demo/fcm.R

In inaparc: Initialization Algorithms for Partitioning Cluster Analysis

# Demo for Fuzzy c-means clustering using kmpp and inofrep prototype initialization
# functions in the package 'inaparc'
#

# Install and/or load the required libraries
for(package in c("inaparc", "kpeaks", "cluster", "factoextra", "vegclust", "NbClust")){
  if(!require(package, character.only=TRUE, quietly=TRUE)){
    install.packages(package)
  }
  library(package, character.only=TRUE)
}

# Data loading and pre-processing

# Use Iris data set
data(iris)
# Pick the features except 5th column 
X <- iris[,-5]

# Convert type of X to the matrix class
X <- as.matrix(X)
str(X)
head(X)
tail(X)

# Omit the NAs
X <- na.omit(X)

# If standardization is required, uncomment the following two lines
# X <- scale(X, center = TRUE, scale = TRUE) 
# head(X); tail(X)

par(ask=TRUE)
# Compute the distance matrix 
dist.x <- factoextra::get_dist(X, stand = TRUE, method = "pearson")
# Visualize the distance matrix 
factoextra::fviz_dist(dist.x, 
   gradient = list(low = "#00AFBB", 
   mid = "white", high = "#FC4E07"))

# Quick estimation of the number of clusters by using the findk function of the kpeaks package
nc1 <- kpeaks::findk(X, nbins=30)$mtlk
cat("The optimal number of clusters (k) suggested by kpeaks is: ", nc1, "\n")

# Finding the optimal number of clusters by using the internal indexes in the NbClust package
nbclust.res <- NbClust::NbClust(X, 
   distance = "euclidean",
   min.nc = 2, max.nc = 10, 
   method = "ward.D", 
   index ="all")

# Finding the most repeated number of clusters and assign it as the optimal number of clusters 
tabnc <- table(nbclust.res$Best.nc[1,])
nc2 <- as.integer(names(tabnc)[which.max(tabnc)])
cat("The optimal number of clusters (k) suggested by NbClust is: ", nc2, "\n")

par(mfrow=c(1,1))
# Plot the frequencies of the number of clusters suggested by
# the internal indexes in the NbClust package
factoextra::fviz_nbclust(nbclust.res, 
   barfill = "#00AFBB", barcolor="#00AFBB", 
   ggtheme = theme_minimal())

# Determining the best initial prototype matrix in 10 runs by using 
# the kmpp function for K-means++ algorithm in the inaparc package 
nruns <- 10
miniter <- Inf
for(i in 1:nruns){
  v <- inaparc::kmpp(X, k=nc2)$v
  km.res <- kmeans(X, centers=v, iter.max=100)
  cat("Prototypes matrix converged ", km.res$iter, " iterations in ", i, "th run.\n")
  if(km.res$iter < miniter){
    miniter <- km.res$iter
    centers.kmpp <- v
  }
}
cat("Best prototypes matrix, built by kmpp initialization, K-means converged in ", miniter, " iterations.\n")
cat("Best prototypes matrix by kmpp initialization is:\n")
print(centers.kmpp)

# Fuzzy c-means clustering with the best initial prototypes matrix 
# produced by the kmmp function of the inaparc package
fcm.res <- vegclust::vegclust(X, method="FCM", mobileCenters=centers.kmpp, m=2, iter.max=100)

# Assign hard cluster labels to the data objects 
clusters <- c(); memberships <- as.matrix(fcm.res$memb)
for(i in 1:nrow(memberships))
  clusters[i] <- which(max(memberships[i,])==memberships[i,])

# Visualize the Fuzzy c-means clustering results using the first two features
plot(X, pch=clusters + 14, col=clusters)
text((X), col="gray", pos=1, cex=0.7)
points(centers.kmpp, pch=12, col=1:nc2, cex=2.0)
points(fcm.res$mobileCenters, pch=10, col=1:nc2, cex=2.0)

# Visualize the Fuzzy c-means clustering results by the feature pairs 
pairs(X, col=clusters, pch=20)

# Plot the clustering results with clustplot of cluster package
cluster::clusplot(X, clusters, color=TRUE, shade=TRUE, labels=3, lines=0)

# Generate the initial prototype matrix using the inofrep function in the inaparc package. 
# Since it is based on a deterministic algorithm which produces the same prototype matrix
# in multiple runs, onone run is needed with this prototypes initialization algorithm
centers.inofrep <- inaparc::inofrep(X, k=nc2, nbins=30)$v

inofrep.res <- kmeans(X, centers=centers.inofrep, iter.max=100)
cat("Using the prototypes matrix, built by Inofrep K-means converged in ", inofrep.res$iter, " iterations.\n")
cat("Best prototypes matrix by Inofrep is:\n")
print(centers.inofrep)

# Fuzzy c-means clustering with the best initial prototypes matrix
fcm.res <- vegclust::vegclust(X, method="FCM", mobileCenters=centers.inofrep, m=2, iter.max=100)

# Assign hard cluster labels to the data objects 
clusters <- c(); memberships <- as.matrix(fcm.res$memb)
for(i in 1:nrow(memberships))
  clusters[i] <- which(max(memberships[i,])==memberships[i,])

# Visualize the Fuzzy c-means clustering results using the first two features
plot(X, pch=clusters + 14, col=clusters)
text((X), col="gray", pos=1, cex=0.7)
points(centers.inofrep, pch=12, col=1:nc2, cex=2.0)
points(fcm.res$mobileCenters, pch=10, col=1:nc2, cex=2.0)

# Visualize the Fuzzy c-means clustering results by the feature pairs 
pairs(X, col=clusters, pch=20)

# Plot the clustering results with clustplot of cluster package
cluster::clusplot(X, clusters, color=TRUE, 
   shade=TRUE, labels=3, lines=0)

# Visual clustering tendency assessment
gradient.color <- list(low = "#FFFFFF",  high = "#00AFBB")
act <- get_clust_tendency(data=X, n = 10, gradient = gradient.color)
plot(act$plot)