Clustering with k-means
Introduction
k-means clustering is an unsupervised machine learning algorithm used to partition a dataset into k clusters, where each data point belongs to the cluster with the nearest mean. In this lecture, we will learn how to perform k-means clustering in R, including model building, evaluation, and interpretation.
Key Concepts
1. What is k-means Clustering?
k-means clustering aims to partition the dataset into k clusters in which each data point belongs to the cluster with the nearest mean. The algorithm works as follows:
Initialize k centroids randomly.
Assign each data point to the nearest centroid, forming k clusters.
Recalculate the centroids as the mean of all data points in each cluster.
Repeat steps 2 and 3 until the centroids no longer change.
2. Choosing the Number of Clusters
The number of clusters, k, is a critical parameter in k-means clustering. It can be chosen using methods like the Elbow Method, Silhouette Analysis, or domain knowledge.
Performing k-means Clustering in R
1. Building the Model
You can build a k-means clustering model using the kmeans() function in R.
# Creating a sample dataset
set.seed(123)
data <- data.frame(
x1 = rnorm(100),
x2 = rnorm(100)
)
# Performing k-means clustering with 3 clusters
k <- 3
model <- kmeans(data, centers = k, nstart = 25)
print(model)2. Evaluating the Model
You can evaluate the model’s performance by looking at the within-cluster sum of squares and plotting the clusters.
# Plotting the clusters
library(ggplot2)
data$cluster <- as.factor(model$cluster)
ggplot(data, aes(x = x1, y = x2, color = cluster)) +
geom_point() +
labs(title = "k-means Clustering", x = "Feature 1", y = "Feature 2")3. Choosing the Optimal Number of Clusters
The Elbow Method helps determine the optimal number of clusters by plotting the within-cluster sum of squares against the number of clusters.
# Elbow Method to determine the optimal number of clusters
wss <- sapply(1:10, function(k) {
kmeans(data[, 1:2], centers = k, nstart = 25)$tot.withinss
})
# Plotting the Elbow Method
plot(1:10, wss, type = "b", pch = 19, frame = FALSE,
xlab = "Number of Clusters", ylab = "Total Within-Cluster Sum of Squares",
main = "Elbow Method for Optimal k")Example: Comprehensive k-means Clustering Analysis
Here’s a comprehensive example of performing k-means clustering analysis in R.
# Creating a sample dataset
set.seed(123)
data <- data.frame(
x1 = rnorm(100),
x2 = rnorm(100)
)
# Performing k-means clustering with 3 clusters
k <- 3
model <- kmeans(data, centers = k, nstart = 25)
# Evaluating the model
print(model)
# Plotting the clusters
library(ggplot2)
data$cluster <- as.factor(model$cluster)
ggplot(data, aes(x = x1, y = x2, color = cluster)) +
geom_point() +
labs(title = "k-means Clustering", x = "Feature 1", y = "Feature 2")
# Elbow Method to determine the optimal number of clusters
wss <- sapply(1:10, function(k) {
kmeans(data[, 1:2], centers = k, nstart = 25)$tot.withinss
})
# Plotting the Elbow Method
plot(1:10, wss, type = "b", pch = 19, frame = FALSE,
xlab = "Number of Clusters", ylab = "Total Within-Cluster Sum of Squares",
main = "Elbow Method for Optimal k")Summary
In this lecture, we covered how to perform k-means clustering in R, including building the model, evaluating its performance, and choosing the optimal number of clusters. k-means clustering is a powerful tool for partitioning data into meaningful groups based on feature similarity.
Further Reading
For more detailed information, consider exploring the following resources:
Call to Action
If you found this lecture helpful, make sure to check out the other lectures in the ML R series. Happy coding!