = NULL,
  highlight.col = "red",
  highlight.lwd = NULL,
  type = c("rectangle", "circular", "phylogenic"),
  phylo_layout = "layout.auto",
  rect = FALSE,
  rect_border = "gray",
  rect_lty = 2,
  rect_fill = FALSE,
  lower_rect,
  horiz = FALSE,
  cex = 0.8,
  main = "Cluster Dendrogram",
  xlab = "",
  ylab = "Height",
  sub = NULL,
  ggtheme = theme_classic(),
  ...
)

Arguments

Details

For branch styling beyond highlight - for example dashed branches or per-branch colours - pre-style a dendextend dendrogram and pass it to fviz_dend(), which honours its set() aesthetics:

  library(dendextend)
  dend <- as.dendrogram(hclust(dist(scale(USArrests))))
  dend <- set(dend, "branches_lty", 2)   # dashed branches
  fviz_dend(dend)
  

Comparing two dendrograms. To compare two hierarchical clusterings of the same observations (e.g. different linkages), draw a tanglegram with dendextend (already a dependency): the two trees face each other, matched leaves are connected, and entanglement() measures agreement (0 = perfect, 1 = worst). This uses base graphics.

  library(dendextend)
  d1 <- as.dendrogram(hclust(dist(scale(USArrests)), "complete"))
  d2 <- as.dendrogram(hclust(dist(scale(USArrests)), "average"))
  dl <- dendlist(d1, d2)
  dl <- untangle(dl, method = "step2side")        # reduce crossings
  tanglegram(dl, common_subtrees_color_branches = TRUE)
  entanglement(dl)                                 # agreement, in [0, 1]
  

Both dendrograms must share the same leaf labels.

Value

an object of class fviz_dend which is a ggplot with the attributes "dendrogram" accessible using attr(x, "dendrogram"), where x is the result of fviz_dend().

See Also

tanglegram, entanglement for comparing two dendrograms (see Details). Online tutorials: Visualizing Dendrograms in R: Color, Zoom & Customize and Comparing Dendrograms in R: Tanglegrams & Correlation.

Examples

# Load and scale the data
data(USArrests)
df <- scale(USArrests)

# Hierarchical clustering
res.hc <- hclust(dist(df))

# Default plot
fviz_dend(res.hc)

# Increase branch and rectangle line widths
fviz_dend(res.hc, lwd = 2)

# Cut the tree
fviz_dend(res.hc, cex = 0.5, k = 4, color_labels_by_k = TRUE)

# Don't color labels, add rectangles
fviz_dend(res.hc, cex = 0.5, k = 4, 
 color_labels_by_k = FALSE, rect = TRUE)
 
# Change the color of tree using black color for all groups
# Change rectangle border colors
fviz_dend(res.hc, rect = TRUE, k_colors ="black",
rect_border = 2:5, rect_lty = 1)

# Customized color for groups
fviz_dend(res.hc, k = 4, 
 k_colors = c("#1B9E77", "#D95F02", "#7570B3", "#E7298A"))
 
 
 # Color labels using k-means clusters
 km.clust <- kmeans(df, 4)$cluster
 fviz_dend(res.hc, k = 4, 
   k_colors = c("blue", "green3", "red", "black"),
   label_cols =  km.clust[res.hc$order], cex = 0.6)

 # Phylogenetic-style tree layouts support both compatibility aliases and
 # current igraph layout names
 if (requireNamespace("igraph", quietly = TRUE)) {
   fviz_dend(res.hc, type = "phylogenic", phylo_layout = "layout_nicely",
             show_labels = FALSE)
 }

Draw confidence ellipses around the categories

Description

Draw confidence ellipses around the categories

Usage

fviz_ellipses(
  X,
  habillage,
  axes = c(1, 2),
  addEllipses = TRUE,
  ellipse.type = "confidence",
  palette = NULL,
  pointsize = 1,
  geom = c("point", "text"),
  ggtheme = theme_bw(),
  ...
)

Arguments

Value

a ggplot

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

Examples

# Multiple Correspondence Analysis
# +++++++++++++++++++++++++++++++++
library(FactoMineR)
data(poison)
res.mca <- MCA(poison, quanti.sup = 1:2, 
              quali.sup = 3:4, graph=FALSE)
              
fviz_ellipses(res.mca, 3:4, geom = "point",
palette = "jco") 

 

Visualize Factor Analysis of Mixed Data

Description

Factor analysis of mixed data (FAMD) is a particular case of MFA, used to analyze a data set containing both quantitative and qualitative variables. fviz_famd() provides ggplot2-based elegant visualization of FAMD outputs from the R function: FAMD [FactoMineR].

• fviz_famd_ind(): Graph of individuals

• fviz_famd_var(): Graph of variables

• fviz_famd(): An alias of fviz_famd_ind(res.famd)

Read more: Factor Analysis of Mixed Data (FAMD) in R: Compute, Visualize & Interpret.

Usage

fviz_famd_ind(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  repel = FALSE,
  habillage = "none",
  palette = NULL,
  addEllipses = FALSE,
  col.ind = "blue",
  col.ind.sup = "darkblue",
  alpha.ind = 1,
  shape.ind = 19,
  col.quali.var = "black",
  select.ind = list(name = NULL, cos2 = NULL, contrib = NULL),
  gradient.cols = NULL,
  ...
)

fviz_famd_var(
  X,
  choice = c("var", "quanti.var", "quali.var", "quali.sup"),
  axes = c(1, 2),
  geom = c("point", "text"),
  repel = FALSE,
  col.var = "red",
  alpha.var = 1,
  shape.var = 17,
  col.var.sup = "darkgreen",
  select.var = list(name = NULL, cos2 = NULL, contrib = NULL),
  ...
)

fviz_famd(X, ...)

Arguments

Value

a ggplot

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

See Also

get_famd. Online tutorial: Factor Analysis of Mixed Data (FAMD) in R: Compute, Visualize & Interpret.

Examples

# Compute FAMD
 library("FactoMineR")
 data(wine)
 res.famd <- FAMD(wine[,c(1,2, 16, 22, 29, 28, 30,31)], graph = FALSE)
 res.famd.sup <- FAMD(wine[,c(1,2, 16, 22, 29, 28, 30,31)],
                      sup.var = 2, graph = FALSE)
               
# Eigenvalues/variances of dimensions
fviz_screeplot(res.famd)
# Graph of variables
fviz_famd_var(res.famd)
# Quantitative variables
fviz_famd_var(res.famd, "quanti.var", repel = TRUE, col.var = "black")
# Qualitative variables
fviz_famd_var(res.famd, "quali.var", col.var = "black")
# Supplementary qualitative variable categories
fviz_famd_var(res.famd.sup, "quali.sup", col.var = "darkgreen")
# Graph of individuals colored by cos2
fviz_famd_ind(res.famd, col.ind = "cos2", 
  gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
  repel = TRUE)

Visualize Hierarchical Multiple Factor Analysis

Description

Hierarchical Multiple Factor Analysis (HMFA) is an extension of MFA, used in a situation where the data are organized into a hierarchical structure. fviz_hmfa() provides ggplot2-based elegant visualization of HMFA outputs from the R function: HMFA [FactoMineR].

• fviz_hmfa_ind(): Graph of individuals

• fviz_hmfa_var(): Graph of variables

• fviz_hmfa_quali_biplot(): Biplot of individuals and qualitative variables

• fviz_hmfa(): An alias of fviz_hmfa_ind()

Read more: Multiple Factor Analysis (MFA) in R: Analyze Groups of Variables.

