Owen Jones 2018-12-01
Cluster Analysis is a statistical tool for identifying structure in data and identifying groups based on similarity. It is used in various fields and has become known as a central tool in unsupervised machine learning. There are numerous algorithms and this worksheet focuses on a couple of use cases.
The main function we will use is the hclust function from the stats package. This package ships with base R, so you should have it available.
data(iris)
summary(iris)## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100
## 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300
## Median :5.800 Median :3.000 Median :4.350 Median :1.300
## Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199
## 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800
## Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500
## Species
## setosa :50
## versicolor:50
## virginica :50
##
##
##
The idea here is that we are experimenting with the clustering algorithm using data where we do know something about the structure. In this case, we know what the species are. Will cluster analysis find this structure? Let's plot stuff.
You can see that there are some clustering here. Let's quantify it by first calculating a distance matrix (dist) and then using hclust to perform a hierarchical cluster analysis. You can then plot the result with plot.
names(iris)## [1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width"
## [5] "Species"
x <- iris[,3:4]
x <- dist(x)
clustResult <- hclust(x,method="average")
#clustResult <- cluster::agnes(x, stand=FALSE,method = "ward")
plot(clustResult)
Let's cut the tree where we find 3 clusters. You can do this with the cutree function.
iris$clusterID <- cutree(clustResult, 3)Then we can see how well our cluster analysis has recovered the actual species.
table(iris$clusterID,iris$Species)##
## setosa versicolor virginica
## 1 50 0 0
## 2 0 45 1
## 3 0 5 49
Try repeating this with the rest of the data (sepals), and with other algorithms (e.g. method = "complete")
clustResult2 <- hclust(x,method="ward.D2")dendextend::tanglegram(as.dendrogram(clustResult),as.dendrogram(clustResult2))