Package 'factoextra'

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 the next version.

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

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

• get_hmfa_var_quali(). 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

res.mfa	an object of class MFA [FactoMineR].
X	an object of class MFA or HMFA [FactoMineR].
...	Other arguments.
res.hmfa	an object of class HMFA [FactoMineR].

Author(s)

Alboukadel Kassambara [email protected]

---

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: STHDA website - clarifying distance measures..

• 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

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

x	a numeric matrix or a data frame.
method	the distance measure to be used. This must be one of "euclidean", "maximum", "manhattan", "canberra", "binary", "minkowski", "pearson", "spearman" or "kendall".
stand	logical value; default is FALSE. If TRUE, then the data will be standardized using the function scale(). Measurements are standardized for each variable (column), by subtracting the variable's mean value and dividing by the variable's standard deviation.
...	other arguments to be passed to the function dist() when using get_dist().
dist.obj	an object of class "dist" as generated by the function dist() or get_dist().
order	logical value. if TRUE the ordered dissimilarity image (ODI) is shown.
show_labels	logical value. If TRUE, the labels are displayed.
lab_size	the size of labels.
gradient	a list containing three elements specifying the colors for low, mid and high values in the ordered dissimilarity image. The element "mid" can take the value of NULL.

Value

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

• fviz_dist(): returns a ggplot2

Author(s)

Alboukadel Kassambara [email protected]

See Also

dist

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 solution for enhancing the workflow of clustering analyses and ggplot2-based elegant data visualization. Read more: Visual enhancement of clustering analysis.

Usage

eclust(
  x,
  FUNcluster = c("kmeans", "pam", "clara", "fanny", "hclust", "agnes", "diana"),
  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

x	numeric vector, data matrix or data frame
FUNcluster	a clustering function including "kmeans", "pam", "clara", "fanny", "hclust", "agnes" and "diana". Abbreviation is allowed.
k	the number of clusters to be generated. If NULL, the gap statistic is used to estimate the appropriate number of clusters. In the case of kmeans, k can be either the number of clusters, or a set of initial (distinct) cluster centers.
k.max	the maximum number of clusters to consider, must be at least two.
stand	logical value; default is FALSE. If TRUE, then the data will be standardized using the function scale(). Measurements are standardized for each variable (column), by subtracting the variable's mean value and dividing by the variable's standard deviation.
graph	logical value. If TRUE, cluster plot is displayed.
hc_metric	character string specifying the metric to be used for calculating dissimilarities between observations. Allowed values are those accepted by the function dist() [including "euclidean", "manhattan", "maximum", "canberra", "binary", "minkowski"] and correlation based distance measures ["pearson", "spearman" or "kendall"]. Used only when FUNcluster is a hierarchical clustering function such as one of "hclust", "agnes" or "diana".
hc_method	the agglomeration method to be used (?hclust): "ward.D", "ward.D2", "single", "complete", "average", ...
gap_maxSE	a list containing the parameters (method and SE.factor) for determining the location of the maximum of the gap statistic (Read the documentation ?cluster::maxSE).
nboot	integer, number of Monte Carlo ("bootstrap") samples. Used only for determining the number of clusters using gap statistic.
verbose	logical value. If TRUE, the result of progress is printed.
seed	integer used for seeding the random number generator.
...	other arguments to be passed to FUNcluster.

Value

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

It includes also:

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

• nbclust: the number of clusters

• silinfo: the silhouette information of observations, 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 method for fviz_silhouette(), fviz_dend(), fviz_cluster().

Author(s)

Alboukadel Kassambara [email protected]

See Also

fviz_silhouette, fviz_dend, fviz_cluster

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) # dendrogam
  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.

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(),
  ...
)

fviz_screeplot(...)

Arguments

X	an object of class PCA, CA, MCA, FAMD, MFA and HMFA [FactoMineR]; prcomp and princomp [stats]; dudi, pca, coa and acm [ade4]; ca and mjca [ca package].
choice	a text specifying the data to be plotted. Allowed values are "variance" or "eigenvalue".
geom	a text specifying the geometry to be used for the graph. Allowed values are "bar" for barplot, "line" for lineplot or c("bar", "line") to use both types.
barfill	fill color for bar plot.
barcolor	outline color for bar plot.
linecolor	color for line plot (when geom contains "line").
ncp	a numeric value specifying the number of dimensions to be shown.
addlabels	logical value. If TRUE, labels are added at the top of bars or points showing the information retained by each dimension.
hjust	horizontal adjustment of the labels.
main, xlab, ylab	plot main and axis titles.
ggtheme	function, ggplot2 theme name. Default value is theme_pubr(). Allowed values include ggplot2 official themes: theme_gray(), theme_bw(), theme_minimal(), theme_classic(), theme_void(), ....
...	optional arguments to be passed to the function ggpar.

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 [email protected]

References

http://www.sthda.com/english/

See Also

fviz_pca, fviz_ca, fviz_mca, fviz_mfa, fviz_hmfa

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")
 
## 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.

Usage

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

Arguments

X	an object of class PCA, CA, MCA, FAMD, MFA and HMFA [FactoMineR]; prcomp and princomp [stats]; dudi, pca, coa and acm [ade4]; ca [ca package]; expoOutput [ExPosition].
element	the element to subset from the output. Possible values are "row" or "col" for CA; "var" or "ind" for PCA and MCA; "mca.cor" for MCA; 'quanti.var', 'quali.var' , 'group' or 'ind' for FAMD, MFA and HMFA.
node.level	a single number indicating the HMFA node level.
group.names	a vector containing the name of the groups (by default, NULL and the group are named group.1, group.2 and so on).
result	the result to be extracted for the element. Possible values are the combination of c("cos2", "contrib", "coord")
axes	a numeric vector specifying the axes of interest. Default values are 1:2 for axes 1 and 2.
select	a selection of variables. Allowed values are NULL or a list containing the arguments name, cos2 or contrib. Default is list(name = NULL, cos2 = NULL, contrib = NULL): name: is a character vector containing variable names to be selected cos2: if cos2 is in [0, 1], ex: 0.6, then variables with a cos2 > 0.6 are selected. if cos2 > 1, ex: 5, then the top 5 variables with the highest cos2 are selected contrib: if contrib > 1, ex: 5, then the top 5 variables with the highest cos2 are selected.