Usage

fviz_hmfa_ind(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  repel = FALSE,
  habillage = "none",
  addEllipses = FALSE,
  shape.ind = 19,
  col.ind = "blue",
  col.ind.sup = "darkblue",
  alpha.ind = 1,
  select.ind = list(name = NULL, cos2 = NULL, contrib = NULL),
  partial = NULL,
  col.partial = "group",
  group.names = NULL,
  node.level = 1,
  ...
)

fviz_hmfa_var(
  X,
  choice = c("quanti.var", "quali.var", "group"),
  axes = c(1, 2),
  geom = c("point", "text"),
  repel = FALSE,
  col.var = "red",
  alpha.var = 1,
  shape.var = 17,
  col.var.sup = "darkgreen",
  select.var = list(name = NULL, cos2 = NULL, contrib = NULL),
  ...
)

fviz_hmfa_quali_biplot(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  repel = FALSE,
  habillage = "none",
  title = "Biplot of individuals and qualitative variables - HMFA",
  ...
)

fviz_hmfa(X, ...)

Arguments

Value

a ggplot

Author(s)

Fabian Mundt f.mundt@inventionate.de

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

See Also

get_hmfa, fviz_mfa. Online tutorial: Multiple Factor Analysis (MFA) in R: Analyze Groups of Variables.

Examples

# Hierarchical Multiple Factor Analysis
# ++++++++++++++++++++++++
# Install and load FactoMineR to compute MFA
# install.packages("FactoMineR")
library("FactoMineR")
data(wine)
hierar <- list(c(2,5,3,10,9,2), c(4,2))
res.hmfa <- HMFA(wine, H = hierar, type=c("n",rep("s",5)), graph = FALSE)

# Graph of individuals
# ++++++++++++++++++++
# Color of individuals: col.ind = "#2E9FDF"
# Use repel = TRUE to avoid overplotting (slow if many points)
fviz_hmfa_ind(res.hmfa, repel = TRUE, col.ind = "#2E9FDF")

# Color individuals by groups, add concentration ellipses
# Remove labels: label = "none".
# Change color palette to "jco". See ?ggpubr::ggpar
grp <- as.factor(wine[,1])
p <- fviz_hmfa_ind(res.hmfa, label="none", habillage=grp,
       addEllipses=TRUE, palette = "jco")
print(p)
 

# Graph of variables
# ++++++++++++++++++++++++++++++++++++++++
# Quantitative variables
fviz_hmfa_var(res.hmfa, "quanti.var")
# Graph of categorical variable categories
fviz_hmfa_var(res.hmfa, "quali.var")
# Groups of variables (correlation square)
fviz_hmfa_var(res.hmfa, "group")


# Biplot of categorical variable categories and individuals
# +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
fviz_hmfa_quali_biplot(res.hmfa)
    
# Graph of partial individuals (starplot)
# +++++++++++++++++++++++++++++++++++++++
fviz_hmfa_ind(res.hmfa, partial = "all", col.partial = "black")
 

Visualize Multiple Correspondence Analysis

Description

Multiple Correspondence Analysis (MCA) is an extension of simple CA to analyse a data table containing more than two categorical variables. fviz_mca() provides ggplot2-based elegant visualization of MCA outputs from the R functions: MCA [in FactoMineR], acm [in ade4], and expoOutput/epMCA [in ExPosition]. Read more: Multiple Correspondence Analysis (MCA) in R: Compute, Visualize & Interpret.

• fviz_mca_ind(): Graph of individuals

• fviz_mca_var(): Graph of variables

• fviz_mca_biplot(): Biplot of individuals and variables

• fviz_mca(): An alias of fviz_mca_biplot()

Usage

fviz_mca_ind(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  geom.ind = geom,
  repel = FALSE,
  habillage = "none",
  palette = NULL,
  addEllipses = FALSE,
  col.ind = "blue",
  col.ind.sup = "darkblue",
  alpha.ind = 1,
  shape.ind = 19,
  map = "symmetric",
  select.ind = list(name = NULL, cos2 = NULL, contrib = NULL),
  quanti.sup = FALSE,
  col.quanti.sup = "#D55E00",
  ...
)

fviz_mca_var(
  X,
  choice = c("var.cat", "mca.cor", "var", "quanti.sup"),
  axes = c(1, 2),
  geom = c("point", "text"),
  geom.var = geom,
  repel = FALSE,
  col.var = "red",
  alpha.var = 1,
  shape.var = 17,
  col.quanti.sup = "blue",
  col.quali.sup = "darkgreen",
  map = "symmetric",
  select.var = list(name = NULL, cos2 = NULL, contrib = NULL),
  ...
)

fviz_mca_biplot(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  geom.ind = geom,
  geom.var = geom,
  repel = FALSE,
  label = "all",
  invisible = "none",
  habillage = "none",
  addEllipses = FALSE,
  palette = NULL,
  arrows = c(FALSE, FALSE),
  map = "symmetric",
  title = "MCA - Biplot",
  quanti.sup = FALSE,
  col.quanti.sup = "#D55E00",
  ...
)

fviz_mca(X, ...)

Arguments

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. The argument "map" can be used to change the plot type. For more explanation, read the details section of fviz_ca documentation.

quanti.sup = TRUE overlays the supplementary quantitative variables on the individuals / biplot map. Each such variable is drawn as an arrow from the origin in the direction of its correlations with the shown dimensions (X$quanti.sup$coord), so the arrow points toward the region of the cloud where the variable takes larger values. Each arrow's length is proportional to the variable's absolute correlation with the shown dimensions (a correlation of 1 reaches about 80% of the individual-cloud extent), so a weak covariate draws a short arrow. The overlay labels are repelled by default (needs the ggrepel package). Arrow lengths are relative to the cloud, so compare directions and relative lengths rather than absolute sizes.

Value

a ggplot

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

See Also

get_mca, fviz_pca, fviz_ca, fviz_mfa, fviz_hmfa. Online tutorial: Multiple Correspondence Analysis (MCA) in R: Compute, Visualize & Interpret.

Examples

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

# Graph of individuals
# +++++++++++++++++++++

# Default Plot
# Color of individuals: col.ind = "steelblue"
fviz_mca_ind(res.mca, col.ind = "steelblue")

# 1. Control automatically the color of individuals 
   # using the "cos2" or the contributions "contrib"
   # cos2 = the quality of the individuals on the factor map
# 2. To keep only point or text use geom = "point" or geom = "text".
# 3. Change themes: https://www.datanovia.com/learn/data-visualization/ggplot2/themes

fviz_mca_ind(res.mca, col.ind = "cos2", repel = TRUE)

## Not run:      
# You can also control the transparency 
# of the color by the cos2
fviz_mca_ind(res.mca, alpha.ind="cos2") 

## End(Not run)
     
# Color individuals by groups, add concentration ellipses
# Remove labels: label = "none".
grp <- as.factor(poison.active[, "Vomiting"])
p <- fviz_mca_ind(res.mca, label="none", habillage=grp,
       addEllipses=TRUE, ellipse.level=0.95)
print(p)

# Overlay supplementary quantitative variables as correlation arrows.
# Fit the MCA with quanti.sup, then set quanti.sup = TRUE when plotting.
res.mca2 <- MCA(poison, quanti.sup = 1:2, quali.sup = 3:4, graph = FALSE)
fviz_mca_ind(res.mca2, label = "none", habillage = poison$Vomiting,
             addEllipses = TRUE, quanti.sup = TRUE)


# Change group colors using RColorBrewer color palettes
# Read more: https://www.datanovia.com/learn/data-visualization/ggplot2/colors
p + scale_color_brewer(palette="Dark2") +
    scale_fill_brewer(palette="Dark2") 
     
