Finding Patterns
Hierarchical clustering¶
As an example, we apply hierarchical clustering to the Iris data set, ignoring the
categorical attribute Species. We use the normalized Iris data set iris.norm that
is constructed in Sect. 6.6.2.3. We can apply hierarchical clustering after removing
the categorical attribute and can plot the dendrogram afterwards:
#
# NORMALIZATION
#
# using the iris data as an example
iris.norm <- iris
# for loop over each coloumn
for (i in c(1:length(iris.norm))){
if (!is.factor(iris.norm[,i])){
attr.mean <- mean(iris.norm[,i])
attr.sd <- sd(iris.norm[,i])
iris.norm[,i] <- (iris.norm[,i]-attr.mean)/attr.sd
}
}
iris.num <- iris.norm[1:4]
iris.cl <- hclust(dist(iris.num), method="ward.D")
plot(iris.cl)
Here, the Ward method for the cluster distance aggregation function as described
in Table 7.3 was chosen. For the other cluster distance aggregation functions in the
table, one simply has to replace ward.D by single (for single linkage), by complete
(for complete linkage), by average (for average linkage), or by centroid.
For heatmaps, the library gplots is required that needs installing first:
library(gplots)
rowv <- as.dendrogram(hclust(dist(iris.num), method="ward.D"))
colv <- as.dendrogram(hclust(dist(t(iris.num)), method="ward.D"))
heatmap.2(as.matrix(iris.num), Rowv=rowv,Colv=colv, trace="none")
iris.km <- kmeans(iris.num,centers=3)
The desired numbers of clusters is specified by the parameter centers. The location
of the cluster centers and the assignment of the data to the clusters is obtained
by the print function:
print(iris.km)
For fuzzy c-means clustering, the library cluster is required. The clustering
is carried out by the method fanny similar to kmeans:
library(cluster)
iris.fcm <- fanny(iris.num,3)
iris.fcm
The last line provides the necessary information on the clustering results, especially the membership degrees to the clusters.
Gaussian mixture decomposition automatically determining the number of clusters
requires the library mclust to be installed first:
library(mclust)
iris.em <- mclustBIC(iris.num[,1:4])
iris.mod <- mclustModel(iris.num[,1:4],iris.em)
summary(iris.mod)
The last line lists the assignment of the data to the clusters.
Density-based clustering with DBSCAN is implemented in the library fpc
which needs installation first:
library(fpc)
iris.dbscan <- dbscan(iris.num[,1:4],1.0,showplot=T)
iris.dbscan$cluster
The last line will print out the assignment of the data to the clusters. Singletons or
outliers are marked by the number zero. The second argument in dbscan (in the
above example 1:0) is the parameter " for DBSCAN. showplot=T will generate
a plot of the clustering result projected to the first two dimensions of the data set.
Self Organizing Maps¶
The library som provides methods for self organizing maps. The library som needs
to be installed:
library(som)
iris.som <- som(iris.num,xdim=5,ydim=5)
plot(iris.som)
xdim and ydim define the number of nodes in the mesh in x- and y-directions,
respectively. plot will show, for each node in the mesh, a representation of the
values in the form of parallel coordinates.
Association Rules¶
For association rule mining, the library arules is required in which the function
apriori is defined. This library does not come along with R directly and needs to
be installed first.
Here we use an artificial data set basket that we enter manually. The data set
is a list of vectors where each vector contains the items that were bought:
library(arules)
baskets <- list(c("a","b","c"), c("a","d","e"),
c("b","c","d"), c("a","b","c","d"),
c("b","c"), c("a","b","d"),
c("d","e"), c("a","b","c","d"),
c("c","d","e"), c("a","b","c"))
rules <- apriori(baskets,parameter = list(supp=0.1,conf=0.8,target="rules"))
inspect(rules)
The last command lists the rules with their support, confidence, and lift.