Details

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

Value

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

Author(s)

Alboukadel Kassambara [email protected]

References

http://www.sthda.com/english/

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)

# 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 categorcial 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)

---

Visualizing Multivariate Analyse Outputs

Description

Generic function to create a scatter plot of multivariate analyse 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,
  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,
  ggtheme = theme_minimal(),
  ggp = NULL,
  font.family = "",
  ...
)

Arguments

X	an object of class PCA, CA, MCA, FAMD, MFA and HMFA [FactoMineR]; prcomp and princomp [stats]; dudi, pca, coa and acm [ade4]; ca [ca package]; expoOutput [ExPosition].
element	the element to subset from the output. Possible values are "row" or "col" for CA; "var" or "ind" for PCA and MCA; "mca.cor" for MCA; 'quanti.var', 'quali.var' , 'group' or 'ind' for FAMD, MFA and HMFA.
axes	a numeric vector specifying the axes of interest. Default values are 1:2 for axes 1 and 2.
geom	a text specifying the geometry to be used for the graph. Default value is "auto". Allowed values are the combination of c("point", "arrow", "text"). Use "point" (to show only points); "text" to show only labels; c("point", "text") or c("arrow", "text") to show both types.
label	a text specifying the elements to be labelled. Default value is "all". Allowed values are "none" or the combination of c("ind", "ind.sup", "quali", "var", "quanti.sup", "group.sup"). "ind" can be used to label only active individuals. "ind.sup" is for supplementary individuals. "quali" is for supplementary qualitative variables. "var" is for active variables. "quanti.sup" is for quantitative supplementary variables.
invisible	a text specifying the elements to be hidden on the plot. Default value is "none". Allowed values are the combination of c("ind", "ind.sup", "quali", "var", "quanti.sup", "group.sup").
labelsize	font size for the labels
pointsize	the size of points
pointshape	the shape of points
arrowsize	the size of arrows. Controls the thickness of arrows.
habillage	an optional factor variable for coloring the observations by groups. Default value is "none". If X is a PCA object from FactoMineR package, habillage can also specify the supplementary qualitative variable (by its index or name) to be used for coloring individuals by groups (see ?PCA in FactoMineR).
addEllipses	logical value. If TRUE, draws ellipses around the individuals when habillage != "none".
ellipse.level	the size of the concentration ellipse in normal probability.
ellipse.type	Character specifying frame type. Possible values are "convex", "confidence" or types supported by stat_ellipse() including one of c("t", "norm", "euclid") for plotting concentration ellipses. "convex": plot convex hull of a set o points. "confidence": plot confidence ellipses arround group mean points as coord.ellipse()[in FactoMineR]. "t": assumes a multivariate t-distribution. "norm": assumes a multivariate normal distribution. "euclid": draws a circle with the radius equal to level, representing the euclidean distance from the center. This ellipse probably won't appear circular unless coord_fixed() is applied.
ellipse.alpha	Alpha for ellipse specifying the transparency level of fill color. Use alpha = 0 for no fill color.
mean.point	logical value. If TRUE (default), group mean points are added to the plot.
color	color to be used for the specified geometries (point, text). Can be a continuous variable or a factor variable. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the colors for individuals/variables are automatically controlled by their qualities of representation ("cos2"), contributions ("contrib"), coordinates (x^2+y^2, "coord"), x values ("x") or y values ("y"). To use automatic coloring (by cos2, contrib, ....), make sure that habillage ="none".
fill	same as the argument color, but for point fill color. Useful when pointshape = 21, for example.
alpha	controls the transparency of individual and variable colors, respectively. The value can variate from 0 (total transparency) to 1 (no transparency). Default value is 1. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the transparency for the individual/variable colors are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2+y^2, "coord"), x values("x") or y values("y"). To use this, make sure that habillage ="none".
gradient.cols	vector of colors to use for n-colour gradient. Allowed values include brewer and ggsci color palettes.
col.col.sup, col.row.sup	colors for the supplementary column and row points, respectively.
select	a selection of individuals/variables to be drawn. Allowed values are NULL or a list containing the arguments name, cos2 or contrib: name: is a character vector containing individuals/variables to be drawn cos2: if cos2 is in [0, 1], ex: 0.6, then individuals/variables with a cos2 > 0.6 are drawn. if cos2 > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn. contrib: if contrib > 1, ex: 5, then the top 5 individuals/variables with the highest contrib are drawn
title	the title of the graph
axes.linetype	linetype of x and y axes.
repel	a boolean, whether to use ggrepel to avoid overplotting text labels or not.
col.circle	a color for the correlation circle. Used only when X is a PCA output.
circlesize	the size of the variable correlation circle.
ggtheme	function, ggplot2 theme name. Default value is theme_pubr(). Allowed values include ggplot2 official themes: theme_gray(), theme_bw(), theme_minimal(), theme_classic(), theme_void(), ....
ggp	a ggplot. If not NULL, points are added to an existing plot.
font.family	character vector specifying font family.
...	Arguments to be passed to the functions ggpubr::ggscatter() & ggpubr::ggpar().

Value

a ggplot

Author(s)

Alboukadel Kassambara [email protected]

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

ggp	a ggplot2 plot.
df	a data frame containing the x and y coordinates
axes	a numeric vector of length 2 specifying the components to be plotted.
geom	a character specifying the geometry to be used for the graph Allowed values are "point" or "arrow" or "text"
color	the color to be used
addlabel	a logical value. If TRUE, labels are added
labelsize	the size of labels. Default value is 4
pointsize	the size of points
shape	point shape when geom ="point"
linetype	the linetype to be used when geom ="arrow"
repel	a boolean, whether to use ggrepel to avoid overplotting text labels or not.
font.family	character vector specifying font family.
...	Additional arguments, not used

Value

a ggplot2 plot

Author(s)

Alboukadel Kassambara [email protected]

References

http://www.sthda.com

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 expOutput/epCA [in ExPosition]. Read more: Correspondence Analysis