# Change group colors manually
# Read more: https://www.datanovia.com/learn/data-visualization/ggplot2/colors
p + scale_color_manual(values=c("#999999", "#E69F00"))+
 scale_fill_manual(values=c("#999999", "#E69F00"))
             
             
# Select and visualize some individuals (ind) with select.ind argument.
 # - ind with cos2 >= 0.4: select.ind = list(cos2 = 0.4)
 # - Top 20 ind according to the cos2: select.ind = list(cos2 = 20)
 # - Top 20 contributing individuals: select.ind = list(contrib = 20)
 # - Select ind by names: select.ind = list(name = c("44", "38", "53",  "39") )
 
# Example: Select the top 40 according to the cos2
fviz_mca_ind(res.mca, select.ind = list(cos2 = 20))

 
# Graph of variable categories
# ++++++++++++++++++++++++++++
# Default plot: use repel = TRUE to avoid overplotting
fviz_mca_var(res.mca, col.var = "#FC4E07")

# Control variable colors using their contributions
# use repel = TRUE to avoid overplotting
fviz_mca_var(res.mca, col.var = "contrib",
  gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"))
        
    
# Biplot
# ++++++++++++++++++++++++++
grp <- as.factor(poison.active[, "Vomiting"])
fviz_mca_biplot(res.mca, repel = TRUE, col.var = "#E7B800",
 habillage = grp, addEllipses = TRUE, ellipse.level = 0.95)
 
 ## Not run: 
# 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")
       
# 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)
               
# 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)) 

## End(Not run)

Plot Model-Based Clustering Results using ggplot2

Description

Plots the classification, the uncertainty and the BIC values returned by the Mclust() function. Read more: Model-Based Clustering in R (Mclust).

Usage

fviz_mclust(
  object,
  what = c("classification", "uncertainty", "BIC"),
  ellipse.type = "norm",
  ellipse.level = 0.4,
  ggtheme = theme_classic(),
  ...
)

fviz_mclust_bic(
  object,
  model.names = NULL,
  shape = 19,
  color = "model",
  palette = NULL,
  legend = NULL,
  main = "Model selection",
  xlab = "Number of components",
  ylab = "BIC",
  ...
)

Arguments

Value

A ggplot2 object.

Functions

• fviz_mclust(): Plots classification and uncertainty.

• fviz_mclust_bic(): Plots the BIC values.

See Also

fviz_cluster. Online tutorial: Model-Based Clustering in R (Mclust).

Examples

if(requireNamespace("mclust", quietly = TRUE)){

# Compute model-based-clustering
library("mclust")
data("diabetes")
mc <- Mclust(diabetes[, -1])

# Visualize BIC values
fviz_mclust_bic(mc)

# Visualize classification
fviz_mclust(mc, "classification", geom = "point")
}

Visualize Multiple Factor Analysis

Description

Multiple factor analysis (MFA) is used to analyze a data set in which individuals are described by several sets of variables (quantitative and/or qualitative) structured into groups. fviz_mfa() provides ggplot2-based elegant visualization of MFA outputs from the R function: MFA [FactoMineR].

• fviz_mfa_ind(): Graph of individuals

• fviz_mfa_var(): Graph of variables

• fviz_mfa_axes(): Graph of partial axes

• fviz_mfa(): An alias of fviz_mfa_ind(res.mfa, partial = "all")

• fviz_mfa_quali_biplot(): Biplot of individuals and qualitative variables

Read more: Multiple Factor Analysis (MFA) in R: Analyze Groups of Variables.

Usage

fviz_mfa_ind(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  repel = FALSE,
  habillage = "none",
  palette = NULL,
  addEllipses = FALSE,
  col.ind = "blue",
  col.ind.sup = "darkblue",
  alpha.ind = 1,
  shape.ind = 19,
  col.quali.var.sup = "black",
  select.ind = list(name = NULL, cos2 = NULL, contrib = NULL),
  partial = NULL,
  col.partial = "group",
  ...
)

fviz_mfa_quali_biplot(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  repel = FALSE,
  title = "Biplot of individuals and qualitative variables - MFA",
  ...
)

fviz_mfa_var(
  X,
  choice = c("quanti.var", "group", "quali.var", "quali.sup"),
  axes = c(1, 2),
  geom = c("point", "text"),
  repel = FALSE,
  habillage = "none",
  col.var = "red",
  alpha.var = 1,
  shape.var = 17,
  col.var.sup = "darkgreen",
  palette = NULL,
  select.var = list(name = NULL, cos2 = NULL, contrib = NULL),
  ...
)

fviz_mfa_axes(
  X,
  axes = c(1, 2),
  geom = c("arrow", "text"),
  col.axes = NULL,
  alpha.axes = 1,
  col.circle = "grey70",
  select.axes = list(name = NULL, contrib = NULL),
  repel = FALSE,
  ...
)

fviz_mfa(X, partial = "all", ...)

Arguments

Value

a ggplot2 plot

Author(s)

Fabian Mundt f.mundt@inventionate.de

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

See Also

get_mfa. Online tutorial: Multiple Factor Analysis (MFA) in R: Analyze Groups of Variables.

Examples

# Compute Multiple Factor Analysis
library("FactoMineR")
data(wine)
res.mfa <- MFA(wine, group=c(2,5,3,10,9,2), type=c("n",rep("s",5)),
               ncp=5, name.group=c("orig","olf","vis","olfag","gust","ens"),
               num.group.sup=c(1,6), graph=FALSE)
               
# Eigenvalues/variances of dimensions
fviz_screeplot(res.mfa)
# Group of variables
fviz_mfa_var(res.mfa, "group")
# Quantitative variables
fviz_mfa_var(res.mfa, "quanti.var", palette = "jco", 
  col.var.sup = "violet", repel = TRUE)
# Graph of individuals colored by cos2
fviz_mfa_ind(res.mfa, col.ind = "cos2", 
  gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
  repel = TRUE)
# Partial individuals
fviz_mfa_ind(res.mfa, partial = rownames(wine)[1:3], col.partial = "black") 
# Partial axes
fviz_mfa_axes(res.mfa)


# Graph of categorical variable categories
# ++++++++++++++++++++++++++++++++++++++++
data(poison)
res.mfa <- MFA(poison, group=c(2,2,5,6), type=c("s","n","n","n"),
               name.group=c("desc","desc2","symptom","eat"),
               num.group.sup=1:2, graph=FALSE)

# Plot of qualitative variables
fviz_mfa_var(res.mfa, "quali.var")
# Plot of supplementary qualitative variables
fviz_mfa_var(res.mfa, "quali.sup")
 
 

# Biplot of categorical variable categories and individuals
# +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 # Use repel = TRUE to avoid overplotting
grp <- as.factor(poison[, "Vomiting"])
fviz_mfa_quali_biplot(res.mfa, repel = FALSE, col.var = "#E7B800",
   habillage = grp, addEllipses = TRUE, ellipse.level = 0.95)

Determining and Visualizing the Optimal Number of Clusters

Description

Partitioning methods, such as k-means clustering require the users to specify the number of clusters to be generated.

• fviz_nbclust(): Determines and visualizes the optimal number of clusters using different methods: within-cluster sum of squares, average silhouette, and the gap statistic. Silhouette values are evaluated only for k = 2, ..., k.max because average silhouette width is undefined for a one-cluster partition. The "silhouette" and "gap_stat" plots mark their optimum with a dashed guide line; set mark_optimal = TRUE to also mark the elbow on the "wss" plot, or mark_optimal = FALSE to omit the guide line for every method.

• fviz_gap_stat(): Visualizes the gap statistic generated by the function clusGap() [in cluster package]. The optimal number of clusters is specified using the maxSE method with method = "firstSEmax".

