K-means clustering is a type of unsupervised machine learning algorithm that analyzes unlabeled data to find relationships within the data. K-means clustering sorts data into different classes, or clusters, based on their similarity. K represents the number of clusters.

In this presentation, we will look at how k-means clustering can be applied to the Iris dataset.

• Randomly initialize centroids (central points)

• Each data point is assigned to its closest centroid

• Clusters are formed around each centroid

• Centroids get updated through finding the average position of all the points in each cluster

• Repeat until the points in each cluster do not get reassigned

• Euclidean distance is used to calculate the similarity between points. \[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

\[\underset{C}{\operatorname{arg\,min}} \sum_{k=1}^{K} \sum_{x_i \in C_k} \|x_i - \mu_k\|^2\] where:

\(C_k\) is the set of points assigned to cluster \(k\),

\(\mu_k\) is the centroid of cluster \(k\),

\(\|x_i - \mu_k\|^2\) is the Euclidean distance squared.

Let’s take a look at K-Means clustering in the Iris dataset for the variables Sepal Length and Petal Length. Here we see that all the data points are plotted and the random centroids are initialized as t marks. Note that the centroids here are randomly chosen among the data values.

Next, let’s take a look at where the final centroids end up when the algorithm finishes and no points get reassigned.

Finally, let’s take a look at the classes assigned to the data points based on their closest centroid.

``` r
iris_dataset <- iris[, 1:4]
kmeans_result <- kmeans(iris_dataset, centers = 3)

iris$Cluster <- as.factor(kmeans_result$cluster)

# find iris species majority in each cluster
species_map <- iris %>%
  group_by(Cluster, Species) %>%
  summarise(n = n(), .groups = "drop") %>%
  group_by(Cluster) %>%
  slice_max(order_by = n, n = 1) %>%
  ungroup()

# map clusters to species names
cluster_labels <- setNames(species_map$Species, species_map$Cluster)
iris$ClusterLabel <- cluster_labels[as.character(iris$Cluster)]
```

``` r
final_centroids <- as.data.frame(kmeans_result$centers)[, c("Sepal.Length", "Petal.Length")]
final_centroids$Cluster <- as.factor(1:3)
final_centroids$ClusterLabel <- cluster_labels[as.character(final_centroids$Cluster)]

iris_plot3 = ggplot(iris, aes(x = Sepal.Length, y = Petal.Length, color = ClusterLabel)) + 
  geom_point(size = 2) + 
  geom_point(data = final_centroids, aes(x = Sepal.Length, y = Petal.Length),
             color = "black", size = 4, shape = 3) + 
  labs(title = "Iris K-Means Clustering (Final Centroids)",
       x = "Sepal Length", y = "Petal Length")

print(iris_plot3)
```

We can also plot this data in three dimensions by adding the variable Petal Width as the z-axis. Use left click and drag to view the 3D plot.