• 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

X	an object of class CA [FactoMineR], ca [ca], coa [ade4]; correspondence [MASS] and expOutput/epCA [ExPosition].
axes	a numeric vector of length 2 specifying the dimensions to be plotted.
geom	a character specifying the geometry to be used for the graph. Allowed values are the combination of c("point", "arrow", "text"). Use "point" (to show only points); "text" to show only labels; c("point", "text") or c("arrow", "text") to show both types.
geom.row, geom.col	as geom but for row and column elements, respectively. Default is geom.row = c("point", "text), geom.col = c("point", "text").
shape.row, shape.col	the point shapes to be used for row/column variables. Default values are 19 for rows and 17 for columns.
map	character string specifying the map type. Allowed options include: "symmetric", "rowprincipal", "colprincipal", "symbiplot", "rowgab", "colgab", "rowgreen" and "colgreen". See details
repel	a boolean, whether to use ggrepel to avoid overplotting text labels or not.
...	Additional arguments. in fviz_ca_row() and fviz_ca_col(): Additional arguments are passed to the functions fviz() and ggpubr::ggpar(). in fviz_ca_biplot() and fviz_ca(): Additional arguments are passed to fviz_ca_row() and fviz_ca_col().
col.col, col.row	color for column/row points. The default values are "red" and "blue", respectively. Can be a continuous variable or a factor variable. Allowed values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the colors for row/column variables are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2 + y^2, "coord"), x values("x") or y values("y")
col.col.sup, col.row.sup	colors for the supplementary column and row points, respectively.
alpha.col, alpha.row	controls the transparency of colors. The value can variate from 0 (total transparency) to 1 (no transparency). Default value is 1. Allowed values include also : "cos2", "contrib", "coord", "x" or "y" as for the arguments col.col and col.row.
select.col, select.row	a selection of columns/rows to be drawn. Allowed values are NULL or a list containing the arguments name, cos2 or contrib: name is a character vector containing column/row names to be drawn cos2 if cos2 is in [0, 1], ex: 0.6, then columns/rows with a cos2 > 0.6 are drawn. if cos2 > 1, ex: 5, then the top 5 columns/rows with the highest cos2 are drawn. contrib if contrib > 1, ex: 5, then the top 5 columns/rows with the highest contrib are drawn
label	a character vector specifying the elements to be labelled. Default value is "all". Allowed values are "none" or the combination of c("row", "row.sup", "col", "col.sup"). Use "col" to label only active column variables; "col.sup" to label only supplementary columns; etc
invisible	a character value specifying the elements to be hidden on the plot. Default value is "none". Allowed values are the combination of c("row", "row.sup","col", "col.sup").
arrows	Vector of two logicals specifying if the plot should contain points (FALSE, default) or arrows (TRUE). First value sets the rows and the second value sets the columns.
title	the title of the graph

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 [email protected]

References

http://www.sthda.com

See Also

get_ca, fviz_pca, fviz_mca

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

# Asymetric biplot, use arrows for columns
fviz_ca_biplot(res.ca, map ="rowprincipal",
 arrow = c(FALSE, TRUE))
 
# Keep only the labels for row points
fviz_ca_biplot(res.ca, label ="row")

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

       
# 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.

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(),
  ...
)

Arguments

object	an object of class "partition" created by the functions pam(), clara() or fanny() in cluster package; "kmeans" [in stats package]; "dbscan" [in fpc package]; "Mclust" [in mclust]; "hkmeans", "eclust" [in factoextra]. Possible value are also any list object with data and cluster components (e.g.: object = list(data = mydata, cluster = myclust)).
data	the data that has been used for clustering. Required only when object is a class of kmeans or dbscan.
choose.vars	a character vector containing variables to be considered for plotting.
stand	logical value; if TRUE, data is standardized before principal component analysis
axes	a numeric vector of length 2 specifying the dimensions to be plotted.
geom	a text specifying the geometry to be used for the graph. Allowed values are the combination of c("point", "text"). Use "point" (to show only points); "text" to show only labels; c("point", "text") to show both types.
repel	a boolean, whether to use ggrepel to avoid overplotting text labels or not.
show.clust.cent	logical; if TRUE, shows cluster centers
ellipse	logical value; if TRUE, draws outline around points of each cluster
ellipse.type	Character specifying frame type. Possible values are 'convex', 'confidence' or types supported by stat_ellipse including one of c("t", "norm", "euclid").
ellipse.level	the size of the concentration ellipse in normal probability. Passed for ggplot2::stat_ellipse 's level. Ignored in 'convex'. Default value is 0.95.
ellipse.alpha	Alpha for frame specifying the transparency level of fill color. Use alpha = 0 for no fill color.
shape	the shape of points.
pointsize	the size of points
labelsize	font size for the labels
main	plot main title.
xlab, ylab	character vector specifying x and y axis labels, respectively. Use xlab = FALSE and ylab = FALSE to hide xlab and ylab, respectively.
outlier.pointsize, outlier.color, outlier.shape, outlier.labelsize	arguments for customizing outliers, which can be detected only in DBSCAN clustering.
ggtheme	function, ggplot2 theme name. Default value is theme_pubr(). Allowed values include ggplot2 official themes: theme_gray(), theme_bw(), theme_minimal(), theme_classic(), theme_void(), ....
...	other arguments to be passed to the functions ggscatter and ggpar.

Value

return a ggpplot.

Author(s)

Alboukadel Kassambara [email protected]

See Also

fviz_silhouette, hcut, hkmeans, eclust, fviz_dend

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

# 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 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.

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(),
  ...
)

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

Arguments

X	an object of class PCA, CA, MCA, FAMD, MFA and HMFA [FactoMineR]; prcomp and princomp [stats]; dudi, pca, coa and acm [ade4]; ca [ca package].
choice	allowed values are "row" and "col" for CA; "var" and "ind" for PCA or MCA; "var", "ind", "quanti.var", "quali.var" and "group" for FAMD, MFA and HMFA.
axes	a numeric vector specifying the dimension(s) of interest.
fill	a fill color for the bar plot.
color	an outline color for the bar plot.
sort.val	a string specifying whether the value should be sorted. Allowed values are "none" (no sorting), "asc" (for ascending) or "desc" (for descending).
top	a numeric value specifying the number of top elements to be shown.
xtickslab.rt	Same as x.text.angle and y.text.angle, respectively. Will be deprecated in the near future.
ggtheme	function, ggplot2 theme name. Default value is theme_pubr(). Allowed values include ggplot2 official themes: theme_gray(), theme_bw(), theme_minimal(), theme_classic(), theme_void(), ....
...	other arguments to be passed to the function ggpar.
sortcontrib	see the argument sort.val

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 where 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 [email protected]

References

http://www.sthda.com/english/

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)

# 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 categorie 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 catecorical variable categorie 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.

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(),
  ...
)

Arguments

X	an object of class PCA, CA, MCA, FAMD, MFA and HMFA [FactoMineR]; prcomp and princomp [stats]; dudi, pca, coa and acm [ade4]; ca [ca package].
choice	allowed values are "row" and "col" for CA; "var" and "ind" for PCA or MCA; "var", "ind", "quanti.var", "quali.var" and "group" for FAMD, MFA and HMFA.
axes	a numeric vector specifying the dimension(s) of interest.
fill	a fill color for the bar plot.
color	an outline color for the bar plot.
sort.val	a string specifying whether the value should be sorted. Allowed values are "none" (no sorting), "asc" (for ascending) or "desc" (for descending).
top	a numeric value specifying the number of top elements to be shown.
xtickslab.rt	Same as x.text.angle and y.text.angle, respectively. Will be deprecated in the near future.
ggtheme	function, ggplot2 theme name. Default value is theme_pubr(). Allowed values include ggplot2 official themes: theme_gray(), theme_bw(), theme_minimal(), theme_classic(), theme_void(), ....
...	not used

Value

a ggplot

Author(s)

Alboukadel Kassambara [email protected]

References

http://www.sthda.com/english/

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)

# 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 categorie 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 catecorical variable categorie 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. Provides also an option for drawing a circular dendrogram and phylogenic trees.