For method = "wss", factoextra computes the k = 1 baseline internally so helper functions such as hcut() and hkmeans() can keep rejecting direct k = 1 inputs.

Read more: Determining the Optimal Number of Clusters in R.

Usage

fviz_nbclust(
  x,
  FUNcluster = NULL,
  method = c("silhouette", "wss", "gap_stat"),
  diss = NULL,
  k.max = 10,
  nboot = 100,
  verbose = interactive(),
  barfill = "steelblue",
  barcolor = "steelblue",
  linecolor = "steelblue",
  print.summary = TRUE,
  ...,
  mark_optimal = NULL
)

fviz_gap_stat(
  gap_stat,
  linecolor = "steelblue",
  maxSE = list(method = "firstSEmax", SE.factor = 1),
  mark_optimal = NULL
)

Arguments

Details

When mark_optimal = TRUE, the "wss" elbow is located with a deterministic chord-distance heuristic: both axes are rescaled to the unit interval [0, 1] (so the choice does not depend on the magnitude of the within-cluster sum of squares) and the marked k is the one whose point lies farthest from the straight line joining the first and last points of the curve. This is related to the chord-distance idea used in knee detection, but it does not implement the full Kneedle sensitivity and local-maximum procedure of Satopää et al. (2011). The heuristic always returns a candidate, even for data with no clear cluster structure, which is why it is opt-in; the "silhouette" and "gap_stat" guide lines instead mark defined optima (the maximum average silhouette width and the maxSE location).

Value

Both fviz_nbclust() and fviz_gap_stat() return a ggplot2 object.

Method selection for gap statistic

The default "firstSEmax" method returns the first value within SE.factor standard errors of the first local maximum. Other maxSE rules can be selected explicitly through maxSE.

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

Satopää, V., Albrecht, J., Irwin, D. & Raghavan, B. (2011). Finding a "Kneedle" in a Haystack: Detecting Knee Points in System Behavior. 2011 31st International Conference on Distributed Computing Systems Workshops, 166-171. doi:10.1109/ICDCSW.2011.20

See Also

fviz_cluster, eclust. Online tutorial: Determining the Optimal Number of Clusters in R.

Examples

set.seed(123)

# Data preparation
# +++++++++++++++
data("iris")
head(iris)
# Remove species column (5) and scale the data
iris.scaled <- scale(iris[, -5])


# Optimal number of clusters in the data
# ++++++++++++++++++++++++++++++++++++++
# Examples are provided only for kmeans, but
# you can also use cluster::pam (for pam) or
#  hcut (for hierarchical clustering)
 
### Elbow method (look at the knee)
# Elbow method for kmeans
fviz_nbclust(iris.scaled, kmeans, method = "wss") +
geom_vline(xintercept = 3, linetype = 2)

# Let factoextra mark the elbow automatically
fviz_nbclust(iris.scaled, kmeans, method = "wss", mark_optimal = TRUE)

# WSS with hierarchical clustering keeps the internal k = 1 baseline
fviz_nbclust(iris.scaled, hcut, method = "wss", hc_method = "complete")

# Average silhouette for kmeans
fviz_nbclust(iris.scaled, kmeans, method = "silhouette")

### Gap statistic
library(cluster)
set.seed(123)
# Compute gap statistic for kmeans
# we used B = 10 for demo. Recommended value is ~500
gap_stat <- clusGap(iris.scaled, FUN = kmeans, nstart = 25,
 K.max = 10, B = 10)
 print(gap_stat, method = "firstSEmax")
fviz_gap_stat(gap_stat)
 
# Gap statistic for hierarchical clustering
gap_stat <- clusGap(iris.scaled, FUN = hcut, K.max = 10, B = 10)
fviz_gap_stat(gap_stat)

 

Visualize Principal Component Analysis

Description

Principal component analysis (PCA) reduces the dimensionality of multivariate data, to two or three that can be visualized graphically with minimal loss of information. fviz_pca() provides ggplot2-based elegant visualization of PCA outputs from: i) prcomp and princomp [in built-in R stats], ii) PCA [in FactoMineR], iii) dudi.pca [in ade4] and epPCA [ExPosition]. Read more: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

• fviz_pca_ind(): Graph of individuals

• fviz_pca_var(): Graph of variables

• fviz_pca_biplot(): Biplot of individuals and variables

• fviz_pca(): An alias of fviz_pca_biplot()

Note that, fviz_pca_xxx() functions are wrapper around the core function fviz(), which is also a wrapper around the function ggscatter() [in ggpubr]. Therefore, further arguments, to be passed to the function fviz() and ggscatter(), can be specified in fviz_pca_ind() and fviz_pca_var().

Usage

fviz_pca(X, ...)

fviz_pca_ind(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  geom.ind = geom,
  repel = FALSE,
  habillage = "none",
  palette = NULL,
  addEllipses = FALSE,
  col.ind = "black",
  fill.ind = "white",
  col.ind.sup = "blue",
  alpha.ind = 1,
  shape.ind = NULL,
  select.ind = list(name = NULL, cos2 = NULL, contrib = NULL),
  max.points = NULL,
  sample.seed = 123,
  ...
)

fviz_pca_var(
  X,
  axes = c(1, 2),
  geom = c("arrow", "text"),
  geom.var = geom,
  repel = FALSE,
  col.var = "black",
  fill.var = "white",
  alpha.var = 1,
  col.quanti.sup = "blue",
  col.circle = "grey70",
  select.var = list(name = NULL, cos2 = NULL, contrib = NULL),
  ...
)

fviz_pca_biplot(
  X,
  axes = c(1, 2),
  geom = c("point", "text"),
  geom.ind = geom,
  geom.var = c("arrow", "text"),
  col.ind = "black",
  fill.ind = "white",
  col.var = "steelblue",
  fill.var = "white",
  gradient.cols = NULL,
  label = "all",
  invisible = "none",
  repel = FALSE,
  habillage = "none",
  palette = NULL,
  addEllipses = FALSE,
  shape.ind = NULL,
  title = "PCA - Biplot",
  biplot.type = c("auto", "form", "covariance"),
  ...
)

Arguments

Value

a ggplot

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

See Also

fviz_ca, fviz_mca. Online tutorial: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

Examples

# Principal component analysis
# ++++++++++++++++++++++++++++++
data(iris)
res.pca <- prcomp(iris[, -5],  scale = TRUE)

# Graph of individuals
# +++++++++++++++++++++

# Default plot
# Use repel = TRUE to avoid overplotting (slow if many points)
fviz_pca_ind(res.pca, col.ind = "#00AFBB",
   repel = TRUE)

 
# 1. Control automatically the color of individuals 
   # using the "cos2" or the contributions "contrib"
   # cos2 = the quality of the individuals on the factor map
# 2. To keep only point or text use geom = "point" or geom = "text".
# 3. Change themes using ggtheme: https://www.datanovia.com/learn/data-visualization/ggplot2/themes

fviz_pca_ind(res.pca, col.ind="cos2", geom = "point",
   gradient.cols = c("white", "#2E9FDF", "#FC4E07" ))

# Color individuals by groups, add concentration ellipses
# Change group colors using RColorBrewer color palettes
# Read more: https://www.datanovia.com/learn/data-visualization/ggplot2/colors
# Remove labels: label = "none".
fviz_pca_ind(res.pca, label="none", habillage=iris$Species,
     addEllipses=TRUE, ellipse.level=0.95, palette = "Dark2")
             
