**Course Title:** Mastering R Programming: Data Analysis, Visualization, and Beyond **Section Title:** Introduction to Machine Learning with R **Topic:** Unsupervised learning: K-means clustering, PCA In this topic, we will dive into the world of unsupervised learning, which involves discovering patterns and relationships within data without any labeled output. We will focus on two popular techniques: K-means clustering and Principal Component Analysis (PCA). **K-means Clustering** ------------------------ K-means clustering is an algorithm that groups similar data points into clusters based on their characteristics. The goal is to identify clusters that are compact and well-separated from each other. ### How K-means Clustering Works 1. **Initialization**: The algorithm starts by randomly selecting k centroids, where k is the number of clusters we want to identify. 2. **Assignment**: Each data point is assigned to the closest centroid based on the Euclidean distance. 3. **Update**: The centroids are updated based on the mean of the data points assigned to each cluster. 4. **Iteration**: Steps 2-3 are repeated until convergence or a stopping criterion is reached. ### Example in R To demonstrate K-means clustering in R, we will use the `iris` dataset, which contains information about different species of flowers. ```r # Load necessary libraries library(dplyr) library(ggplot2) # Load iris dataset data(iris) # Scale the data iris_scaled <- iris[, 1:4] %>% as.data.frame() %>% scale() # Perform K-means clustering with k = 3 set.seed(123) # for reproducibility kmeans_model <- kmeans(iris_scaled, centers = 3) # View the cluster assignments kmeans_model$cluster # Visualize the clusters ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width, color = factor(kmeans_model$cluster))) + geom_point() + theme_minimal() ``` ### Principal Component Analysis (PCA) ---------------------------------------- PCA is a technique used to reduce the dimensionality of a dataset by transforming the original features into a new set of orthogonal features called principal components. These components are ordered in descending order of their variance. ### How PCA Works 1. **Standardization**: The data is standardized to have zero mean and unit variance. 2. **Covariance matrix calculation**: The covariance matrix is calculated to identify the relationships between the original features. 3. **Eigenvectors and eigenvalues**: The eigenvectors and eigenvalues are calculated from the covariance matrix. 4. **Component selection**: The principal components are selected based on their eigenvalues. ### Example in R To demonstrate PCA in R, we will use the `mtcars` dataset, which contains information about various car models. ```r # Load necessary libraries library(ggplot2) library(dplyr) # Load mtcars dataset data(mtcars) # Perform PCA on mtcars dataset pca_model <- prcomp(mtcars[, 1:11], scale. = TRUE) # View the summary of PCA model summary(pca_model) # Extract the first two principal components pc1 <- pca_model$x[, 1] pc2 <- pca_model$x[, 2] # Visualize the first two principal components ggplot(data.frame(pc1, pc2), aes(x = pc1, y = pc2)) + geom_point() + theme_minimal() ``` **Conclusion** ---------- In this topic, we explored K-means clustering and PCA, two popular unsupervised learning techniques in R. K-means clustering groups similar data points into clusters, while PCA reduces the dimensionality of a dataset by transforming the original features into principal components. **Key Takeaways** * K-means clustering is a technique used to identify clusters in a dataset. * PCA is a technique used to reduce the dimensionality of a dataset. * K-means clustering and PCA can be performed using R's built-in functions, such as `kmeans()` and `prcomp()`. If you have any questions or comments about this topic, you can ask them below. In the next topic, we will cover "Model evaluation techniques: Cross-validation and performance metrics."