Usage

fviz_dend(
  x,
  k = NULL,
  h = NULL,
  k_colors = NULL,
  palette = NULL,
  show_labels = TRUE,
  color_labels_by_k = TRUE,
  label_cols = NULL,
  labels_track_height = NULL,
  repel = FALSE,
  lwd = 0.7,
  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

x	an object of class dendrogram, hclust, agnes, diana, hcut, hkmeans or HCPC (FactoMineR).
k	the number of groups for cutting the tree.
h	a numeric value. Cut the dendrogram by cutting at height h. (k overrides h)
k_colors, palette	a vector containing colors to be used for the groups. It should contains k number of colors. Allowed values include also "grey" for grey color palettes; brewer palettes e.g. "RdBu", "Blues", ...; and scientific journal palettes from ggsci R package, e.g.: "npg", "aaas", "lancet", "jco", "ucscgb", "uchicago", "simpsons" and "rickandmorty".
show_labels	a logical value. If TRUE, leaf labels are shown. Default value is TRUE.
color_labels_by_k	logical value. If TRUE, labels are colored automatically by group when k != NULL.
label_cols	a vector containing the colors for labels.
labels_track_height	a positive numeric value for adjusting the room for the labels. Used only when type = "rectangle".
repel	logical value. Use repel = TRUE to avoid label overplotting when type = "phylogenic".
lwd	a numeric value specifying branches and rectangle line width.
type	type of plot. Allowed values are one of "rectangle", "triangle", "circular", "phylogenic".
phylo_layout	the layout to be used for phylogenic trees. Default value is "layout.auto". Allowed values include: layout.auto, layout_with_drl, layout_as_tree, layout.gem, layout.mds and layout_with_lgl.
rect	logical value specifying whether to add a rectangle around groups. Used only when k != NULL.
rect_border, rect_lty	border color and line type for rectangles.
rect_fill	a logical value. If TRUE, fill the rectangle.
lower_rect	a value of how low should the lower part of the rectangle around clusters. Ignored when rect = FALSE.
horiz	a logical value. If TRUE, an horizontal dendrogram is drawn.
cex	size of labels
main, xlab, ylab	main and axis titles
sub	Plot subtitle. If NULL, the method used hierarchical clustering is shown. To remove the subtitle use sub = "".
ggtheme	function, ggplot2 theme name. Default value is theme_classic(). Allowed values include ggplot2 official themes: theme_gray(), theme_bw(), theme_minimal(), theme_classic(), theme_void(), ....
...	other arguments to be passed to the function plot.dendrogram()

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().

Examples

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

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

# Default plot
fviz_dend(res.hc)

# 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)

---

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

X	an object of class MCA, PCA or MFA.
habillage	a numeric vector of indexes of variables or a character vector of names of variables. Can be also a data frame containing grouping variables.
axes	a numeric vector specifying the axes of interest. Default values are 1:2 for axes 1 and 2.
addEllipses	logical value. If TRUE, draws ellipses around the individuals when habillage != "none".
ellipse.type	Character specifying frame type. Possible values are "convex", "confidence" or types supported by stat_ellipse() including one of c("t", "norm", "euclid") for plotting concentration ellipses. "convex": plot convex hull of a set o points. "confidence": plot confidence ellipses arround group mean points as coord.ellipse()[in FactoMineR]. "t": assumes a multivariate t-distribution. "norm": assumes a multivariate normal distribution. "euclid": draws a circle with the radius equal to level, representing the euclidean distance from the center. This ellipse probably won't appear circular unless coord_fixed() is applied.
palette	the color palette to be used for coloring or filling by groups. Allowed values include "grey" for grey color palettes; brewer palettes e.g. "RdBu", "Blues", ...; or custom color palette e.g. c("blue", "red"); and scientific journal palettes from ggsci R package, e.g.: "npg", "aaas", "lancet", "jco", "ucscgb", "uchicago", "simpsons" and "rickandmorty". Can be also a numeric vector of length(groups); in this case a basic color palette is created using the function palette.
pointsize	the size of points
geom	a text specifying the geometry to be used for the graph. Allowed values are the combination of c("point", "text"). Use "point" (to show only points); "text" to show only labels; c("point", "text") to show both types.
ggtheme	function, ggplot2 theme name. Default value is theme_pubr(). Allowed values include ggplot2 official themes: theme_gray(), theme_bw(), theme_minimal(), theme_classic(), theme_void(), ....
...	Arguments to be passed to the functions ggpubr::ggscatter() & ggpubr::ggpar().

Value

a ggplot

Author(s)

Alboukadel Kassambara [email protected]

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, 1:4, 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)

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"),
  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

X	an object of class FAMD [FactoMineR].
axes	a numeric vector of length 2 specifying the dimensions to be plotted.
geom	a text specifying the geometry to be used for the graph. Allowed values are the combination of c("point", "arrow", "text"). Use "point" (to show only points); "text" to show only labels; c("point", "text") or c("arrow", "text") to show arrows and texts. Using c("arrow", "text") is sensible only for the graph of variables.
repel	a boolean, whether to use ggrepel to avoid overplotting text labels or not.
habillage	an optional factor variable for coloring the observations by groups. Default value is "none". If X is an MFA object from FactoMineR package, habillage can also specify the index of the factor variable in the data.
palette	the color palette to be used for coloring or filling by groups. Allowed values include "grey" for grey color palettes; brewer palettes e.g. "RdBu", "Blues", ...; or custom color palette e.g. c("blue", "red"); and scientific journal palettes from ggsci R package, e.g.: "npg", "aaas", "lancet", "jco", "ucscgb", "uchicago", "simpsons" and "rickandmorty". Can be also a numeric vector of length(groups); in this case a basic color palette is created using the function palette.
addEllipses	logical value. If TRUE, draws ellipses around the individuals when habillage != "none".
col.ind, col.var	color for individuals and variables, respectively. Can be a continuous variable or a factor variable. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the colors for individuals/variables are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2 + y^2 , "coord"), x values("x") or y values("y"). To use automatic coloring (by cos2, contrib, ....), make sure that habillage ="none".
col.ind.sup	color for supplementary individuals
alpha.ind, alpha.var	controls the transparency of individuals and variables, respectively. The value can variate from 0 (total transparency) to 1 (no transparency). Default value is 1. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the transparency for individual/variable colors are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2 + y^2 , "coord"), x values("x") or y values("y"). To use this, make sure that habillage ="none".
shape.ind, shape.var	point shapes of individuals, variables, groups and axes
col.quali.var	color for qualitative variables in fviz_mfa_ind(). Default is "black".
select.ind, select.var	a selection of individuals and variables to be drawn. Allowed values are NULL or a list containing the arguments name, cos2 or contrib: name is a character vector containing individuals/variables to be drawn cos2 if cos2 is in [0, 1], ex: 0.6, then individuals/variables with a cos2 > 0.6 are drawn. if cos2 > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn. contrib if contrib > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn
gradient.cols	vector of colors to use for n-colour gradient. Allowed values include brewer and ggsci color palettes.
...	Arguments to be passed to the function fviz()
choice	The graph to plot inf fviz_mfa_var(). Allowed values include one of c("var", quanti.var", "quali.var").
col.var.sup	color for supplementary variables.