     
# Change group colors manually
# Read more: https://www.datanovia.com/learn/data-visualization/ggplot2/colors
fviz_pca_ind(res.pca, label="none", habillage=iris$Species,
     addEllipses=TRUE, ellipse.level=0.95,
     palette = c("#999999", "#E69F00", "#56B4E9"))
      
# Select and visualize some individuals (ind) with select.ind argument.
 # - ind with cos2 >= 0.96: select.ind = list(cos2 = 0.96)
 # - Top 20 ind according to the cos2: select.ind = list(cos2 = 20)
 # - Top 20 contributing individuals: select.ind = list(contrib = 20)
 # - Select ind by names: select.ind = list(name = c("23", "42", "119") )
 
 # Example: Select the top 40 according to the cos2
fviz_pca_ind(res.pca, select.ind = list(cos2 = 40))

 # By default several conditions combine with AND (intersection).
 # Use union = TRUE for OR: keep named individuals PLUS the top-contrib ones.
fviz_pca_ind(res.pca,
             select.ind = list(name = c("23", "42"), contrib = 20, union = TRUE))

 
# Graph of variables
# ++++++++++++++++++++++++++++
  
# Default plot
fviz_pca_var(res.pca, col.var = "steelblue")
 
# Control variable colors using their contributions
fviz_pca_var(res.pca, col.var = "contrib", 
   gradient.cols = c("white", "blue", "red"),
   ggtheme = theme_minimal())
 
    
# Biplot of individuals and variables
# ++++++++++++++++++++++++++
# Keep only the labels for variables
# Change the color by groups, add ellipses
fviz_pca_biplot(res.pca, label = "var", habillage=iris$Species,
               addEllipses=TRUE, ellipse.level=0.95,
               ggtheme = theme_minimal())

# Biplot scaling modes:
# Form biplot - focus on individual distances
fviz_pca_biplot(res.pca, biplot.type = "form",
               label = "var", habillage = iris$Species)
# Covariance biplot - focus on variable correlations
fviz_pca_biplot(res.pca, biplot.type = "covariance",
               label = "var", habillage = iris$Species)

 

Visualize Silhouette Information from Clustering

Description

Silhouette (Si) analysis compares an observation's average dissimilarity within its assigned cluster with its average dissimilarity to the nearest alternative cluster. fviz_silhouette() provides a ggplot2-based visualization of silhouette information from i) the result of silhouette(), pam(), clara() and fanny() [in cluster package]; ii) eclust() and hcut() [in factoextra]. Results without silhouette information, such as one-cluster eclust/hcut objects, are rejected with a package-level error.

Read more: Cluster Validation Statistics in R.

Usage

fviz_silhouette(sil.obj, label = FALSE, print.summary = TRUE, ...)

Arguments

Details

- Observations with a large silhouette Si (almost 1) are very well clustered.

- A small Si (around 0) means that the observation lies between two clusters.

- A negative Si means that the observation is, on average, closer to another cluster than to its assigned cluster.

- Silhouette plots require at least two clusters and available silhouette widths.

Value

a ggplot2 object.

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

See Also

fviz_cluster, hcut, hkmeans, eclust, fviz_dend. Online tutorial: Cluster Validation Statistics in R.

Examples

set.seed(123)

# Data preparation
# +++++++++++++++
data("iris")
head(iris)
# Remove species column (5) and scale the data
iris.scaled <- scale(iris[, -5])

# K-means clustering
# +++++++++++++++++++++
km.res <- kmeans(iris.scaled, 3, nstart = 2)

# Visualize kmeans clustering
fviz_cluster(km.res, iris[, -5], ellipse.type = "norm")+
theme_minimal()

# Visualize silhouette information
requireNamespace("cluster", quietly = TRUE)
sil <- cluster::silhouette(km.res$cluster, dist(iris.scaled))
fviz_silhouette(sil)

# Identify observation with negative silhouette
neg_sil_index <- which(sil[, "sil_width"] < 0)
sil[neg_sil_index, , drop = FALSE]
## Not run: 
# PAM clustering
# ++++++++++++++++++++
requireNamespace("cluster", quietly = TRUE)
pam.res <- cluster::pam(iris.scaled, 3)
# Visualize pam clustering
fviz_cluster(pam.res, ellipse.type = "norm")+
theme_minimal()
# Visualize silhouette information
fviz_silhouette(pam.res)

# Hierarchical clustering
# ++++++++++++++++++++++++
# Use hcut() which compute hclust and cut the tree
hc.cut <- hcut(iris.scaled, k = 3, hc_method = "complete")
# Visualize dendrogram
fviz_dend(hc.cut, show_labels = FALSE, rect = TRUE)
# Visualize silhouette information
if (hc.cut$nbclust > 1) fviz_silhouette(hc.cut)

## End(Not run)

Visualize a UMAP or t-SNE embedding

Description

fviz_umap() and fviz_tsne() draw a ggplot2 scatter plot of a two-dimensional embedding produced by UMAP or t-SNE, with factoextra's grouping, ellipse and palette styling. They accept the result of uwot::umap() / umap::umap() / Rtsne::Rtsne(), or a plain matrix / data frame of coordinates.

Unlike PCA, an embedding has no eigenvalues: the axes explain no fixed percentage of variance, so they are labelled UMAP1/UMAP2 (tSNE1/tSNE2) without a percentage, and there is deliberately no scree plot, no variable loadings, and no correlation circle - those are meaningless for an embedding. For methods that do have eigenvalues (PCA, CA, MCA, MDS) see fviz_pca and as_factoextra_pca.

Read more: UMAP in R: Nonlinear Dimension Reduction & Visualization and t-SNE in R: Visualize High-Dimensional Data.

Usage

fviz_umap(
  X,
  dims = c(1L, 2L),
  habillage = NULL,
  col.ind = NULL,
  geom = "point",
  label = FALSE,
  pointsize = 1.5,
  labelsize = 4,
  addEllipses = FALSE,
  ellipse.type = "convex",
  ellipse.level = 0.95,
  mean.point = FALSE,
  palette = NULL,
  gradient.cols = NULL,
  density = FALSE,
  facet.by = NULL,
  repel = TRUE,
  max.points = NULL,
  sample.seed = 123,
  legend.title = NULL,
  caption = NULL,
  ggtheme = theme_minimal(),
  ...
)

fviz_tsne(
  X,
  dims = c(1L, 2L),
  habillage = NULL,
  col.ind = NULL,
  geom = "point",
  label = FALSE,
  pointsize = 1.5,
  labelsize = 4,
  addEllipses = FALSE,
  ellipse.type = "convex",
  ellipse.level = 0.95,
  mean.point = FALSE,
  palette = NULL,
  gradient.cols = NULL,
  density = FALSE,
  facet.by = NULL,
  repel = TRUE,
  max.points = NULL,
  sample.seed = 123,
  legend.title = NULL,
  caption = NULL,
  ggtheme = theme_minimal(),
  ...
)

Arguments

Details

UMAP and t-SNE produce a low-dimensional embedding, not a variance decomposition. Local relationships are often more informative than global geometry, but both remain method- and parameter-dependent. In particular, the size of a cluster, the distance between well-separated clusters, and the amount of empty space between them are not quantitatively meaningful and change with perplexity or n_neighbors (Wattenberg et al., 2016). Similar embedding scatter plots are drawn by Seurat::DimPlot() / FeaturePlot() and ggpca.

Value

a ggplot2 object.

References

McInnes, L., Healy, J. and Melville, J. (2018). UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction. arXiv:1802.03426.

Wattenberg, M., Viégas, F. and Johnson, I. (2016). How to Use t-SNE Effectively. Distill. doi:10.23915/distill.00002.

