Exploration of IRIS Dataset

1 Overview

This dataset contains the measurements of the variables sepal width and length, petal width and length for 50 flowers from 3 species of iris.

Necessary packages:

require(ggplot2)

Loading required package: ggplot2

str(iris)

'data.frame':   150 obs. of  5 variables:
 $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
 $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
 $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
 $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
 $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

head(iris)

2 Variables

2.1 Sepal.Length

summary(iris$Sepal.Length)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  4.300   5.100   5.800   5.843   6.400   7.900 

Histogram of sepal length

qplot(Sepal.Length, data=iris, geom='histogram', fill=Species, alpha=I(1/2))

2.2 Sepal.Width

summary(iris$Sepal.Width)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   2.800   3.000   3.057   3.300   4.400 

2.3 Petal.Length

summary(iris$Petal.Length)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   1.600   4.350   3.758   5.100   6.900 

Histogram of petal length

qplot(Petal.Length, data=iris, geom='histogram')

Estimating a kernel denstiy for the distribution of petal length:

qplot(Petal.Length, data=iris, geom='density')

Separating the petal length histogram on the basis of species:

qplot(Petal.Length, data=iris, geom='histogram', fill=Species, alpha=I(0.5))

Densities on the basis of species

qplot(Petal.Length, data=iris, geom='density', color=Species, fill=Species)

2.4 Petal.Width

summary(iris$Petal.Width)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.100   0.300   1.300   1.199   1.800   2.500 

3 Correlations

3.1 With Species

cor(iris$Sepal.Length, as.numeric(iris$Species), method='spearman')

[1] 0.7980781

cor(iris$Sepal.Width, as.numeric(iris$Species), method='spearman')

[1] -0.4402896

cor(iris$Petal.Length, as.numeric(iris$Species), method='spearman')

[1] 0.9354305

cor(iris$Petal.Length, as.numeric(iris$Species), method='spearman')

[1] 0.9354305

4 Clustering

4.1 K-means

We note that petal length and width are very strongly correlated with species. Are these two numbers enough to correctly predict the species?

Let us prepare a data frame with only these two columns:

iris2 <- iris[, c("Petal.Length", "Petal.Width")]

Let us perform k-means clustering on this data set

num_clusters <- 3
set.seed(1111)
result <- kmeans(iris2, num_clusters, nstart=20)

The k-means algorithm has identified 3 centers:

result$centers

  Petal.Length Petal.Width
1     5.595833    2.037500
2     1.462000    0.246000
3     4.269231    1.342308

The cluster assignments are as follows:

result$cluster

  [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
 [42] 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 3 3 3
 [83] 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1
[124] 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1

Mapping between cluster assignment and original species labels:

table(result$cluster, iris$Species)

   
    setosa versicolor virginica
  1      0          2        46
  2     50          0         0
  3      0         48         4

Only 6 measurements have been misclassified.

qplot(Petal.Width, Petal.Length, data=iris, color=Species)

qplot(Petal.Width, Petal.Length, data=iris, color=factor(result$cluster))