Value

a ggplot

Author(s)

Alboukadel Kassambara [email protected]

Examples

# Compute FAMD
 library("FactoMineR")
 data(wine)
 res.famd <- FAMD(wine[,c(1,2, 16, 22, 29, 28, 30,31)], 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")
# 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()

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

X	an object of class HMFA [FactoMineR].
axes	a numeric vector of length 2 specifying the dimensions to be plotted.
geom	a text specifying the geometry to be used for the graph. Allowed values are the combination of c("point", "arrow", "text"). Use "point" (to show only points); "text" to show only labels; c("point", "text") or c("arrow", "text") to show arrows and texts. Using c("arrow", "text") is sensible only for the graph of variables.
repel	a boolean, whether to use ggrepel to avoid overplotting text labels or not.
habillage	an optional factor variable for coloring the observations by groups. Default value is "none". If X is an HMFA object from FactoMineR package, habillage can also specify the index of the factor variable in the data.
addEllipses	logical value. If TRUE, draws ellipses around the individuals when habillage != "none".
shape.ind, shape.var	point shapes of individuals and variables, respectively.
col.ind, col.var	color for individuals, partial individuals and variables, respectively. Can be a continuous variable or a factor variable. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the colors for individuals/variables are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2 + y^2 , "coord"), x values("x") or y values("y"). To use automatic coloring (by cos2, contrib, ....), make sure that habillage ="none".
col.ind.sup	color for supplementary individuals
alpha.ind, alpha.var	controls the transparency of individual, partial individual and variable, respectively. The value can variate from 0 (total transparency) to 1 (no transparency). Default value is 1. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the transparency for individual/variable colors are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2 + y^2 , "coord"), x values("x") or y values("y"). To use this, make sure that habillage ="none".
select.ind, select.var	a selection of individuals and variables to be drawn. Allowed values are NULL or a list containing the arguments name, cos2 or contrib: name is a character vector containing individuals/variables to be drawn cos2 if cos2 is in [0, 1], ex: 0.6, then individuals/variables with a cos2 > 0.6 are drawn. if cos2 > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn. contrib if contrib > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn
partial	list of the individuals for which the partial points should be drawn. (by default, partial = NULL and no partial points are drawn). Use partial = "All" to visualize partial points for all individuals.
col.partial	color for partial individuals. By default, points are colored according to the groups.
group.names	a vector containing the name of the groups (by default, NULL and the group are named group.1, group.2 and so on).
node.level	a single number indicating the HMFA node level to plot.
...	Arguments to be passed to the function fviz() and ggpubr::ggpar()
choice	the graph to plot. Allowed values include one of c("quanti.var", "quali.var", "group") for plotting quantitative variables, qualitative variables and group of variables, respectively.
col.var.sup	color for supplementary variables.
title	the title of the graph

Value

a ggplot

Author(s)

Fabian Mundt [email protected]

Alboukadel Kassambara [email protected]

References

http://www.sthda.com/english/

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", palette = "Dark2")

---

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 expOutput/epMCA [in ExPosition]. Read more: Multiple Correspondence Analysis Essentials.

• 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),
  ...
)

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",
  ...
)

fviz_mca(X, ...)

Arguments

X	an object of class MCA [FactoMineR], acm [ade4] and expOutput/epMCA [ExPosition].
axes	a numeric vector of length 2 specifying the dimensions to be plotted.
geom	a text specifying the geometry to be used for the graph. Allowed values are the combination of c("point", "arrow", "text"). Use "point" (to show only points); "text" to show only labels; c("point", "text") or c("arrow", "text") to show arrows and texts. Using c("arrow", "text") is sensible only for the graph of variables.
geom.ind, geom.var	as geom but for individuals and variables, respectively. Default is geom.ind = c("point", "text), geom.var = c("point", "text").
repel	a boolean, whether to use ggrepel to avoid overplotting text labels or not.
habillage	an optional factor variable for coloring the observations by groups. Default value is "none". If X is an MCA object from FactoMineR package, habillage can also specify the index of the factor variable in the data.
palette	the color palette to be used for coloring or filling by groups. Allowed values include "grey" for grey color palettes; brewer palettes e.g. "RdBu", "Blues", ...; or custom color palette e.g. c("blue", "red"); and scientific journal palettes from ggsci R package, e.g.: "npg", "aaas", "lancet", "jco", "ucscgb", "uchicago", "simpsons" and "rickandmorty". Can be also a numeric vector of length(groups); in this case a basic color palette is created using the function palette.
addEllipses	logical value. If TRUE, draws ellipses around the individuals when habillage != "none".
col.ind, col.var	color for individuals and variables, respectively. Can be a continuous variable or a factor variable. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the colors for individuals/variables are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2 + y^2 , "coord"), x values("x") or y values("y"). To use automatic coloring (by cos2, contrib, ....), make sure that habillage ="none".
col.ind.sup	color for supplementary individuals
alpha.ind, alpha.var	controls the transparency of individual and variable colors, respectively. The value can variate from 0 (total transparency) to 1 (no transparency). Default value is 1. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the transparency for individual/variable colors are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2 + y^2 , "coord"), x values("x") or y values("y"). To use this, make sure that habillage ="none".
shape.ind, shape.var	point shapes of individuals and variables.
map	character string specifying the map type. Allowed options include: "symmetric", "rowprincipal", "colprincipal", "symbiplot", "rowgab", "colgab", "rowgreen" and "colgreen". See details
select.ind, select.var	a selection of individuals/variables to be drawn. Allowed values are NULL or a list containing the arguments name, cos2 or contrib: name is a character vector containing individuals/variables to be drawn cos2 if cos2 is in [0, 1], ex: 0.6, then individuals/variables with a cos2 > 0.6 are drawn. if cos2 > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn. contrib if contrib > 1, ex: 5, then the top 5 individuals/variables with the highest contrib are drawn
...	Additional arguments. in fviz_mca_ind(), fviz_mca_var() and fviz_mca_cor(): Additional arguments are passed to the functions fviz() and ggpubr::ggpar(). in fviz_mca_biplot() and fviz_mca(): Additional arguments are passed to fviz_mca_ind() and fviz_mca_var().
choice	the graph to plot. Allowed values include: i) "var" and "mca.cor" for plotting the correlation between variables and principal dimensions; ii) "var.cat" for variable categories and iii) "quanti.sup" for the supplementary quantitative variables.
col.quanti.sup, col.quali.sup	a color for the quantitative/qualitative supplementary variables.
label	a text specifying the elements to be labelled. Default value is "all". Allowed values are "none" or the combination of c("ind", "ind.sup","var", "quali.sup", "quanti.sup"). "ind" can be used to label only active individuals. "ind.sup" is for supplementary individuals. "var" is for active variable categories. "quali.sup" is for supplementary qualitative variable categories. "quanti.sup" is for quantitative supplementary variables.
invisible	a text specifying the elements to be hidden on the plot. Default value is "none". Allowed values are the combination of c("ind", "ind.sup","var", "quali.sup", "quanti.sup").
arrows	Vector of two logicals specifying if the plot should contain points (FALSE, default) or arrows (TRUE). First value sets the rows and the second value sets the columns.
title	the title of the graph