See Also

fviz_pca, as_factoextra_pca, fviz_cluster. Online tutorials: UMAP in R: Nonlinear Dimension Reduction & Visualization and t-SNE in R: Visualize High-Dimensional Data.

Examples

if (requireNamespace("uwot", quietly = TRUE)) {
  set.seed(123)
  um <- uwot::umap(iris[, 1:4], n_neighbors = 15)
  fviz_umap(um, habillage = iris$Species, addEllipses = TRUE)
  # colour by a continuous feature value
  fviz_umap(um, col.ind = iris$Petal.Length)
}

Extract the results for rows/columns - CA

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

Read more: Correspondence Analysis (CA) in R: Contingency Tables, Biplot & Interpretation.

Usage

get_ca(res.ca, element = c("row", "col"))

get_ca_col(res.ca)

get_ca_row(res.ca)

Arguments

Value

a list of matrices containing the results for the active rows/columns, including:

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

See Also

fviz_ca. Online tutorial: Correspondence Analysis (CA) in R: Contingency Tables, Biplot & Interpretation.

Examples

# Install and load FactoMineR to compute CA
# install.packages("FactoMineR")
 library("FactoMineR")
 data("housetasks")
 res.ca <- CA(housetasks, graph = FALSE)
 
# Result for column variables
 col <- get_ca_col(res.ca)
 col # print
 head(col$coord) # column coordinates
 head(col$cos2) # column cos2
 head(col$contrib) # column contributions
 
# Result for row variables
 row <- get_ca_row(res.ca)
 row # print
 head(row$coord) # row coordinates
 head(row$cos2) # row cos2
 head(row$contrib) # row contributions
 
 # You can also use the function get_ca()
 get_ca(res.ca, "row") # Results for rows
 get_ca(res.ca, "col") # Results for columns
 

Assessing Clustering Tendency

Description

Before applying clustering methods, assess whether the data show non-random structure, a process known as assessing clustering tendency. get_clust_tendency() uses the Hopkins statistic and, optionally, an ordered dissimilarity image (ODI). Rows containing missing values are omitted, and the remaining matrix must be numeric and finite. The observed rows are sampled without replacement; artificial points are sampled uniformly within the observed bounding box. Zero-range columns are ignored for the Hopkins calculation when at least one column varies; an all-constant data set remains undefined. In the ODI, objects grouped by hierarchical clustering are displayed in consecutive order. For more details and interpretation, see Assessing Clustering Tendency in R.

Usage

get_clust_tendency(
  data,
  n,
  graph = TRUE,
  gradient = list(low = "red", mid = "white", high = "blue"),
  seed = NULL
)

Arguments

Details

Hopkins statistic: Values near 1 support a clustered tendency, values near 0.5 are consistent with complete spatial randomness, and values near 0 indicate regular spacing. The statistic uses the formula from Cross and Jain (1982), with exponent d = D, where D is the number of varying columns. Redundant constant columns therefore do not change the statistic. A Beta(n, n) comparison is an approximation under ideal complete-spatial-randomness assumptions, not an unconditional finite-sample distribution for every data set.

Note on interpretation: This function returns the Hopkins statistic H where values close to 1 indicate clusterable data. Some other packages (e.g., performance::check_clusterstructure) return 1-H, where values close to 0 indicate clusterability. Always check the documentation of the specific implementation you are using.

Breaking change: factoextra uses the corrected Hopkins statistic formula (Wright 2022). Results differ from legacy factoextra and a one-time warning is emitted. Set options(factoextra.warn_hopkins = FALSE) to silence the warning.

For large datasets, nearest-neighbor distances are computed with a low-memory fallback when the full pairwise matrix would exceed getOption("factoextra.hopkins.max_matrix_cells", 2e7) cells. Only the sampled row's own occurrence is excluded from its nearest-neighbor search; a duplicated row therefore remains a valid zero-distance neighbor.

VAT (Visual Assessment of Cluster Tendency): The VAT displays clustering tendency by showing square-shaped dark (or colored) blocks along the diagonal in a VAT image.

Value

A list containing:

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

See Also

fviz_dist. Online tutorial: Assessing Clustering Tendency in R.

Examples

data(iris)

# Silence the one-time compatibility warning in examples
old_hopkins_warn <- getOption("factoextra.warn_hopkins")
options(factoextra.warn_hopkins = FALSE)

# Clustering tendency
gradient_col = list(low = "steelblue", high = "white")
get_clust_tendency(iris[,-5], n = 50, gradient = gradient_col)
   
# Random uniformly distributed dataset
# (without any inherent clusters)
set.seed(123)
random_df <- apply(iris[, -5], 2, 
                   function(x){runif(length(x), min(x), max(x))}
                   )
get_clust_tendency(random_df, n = 50, gradient = gradient_col)
options(factoextra.warn_hopkins = old_hopkins_warn)

Extract the results for individuals and variables - FAMD

Description

Extract all the results (coordinates, squared cosine and contributions) for the active individuals and variables from Factor Analysis of Mixed Data (FAMD) outputs.

• get_famd(): Extract the results for variables and individuals

• get_famd_ind(): Extract the results for individuals only

• get_famd_var(): Extract the results for quantitative and qualitative variables only

Read more: Factor Analysis of Mixed Data (FAMD) in R: Compute, Visualize & Interpret.

Usage

get_famd(
  res.famd,
  element = c("ind", "var", "quanti.var", "quali.var", "quali.sup")
)

get_famd_ind(res.famd)

get_famd_var(
  res.famd,
  element = c("var", "quanti.var", "quali.var", "quali.sup")
)

Arguments

Value

a list of matrices containing the results for the active individuals and variables, including:

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

See Also

fviz_famd. Online tutorial: Factor Analysis of Mixed Data (FAMD) in R: Compute, Visualize & Interpret.

Examples

 # Compute FAMD
 library("FactoMineR")
 data(wine)
 res.famd <- FAMD(wine[,c(1,2, 16, 22, 29, 28, 30,31)], graph = FALSE)
 res.famd.sup <- FAMD(wine[,c(1,2, 16, 22, 29, 28, 30,31)],
                      sup.var = 2, graph = FALSE)
 
 # Extract the results for qualitative variable categories
 quali.var <- get_famd_var(res.famd, "quali.var")
 print(quali.var)
 head(quali.var$coord) # coordinates of qualitative variables

 # Extract the results for supplementary qualitative variable categories
 quali.sup <- get_famd_var(res.famd.sup, "quali.sup")
 print(quali.sup)
 head(quali.sup$coord) # coordinates of supplementary qualitative variables
 
 # Extract the results for quantitative variables
 quanti.var <- get_famd_var(res.famd, "quanti.var")
 print(quanti.var)
 head(quanti.var$coord) # coordinates
 
 # Extract the results for individuals
 ind <- get_famd_ind(res.famd)
 print(ind)
 head(ind$coord) # coordinates of individuals
 
 

Extract the results for individuals/variables/group/partial axes - HMFA

Description

Extract all the results (coordinates, squared cosine and contributions) for the active individuals/quantitative variables/qualitative variable categories/groups/partial axes from Hierarchical Multiple Factor Analysis (HMFA) outputs.

• get_hmfa(): Extract the results for variables and individuals

• get_hmfa_ind(): Extract the results for individuals only

• get_hmfa_var(): Extract the results for quantitative variables, qualitative variables, and groups

• get_hmfa_partial(): Extract the results for partial.node.

Read more: Multiple Factor Analysis (MFA) in R: Analyze Groups of Variables.