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.

Value

a ggplot

Author(s)

Alboukadel Kassambara [email protected]

See Also

get_mca, fviz_pca, fviz_ca, fviz_mfa, fviz_hmfa

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: http://www.sthda.com/english/wiki/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)
      
    
# Change group colors using RColorBrewer color palettes
# Read more: http://www.sthda.com/english/wiki/ggplot2-colors
p + scale_color_brewer(palette="Dark2") +
    scale_fill_brewer(palette="Dark2") 
     
# Change group colors manually
# Read more: http://www.sthda.com/english/wiki/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.

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

object	an object of class Mclust
what	choose from one of the following three options: "classification" (default), "uncertainty" and "BIC".
ellipse.type	Character specifying frame type. Possible values are 'convex', 'confidence' or types supported by stat_ellipse including one of c("t", "norm", "euclid").
ellipse.level	the size of the concentration ellipse in normal probability. Passed for ggplot2::stat_ellipse 's level. Ignored in 'convex'. Default value is 0.95.
ggtheme	function, ggplot2 theme name. Default value is theme_pubr(). Allowed values include ggplot2 official themes: theme_gray(), theme_bw(), theme_minimal(), theme_classic(), theme_void(), ....
...	other arguments to be passed to the functions fviz_cluster and ggpar.
model.names	one or more model names corresponding to models fit in object. The default is to plot the BIC for all of the models fit.
shape	point shape. To change point shape by model names use shape = "model".
color	point and line color.
palette	the color palette to be used for coloring or filling by groups. Allowed values include "grey" for grey color palettes; brewer palettes e.g. "RdBu", "Blues", ...; or custom color palette e.g. c("blue", "red"); and scientific journal palettes from ggsci R package, e.g.: "npg", "aaas", "lancet", "jco", "ucscgb", "uchicago", "simpsons" and "rickandmorty". Can be also a numeric vector of length(groups); in this case a basic color palette is created using the function palette.
legend	character specifying legend position. Allowed values are one of c("top", "bottom", "left", "right", "none"). To remove the legend use legend = "none". Legend position can be also specified using a numeric vector c(x, y); see details section.
main	plot main title.
xlab	character vector specifying x axis labels. Use xlab = FALSE to hide xlab.
ylab	character vector specifying y axis labels. Use ylab = FALSE to hide ylab.

Functions

• fviz_mclust: Plots classification and uncertainty.

• fviz_mclust_bic: Plots the BIC values.

Examples

if(require("mclust")){

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

# Visaulize 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

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 = repel,
  title = "Biplot of individuals and qualitative variables - MFA",
  ...
)

fviz_mfa_var(
  X,
  choice = c("quanti.var", "group", "quali.var"),
  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

X	an object of class MFA [FactoMineR].
axes	a numeric vector of length 2 specifying the dimensions to be plotted.
geom	a text specifying the geometry to be used for the graph. Allowed values are the combination of c("point", "arrow", "text"). Use "point" (to show only points); "text" to show only labels; c("point", "text") or c("arrow", "text") to show arrows and texts. Using c("arrow", "text") is sensible only for the graph of variables.
repel	a boolean, whether to use ggrepel to avoid overplotting text labels or not.
habillage	an optional factor variable for coloring the observations by groups. Default value is "none". If X is an MFA object from FactoMineR package, habillage can also specify the index of the factor variable in the data.
palette	the color palette to be used for coloring or filling by groups. Allowed values include "grey" for grey color palettes; brewer palettes e.g. "RdBu", "Blues", ...; or custom color palette e.g. c("blue", "red"); and scientific journal palettes from ggsci R package, e.g.: "npg", "aaas", "lancet", "jco", "ucscgb", "uchicago", "simpsons" and "rickandmorty". Can be also a numeric vector of length(groups); in this case a basic color palette is created using the function palette.
addEllipses	logical value. If TRUE, draws ellipses around the individuals when habillage != "none".
col.ind, col.var, col.axes	color for individuals, variables and col.axes respectively. Can be a continuous variable or a factor variable. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the colors for individuals/variables are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2 + y^2 , "coord"), x values("x") or y values("y"). To use automatic coloring (by cos2, contrib, ....), make sure that habillage ="none".
col.ind.sup	color for supplementary individuals
alpha.ind, alpha.var, alpha.axes	controls the transparency of individual, variable, group and axes colors, respectively. The value can variate from 0 (total transparency) to 1 (no transparency). Default value is 1. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the transparency for individual/variable colors are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2 + y^2 , "coord"), x values("x") or y values("y"). To use this, make sure that habillage ="none".
shape.ind, shape.var	point shapes of individuals, variables, groups and axes
col.quali.var.sup	color for supplementary qualitative variables. Default is "black".
select.ind, select.var, select.axes	a selection of individuals/partial individuals/ variables/groups/axes to be drawn. Allowed values are NULL or a list containing the arguments name, cos2 or contrib: name is a character vector containing individuals/variables to be drawn cos2 if cos2 is in [0, 1], ex: 0.6, then individuals/variables with a cos2 > 0.6 are drawn. if cos2 > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn. contrib if contrib > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn
partial	list of the individuals for which the partial points should be drawn. (by default, partial = NULL and no partial points are drawn). Use partial = "All" to visualize partial points for all individuals.
col.partial	color for partial individuals. By default, points are colored according to the groups.
...	Arguments to be passed to the function fviz()
title	the title of the graph
choice	the graph to plot. Allowed values include one of c("quanti.var", "quali.var", "group") for plotting quantitative variables, qualitative variables and group of variables, respectively.
col.var.sup	color for supplementary variables.
col.circle	a color for the correlation circle. Used only when X is a PCA output.