Usage

get_hmfa(
  res.hmfa,
  element = c("ind", "quanti.var", "quali.var", "group", "partial.node")
)

get_hmfa_ind(res.hmfa)

get_hmfa_var(res.hmfa, element = c("quanti.var", "quali.var", "group"))

get_hmfa_partial(res.hmfa)

Arguments

Value

a list of matrices containing the results for the active individuals, variables, groups, and partial nodes, including:

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

Fabian Mundt f.mundt@inventionate.de

See Also

fviz_hmfa, fviz_mfa. Online tutorial: Multiple Factor Analysis (MFA) in R: Analyze Groups of Variables.

Examples

# Multiple Factor Analysis
# ++++++++++++++++++++++++
# Install and load FactoMineR to compute MFA
# install.packages("FactoMineR")
library("FactoMineR")
data(wine)
hierar <- list(c(2,5,3,10,9,2), c(4,2))
res.hmfa <- HMFA(wine, H = hierar, type=c("n",rep("s",5)), graph = FALSE)
 
 # Extract the results for qualitative variable categories
 var <- get_hmfa_var(res.hmfa, "quali.var")
 print(var)
 head(var$coord) # coordinates of qualitative variables
 head(var$cos2) # cos2 of qualitative variables
 head(var$contrib) # contributions of qualitative variables
 
 # Extract the results for individuals
 ind <- get_hmfa_ind(res.hmfa)
 print(ind)
 head(ind$coord) # coordinates of individuals
 head(ind$cos2) # cos2 of individuals
 head(ind$contrib) # contributions of individuals
 
 # You can also use the function get_hmfa()
 get_hmfa(res.hmfa, "ind") # Results for individuals
 get_hmfa(res.hmfa, "quali.var") # Results for qualitative variable categories
 

Extract the results for individuals/variables - MCA

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

For FactoMineR MCA results, get_mca() and get_mca_var() also support element = "quanti.sup" for quantitative supplementary variables and report a clean package-level error when that result is absent.

Read more: Multiple Correspondence Analysis (MCA) in R: Compute, Visualize & Interpret.

Usage

get_mca(res.mca, element = c("var", "ind", "mca.cor", "quanti.sup"))

get_mca_var(res.mca, element = c("var", "mca.cor", "quanti.sup"))

get_mca_ind(res.mca)

Arguments

Value

a list of matrices containing the results for the active individuals/variable categories, including:

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

See Also

fviz_mca. Online tutorial: Multiple Correspondence Analysis (MCA) in R: Compute, Visualize & Interpret.

Examples

# Multiple Correspondence Analysis
# ++++++++++++++++++++++++++++++
# Install and load FactoMineR to compute MCA
# install.packages("FactoMineR")
library("FactoMineR")
data(poison)
res.mca <- MCA(poison, quanti.sup = 1:2, graph = FALSE)
 
 # Extract the results for variable categories
 var <- get_mca_var(res.mca)
 print(var)
 head(var$coord) # coordinates of variables
 head(var$cos2) # cos2 of variables
 head(var$contrib) # contributions of variables
 
 # Extract the results for individuals
 ind <- get_mca_ind(res.mca)
 print(ind)
 head(ind$coord) # coordinates of individuals
 head(ind$cos2) # cos2 of individuals
 head(ind$contrib) # contributions of individuals
 
 # You can also use the function get_mca()
 get_mca(res.mca, "ind") # Results for individuals
 get_mca(res.mca, "var") # Results for variable categories
 quanti.sup <- get_mca(res.mca, "quanti.sup")
 head(quanti.sup$coord) # coordinates of quantitative supplementary variables
 
 

Extract the results for individuals/variables/group/partial axes - MFA

Description

Extract all the results (coordinates, squared cosine and contributions) for the active individuals/quantitative variables/qualitative variable categories/groups/partial axes from Multiple Factor Analysis (MFA) outputs.

• get_mfa(): Extract the results for variables and individuals

• get_mfa_ind(): Extract the results for individuals only

• get_mfa_var(): Extract the results for quantitative variables, qualitative variables, and groups

• get_mfa_partial_axes(): Extract the results for partial axes only

Read more: Multiple Factor Analysis (MFA) in R: Analyze Groups of Variables.

Usage

get_mfa(
  res.mfa,
  element = c("ind", "quanti.var", "quali.var", "quali.sup", "group", "partial.axes")
)

get_mfa_ind(res.mfa)

get_mfa_var(
  res.mfa,
  element = c("quanti.var", "quali.var", "quali.sup", "group")
)

get_mfa_partial_axes(res.mfa)

Arguments

Value

a list of matrices containing the results for the active individuals, quantitative variables, qualitative variable categories, groups, and partial axes, including:

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

Fabian Mundt f.mundt@inventionate.de

See Also

fviz_mfa. Online tutorial: Multiple Factor Analysis (MFA) in R: Analyze Groups of Variables.

Examples

# Multiple Factor Analysis
# ++++++++++++++++++++++++
# Install and load FactoMineR to compute MFA
# install.packages("FactoMineR")
library("FactoMineR")
data(poison)
res.mfa <- MFA(poison, group=c(2,2,5,6), type=c("s","n","n","n"),
name.group=c("desc","desc2","symptom","eat"), num.group.sup=1:2,
graph = FALSE)
 
 # Extract the results for qualitative variable categories
 var <- get_mfa_var(res.mfa, "quali.var")
 print(var)
 head(var$coord) # coordinates of qualitative variables
 head(var$cos2) # cos2 of qualitative variables
 head(var$contrib) # contributions of qualitative variables
 
 # Extract the results for individuals
 ind <- get_mfa_ind(res.mfa)
 print(ind)
 head(ind$coord) # coordinates of individuals
 head(ind$cos2) # cos2 of individuals
 head(ind$contrib) # contributions of individuals
 
 # You can also use the function get_mfa()
 get_mfa(res.mfa, "ind") # Results for individuals
 get_mfa(res.mfa, "quali.var") # Results for qualitative variable categories
 get_mfa(res.mfa, "quali.sup") # Results for supplementary qualitative variable categories
 

Extract the results for individuals/variables - PCA

Description

Extract all the results (coordinates, squared cosines, and 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

Read more: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

Usage

get_pca(res.pca, element = c("var", "ind"))

get_pca_ind(res.pca, ...)

get_pca_var(res.pca)

Arguments

Value

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

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

See Also

fviz_pca. Online tutorial: Principal Component Analysis (PCA) in R: Compute, Visualize & Interpret.

Examples

# Principal Component Analysis
# +++++++++++++++++++++++++++++
 data(iris)
 res.pca <- prcomp(iris[, -5],  scale = TRUE)
 # Extract the results for individuals
 ind <- get_pca_ind(res.pca)
 print(ind)
 head(ind$coord) # coordinates of individuals
 head(ind$cos2) # cos2 of individuals
 head(ind$contrib) # contributions of individuals
 
 # Extract the results for variables
 var <- get_pca_var(res.pca)
 print(var)
 head(var$coord) # coordinates of variables
 head(var$cos2) # cos2 of variables
 head(var$contrib) # contributions of variables
 
 # You can also use the function get_pca()
 get_pca(res.pca, "ind") # Results for individuals
 get_pca(res.pca, "var") # Results for variable categories
 

Computes Hierarchical Clustering and Cut the Tree

Description

Computes hierarchical clustering (hclust, agnes, diana) and cuts the tree into k clusters. It also accepts correlation-based distance measures such as "pearson", "spearman" and "kendall". Direct calls require k >= 2; helper-level one-cluster handling is implemented in callers such as eclust() and fviz_nbclust().

Read more: Hierarchical Clustering in R: Dendrograms, Agglomerative & Divisive.