Value

a ggplot2 plot

Author(s)

Fabian Mundt [email protected]

Alboukadel Kassambara [email protected]

References

http://www.sthda.com/english/

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 = "all") 
# 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")
 
 

# 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)

---

Dertermining 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(): Dertemines and visualize the optimal number of clusters using different methods: within cluster sums of squares, average silhouette and gap statistics.

• fviz_gap_stat(): Visualize the gap statistic generated by the function clusGap() [in cluster package]. The optimal number of clusters is specified using the "firstmax" method (?cluster::clustGap).

Read more: Determining the optimal number of clusters

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,
  ...
)

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

Arguments

x	numeric matrix or data frame. In the function fviz_nbclust(), x can be the results of the function NbClust().
FUNcluster	a partitioning function which accepts as first argument a (data) matrix like x, second argument, say k, k >= 2, the number of clusters desired, and returns a list with a component named cluster which contains the grouping of observations. Allowed values include: kmeans, cluster::pam, cluster::clara, cluster::fanny, hcut, etc. This argument is not required when x is an output of the function NbClust::NbClust().
method	the method to be used for estimating the optimal number of clusters. Possible values are "silhouette" (for average silhouette width), "wss" (for total within sum of square) and "gap_stat" (for gap statistics).
diss	dist object as produced by dist(), i.e.: diss = dist(x, method = "euclidean"). Used to compute the average silhouette width of clusters, the within sum of square and hierarchical clustering. If NULL, dist(x) is computed with the default method = "euclidean"
k.max	the maximum number of clusters to consider, must be at least two.
nboot	integer, number of Monte Carlo ("bootstrap") samples. Used only for determining the number of clusters using gap statistic.
verbose	logical value. If TRUE, the result of progress is printed.
barfill, barcolor	fill color and outline color for bars
linecolor	color for lines
print.summary	logical value. If true, the optimal number of clusters are printed in fviz_nbclust().
...	optionally further arguments for FUNcluster()
gap_stat	an object of class "clusGap" returned by the function clusGap() [in cluster package]
maxSE	a list containing the parameters (method and SE.factor) for determining the location of the maximum of the gap statistic (Read the documentation ?cluster::maxSE). Allowed values for maxSE$method include: "globalmax": simply corresponds to the global maximum, i.e., is which.max(gap) "firstmax": gives the location of the first local maximum "Tibs2001SEmax": uses the criterion, Tibshirani et al (2001) proposed: "the smallest k such that gap(k) >= gap(k+1) - s_k+1". It's also possible to use "the smallest k such that gap(k) >= gap(k+1) - SE.factor*s_k+1" where SE.factor is a numeric value which can be 1 (default), 2, 3, etc. "firstSEmax": location of the first f() value which is not larger than the first local maximum minus SE.factor * SE.f[], i.e, within an "f S.E." range of that maximum. see ?cluster::maxSE for more options

Value

• fviz_nbclust, fviz_gap_stat: return a ggplot2

Author(s)

Alboukadel Kassambara [email protected]

See Also

fviz_cluster, eclust

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)

# 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 = "firstmax")
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

• 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 arround the core function fviz(), whih is also a wrapper arround the function ggscatter() [in ggpubr]. Therfore, 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,
  select.ind = list(name = NULL, cos2 = NULL, contrib = NULL),
  ...
)

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,
  title = "PCA - Biplot",
  ...
)

Arguments

X	an object of class PCA [FactoMineR]; prcomp and princomp [stats]; dudi and pca [ade4]; expOutput/epPCA [ExPosition].
...	Additional arguments. in fviz_pca_ind() and fviz_pca_var(): Additional arguments are passed to the functions fviz() and ggpubr::ggpar(). in fviz_pca_biplot() and fviz_pca(): Additional arguments are passed to fviz_pca_ind() and fviz_pca_var().
axes	a numeric vector of length 2 specifying the dimensions to be plotted.
geom	a text specifying the geometry to be used for the graph. Allowed values are the combination of c("point", "arrow", "text"). Use "point" (to show only points); "text" to show only labels; c("point", "text") or c("arrow", "text") to show arrows and texts. Using c("arrow", "text") is sensible only for the graph of variables.
geom.ind, geom.var	as geom but for individuals and variables, respectively. Default is geom.ind = c("point", "text), geom.var = c("arrow", "text").
repel	a boolean, whether to use ggrepel to avoid overplotting text labels or not.
habillage	an optional factor variable for coloring the observations by groups. Default value is "none". If X is a PCA object from FactoMineR package, habillage can also specify the supplementary qualitative variable (by its index or name) to be used for coloring individuals by groups (see ?PCA in FactoMineR).
palette	the color palette to be used for coloring or filling by groups. Allowed values include "grey" for grey color palettes; brewer palettes e.g. "RdBu", "Blues", ...; or custom color palette e.g. c("blue", "red"); and scientific journal palettes from ggsci R package, e.g.: "npg", "aaas", "lancet", "jco", "ucscgb", "uchicago", "simpsons" and "rickandmorty". Can be also a numeric vector of length(groups); in this case a basic color palette is created using the function palette.
addEllipses	logical value. If TRUE, draws ellipses around the individuals when habillage != "none".
col.ind, col.var	color for individuals and variables, respectively. Can be a continuous variable or a factor variable. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the colors for individuals/variables are automatically controlled by their qualities of representation ("cos2"), contributions ("contrib"), coordinates (x^2+y^2, "coord"), x values ("x") or y values ("y"). To use automatic coloring (by cos2, contrib, ....), make sure that habillage ="none".
fill.ind, fill.var	same as col.ind and col.var but for the fill color.
col.ind.sup	color for supplementary individuals
alpha.ind, alpha.var	controls the transparency of individual and variable colors, respectively. The value can variate from 0 (total transparency) to 1 (no transparency). Default value is 1. Possible values include also : "cos2", "contrib", "coord", "x" or "y". In this case, the transparency for the individual/variable colors are automatically controlled by their qualities ("cos2"), contributions ("contrib"), coordinates (x^2+y^2, "coord"), x values("x") or y values("y"). To use this, make sure that habillage ="none".
select.ind, select.var	a selection of individuals/variables to be drawn. Allowed values are NULL or a list containing the arguments name, cos2 or contrib: name: is a character vector containing individuals/variables to be drawn cos2: if cos2 is in [0, 1], ex: 0.6, then individuals/variables with a cos2 > 0.6 are drawn. if cos2 > 1, ex: 5, then the top 5 individuals/variables with the highest cos2 are drawn. contrib: if contrib > 1, ex: 5, then the top 5 individuals/variables with the highest contrib are drawn
col.quanti.sup	a color for the quantitative supplementary variables.
col.circle	a color for the correlation circle. Used only when X is a PCA output.
gradient.cols	vector of colors to use for n-colour gradient. Allowed values include brewer and ggsci color palettes.
label	a text specifying the elements to be labelled. Default value is "all". Allowed values are "none" or the combination of c("ind", "ind.sup", "quali", "var", "quanti.sup"). "ind" can be used to label only active individuals. "ind.sup" is for supplementary individuals. "quali" is for supplementary qualitative variables. "var" is for active variables. "quanti.sup" is for quantitative supplementary variables.
invisible	a text specifying the elements to be hidden on the plot. Default value is "none". Allowed values are the combination of c("ind", "ind.sup", "quali", "var", "quanti.sup").
title	the title of the graph

Value

a ggplot

Author(s)

Alboukadel Kassambara [email protected]

See Also

fviz_ca, fviz_mca

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: http://www.sthda.com/english/wiki/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: http://www.sthda.com/english/wiki/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: http://www.sthda.com/english/wiki/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))

 
# 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())

---

Visualize Silhouette Information from Clustering

Description

Silhouette (Si) analysis is a cluster validation approach that measures how well an observation is clustered and it estimates the average distance between clusters. fviz_silhouette() provides ggplot2-based elegant visualization of silhouette information from i) the result of silhouette(), pam(), clara() and fanny() [in cluster package]; ii) eclust() and hcut() [in factoextra].

Read more: Clustering Validation Statistics.

Usage

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

Arguments

sil.obj	an object of class silhouette: pam, clara, fanny [in cluster package]; eclust and hcut [in factoextra].
label	logical value. If true, x axis tick labels are shown
print.summary	logical value. If true a summary of cluster silhouettes are printed in fviz_silhouette().
...	other arguments to be passed to the function ggpubr::ggpar().

Details

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

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

- Observations with a negative Si are probably placed in the wrong cluster.

Value

return a ggplot

Author(s)

Alboukadel Kassambara [email protected]

See Also

fviz_cluster, hcut, hkmeans, eclust, fviz_dend

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 silhouhette information
require("cluster")
sil <- 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
# ++++++++++++++++++++
require(cluster)
pam.res <- pam(iris.scaled, 3)
# Visualize pam clustering
fviz_cluster(pam.res, ellipse.type = "norm")+
theme_minimal()
# Visualize silhouhette 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 silhouhette information
fviz_silhouette(hc.cut)

## End(Not run)

---

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

Usage

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

get_ca_col(res.ca)

get_ca_row(res.ca)

Arguments

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

Value

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

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

Author(s)

Alboukadel Kassambara [email protected]

References

http://www.sthda.com

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 cluster methods, the first step is to assess whether the data is clusterable, a process defined as the assessing of clustering tendency. get_clust_tendency() assesses clustering tendency using Hopkins' statistic and a visual approach. An ordered dissimilarity image (ODI) is shown. Objects belonging to the same cluster are displayed in consecutive order using hierarchical clustering. For more details and interpretation, see STHDA website: Assessing clustering tendency.

Usage

get_clust_tendency(
  data,
  n,
  graph = TRUE,
  gradient = list(low = "red", mid = "white", high = "blue"),
  seed = 123
)

Arguments

data	a numeric data frame or matrix. Columns are variables and rows are samples. Computation are done on rows (samples) by default. If you want to calculate Hopkins statistic on variables, transpose the data before.
n	the number of points selected from sample space which is also the number of points selected from the given sample(data).
graph	logical value; if TRUE the ordered dissimilarity image (ODI) is shown.
gradient	a list containing three elements specifying the colors for low, mid and high values in the ordered dissimilarity image. The element "mid" can take the value of NULL.
seed	an integer specifying the seed for random number generator. Specify seed for reproducible results.

Details

Hopkins statistic: If the value of Hopkins statistic is close to 1 (far above 0.5), then we can conclude that the dataset is significantly clusterable.

VAT (Visual Assessment of cluster Tendency): The VAT detects the clustering tendency in a visual form by counting the number of square shaped dark (or colored) blocks along the diagonal in a VAT image.

Value

A list containing the elements:

- hopkins_stat for Hopkins statistic value

- plot for ordered dissimilarity image. This is generated using the function fviz_dist(dist.obj).

Author(s)

Alboukadel Kassambara [email protected]

See Also

fviz_dist

Examples

data(iris)

# 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)

---

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 Date (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

Usage

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

get_famd_ind(res.famd)

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

Arguments

res.famd	an object of class FAMD [FactoMineR].
element	the element to subset from the output. Possible values are "ind", "quanti.var" or "quali.var".

Value

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

coord	coordinates of indiiduals/variables.
cos2	cos2 values representing the quality of representation on the factor map.
contrib	contributions of individuals / variables to the principal components.

Author(s)

Alboukadel Kassambara [email protected]

Examples

# Compute FAMD
 library("FactoMineR")
 data(wine)
 res.famd <- FAMD(wine[,c(1,2, 16, 22, 29, 28, 30,31)], 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 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_mfa_var(): Extract the results for variables (quantitatives, qualitatives and groups)

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

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

res.hmfa	an object of class HMFA [FactoMineR].
element	the element to subset from the output. Possible values are "ind", "quanti.var", "quali.var", "group" or "partial.node".

Value

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

coord	coordinates
cos2	cos2
contrib	contributions

Author(s)

Alboukadel Kassambara [email protected]

Fabian Mundt [email protected]

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

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

res.mca	an object of class MCA [FactoMineR], acm [ade4], expoOutput/epMCA [ExPosition].
element	the element to subset from the output. Possible values are "var" for variables, "ind" for individuals, "mca.cor" for correlation between variables and principal dimensions, "quanti.sup" for quantitative supplementary variables.

Value

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

coord	coordinates for the individuals/variable categories
cos2	cos2 for the individuals/variable categories
contrib	contributions of the individuals/variable categories
inertia	inertia of the individuals/variable categories

Author(s)

Alboukadel Kassambara [email protected]

References

http://www.sthda.com/english/

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[, 1:6])
res.mca <- MCA(poison.active, 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

---

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 variables (quantitatives, qualitatives and groups)

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

Usage

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

get_mfa_ind(res.mfa)

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

get_mfa_partial_axes(res.mfa)

Arguments

res.mfa	an object of class MFA [FactoMineR].
element	the element to subset from the output. Possible values are "ind", "quanti.var", "quali.var", "group" or "partial.axes".

Value

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

coord	coordinates for the individuals/quantitative variable categories/qualitative variable categories/groups/partial axes
cos2	cos2 for the individuals/quantitative variable categories/qualitative variable categories/groups/partial axes
contrib	contributions of the individuals/quantitative variable categories/qualitative variable categories/groups/partial axes
inertia	inertia of the individuals/quantitative variable categories/qualitative variable categories/groups/partial axes

Author(s)

Alboukadel Kassambara [email protected]

Fabian Mundt [email protected]

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

---