Usage

hcut(
  x,
  k = 2,
  isdiss = inherits(x, "dist"),
  hc_func = c("hclust", "agnes", "diana"),
  hc_method = "ward.D2",
  hc_metric = "euclidean",
  stand = FALSE,
  graph = FALSE,
  ...
)

Arguments

Value

an object of class "hcut" containing the result of the standard function used (read the documentation of hclust, agnes, diana).

It includes also:

• cluster: the cluster assignment of observations after cutting the tree

• nbclust: the number of clusters

• silinfo: the silhouette information of observations (available when k > 1)

• size: the size of clusters

• data: a matrix containing the original or the standardized data (if stand = TRUE)

See Also

fviz_dend, hkmeans, eclust. Online tutorial: Hierarchical Clustering in R: Dendrograms, Agglomerative & Divisive.

Examples

data(USArrests)

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

# Cluster assignments of observations
res$cluster
# Size of clusters
res$size

# Visualize the dendrogram
fviz_dend(res, rect = TRUE)

# Visualize the silhouette
fviz_silhouette(res)

# Visualize clusters as scatter plots
fviz_cluster(res)

Hierarchical k-means clustering

Description

The final k-means clustering solution is very sensitive to the initial random selection of cluster centers. This function provides a solution using an hybrid approach by combining the hierarchical clustering and the k-means methods. The procedure is explained in "Details" section. Read more: Hierarchical K-Means Clustering in R: A Hybrid for Stable Clusters.

• hkmeans(): compute hierarchical k-means clustering

• print.hkmeans(): prints the result of hkmeans

• hkmeans_tree(): plots the initial dendrogram

Usage

hkmeans(
  x,
  k,
  hc.metric = "euclidean",
  hc.method = "ward.D2",
  iter.max = 10,
  km.algorithm = "Hartigan-Wong"
)

## S3 method for class 'hkmeans'
print(x, ...)

hkmeans_tree(hkmeans, rect.col = NULL, ...)

Arguments

Details

The procedure is as follows:

1. Compute hierarchical clustering

2. Cut the tree in k-clusters

3. compute the center (i.e the mean) of each cluster

4. Do k-means by using the set of cluster centers (defined in step 3) as the initial cluster centers. Optimize the clustering.

This means that the final optimized partitioning obtained at step 4 might be different from the initial partitioning obtained at step 2. Consider mainly the result displayed by fviz_cluster().

Value

hkmeans returns an object of class "hkmeans" containing the following components:

• The elements returned by the standard function kmeans() (see ?kmeans)

• data: the data used for the analysis

• hclust: an object of class "hclust" generated by the function hclust()

See Also

eclust, hcut, fviz_dend. Online tutorial: Hierarchical K-Means Clustering in R: A Hybrid for Stable Clusters.

Examples

# Load data
data(USArrests)
# Scale the data
df <- scale(USArrests)

# Compute hierarchical k-means clustering
res.hk <-hkmeans(df, 4)

# Elements returned by hkmeans()
names(res.hk)

# Print the results
res.hk

# Visualize the tree
hkmeans_tree(res.hk, cex = 0.6)
# or use this
fviz_dend(res.hk, cex = 0.6)


# Visualize the hkmeans final clusters
fviz_cluster(res.hk, ellipse.type = "norm", ellipse.level = 0.68)

House tasks contingency table

Description

A data frame containing the frequency of execution of 13 house tasks in the couple. This table is also available in ade4 package.

Usage

data("housetasks")

Format

A data frame with 13 observations (house tasks) on the following 4 columns.

Wife

a numeric vector

Alternating

a numeric vector

Husband

a numeric vector

Jointly

a numeric vector

Source

This data is from FactoMineR package.

Examples

library(FactoMineR)
data(housetasks)
res.ca <- CA(housetasks, graph=FALSE)
fviz_ca_biplot(res.ca, repel = TRUE)+
theme_minimal()

Map legacy FactoMineR category names to current labels

Description

Map legacy FactoMineR category names to current labels

Usage

map_factominer_legacy_names(
  X,
  names,
  element = c("quali.var", "quali.sup", "var"),
  quiet = FALSE
)

Arguments

Value

Character vector of mapped labels.

Examples

if (requireNamespace("FactoMineR", quietly = TRUE)) {
  data(poison)
  res.mca <- FactoMineR::MCA(poison, quanti.sup = 1:2, quali.sup = 3:4, graph = FALSE)
  map <- factominer_category_map(res.mca, element = "var")
  map_factominer_legacy_names(res.mca, map$legacy_underscore[1:3], element = "var", quiet = TRUE)
}

A dataset containing clusters of multiple shapes

Description

Data containing clusters of any shapes. Useful for comparing density-based clustering (DBSCAN) and standard partitioning methods such as k-means clustering.

Usage

data("multishapes")

Format

A data frame with 1100 observations on the following 3 variables.

x

a numeric vector containing the x coordinates of observations

y

a numeric vector containing the y coordinates of observations

shape

a numeric vector corresponding to the cluster number of each observation.

Details

The dataset contains 5 clusters and some outliers/noises.

Examples

data(multishapes)
plot(multishapes[,1], multishapes[, 2],
    col = multishapes[, 3], pch = 19, cex = 0.8)

Poison

Description

This data is a result from a survey carried out on children of primary school who suffered from food poisoning. They were asked about their symptoms and about what they ate.

Usage

data("poison")

Format

A data frame with 55 rows and 15 columns.

Source

This data is from FactoMineR package.

Examples

library(FactoMineR)
data(poison)
res.mca <- MCA(poison, quanti.sup = 1:2, quali.sup = c(3,4), 
   graph = FALSE)
fviz_mca_biplot(res.mca, repel = TRUE)+
theme_minimal()

Print method for an object of class factoextra

Description

Print method for an object of class factoextra

Usage

## S3 method for class 'factoextra'
print(x, ...)

Arguments

Author(s)

Alboukadel Kassambara alboukadel.kassambara@gmail.com

Examples

 data(iris)
 res.pca <- prcomp(iris[, -5],  scale = TRUE)
 ind <- get_pca_ind(res.pca)
 print(ind)
 

A clean publication theme for factoextra plots

Description

A ggplot2 theme tuned for the dimension-reduction scatter plots and biplots produced by the fviz_*() functions: a light, unobtrusive coordinate grid (so points can be read against the axes), a clean background, and de-emphasized axis lines. Pass it through the ggtheme argument, e.g. fviz_pca_ind(res, ggtheme = theme_factoextra()), or add it to any returned plot with + theme_factoextra().

Read more: ggplot2 Themes in R: Customize the Look.

Usage

theme_factoextra(base_size = 12, base_family = "")

Arguments

Details

The fviz_* functions have different default themes (fviz_pca_* use theme_minimal(), fviz_cluster() uses theme_grey(), fviz_dend() uses theme_classic(), ...). For one consistent look across several plots in the same document, pass ggtheme = theme_factoextra() to each call (see the last example) rather than relying on ggplot2::theme_set(), which the fviz_* functions override with their explicit ggtheme default.

Value

A ggplot2 theme object.

See Also

factoextra_palette. Online tutorial: ggplot2 Themes in R: Customize the Look.

Examples

data(iris)
res.pca <- prcomp(iris[, 1:4], scale. = TRUE)
fviz_pca_ind(res.pca, habillage = iris$Species,
             palette = factoextra_palette("okabe"),
             ggtheme = theme_factoextra())

# or add it to an existing plot
fviz_pca_var(res.pca) + theme_factoextra()

# a consistent look across the family: pass the same ggtheme to each call
km <- kmeans(scale(iris[, 1:4]), 3)
fviz_pca_ind(res.pca, ggtheme = theme_factoextra())
fviz_cluster(km, data = iris[, 1:4], ggtheme = theme_factoextra())