Unsupervised Learning: Dimensionality Reduction and Clustering

Apply Principal Component Analysis (PCA) to reduce data dimensionality.

Interpret principal components by examining the explained variance and component loadings.

Use scree plots to select the optimal number of principal components.

Apply the k-means algorithm to partition data into clusters.

Select the number of clusters for k-means using the elbow method or silhouette scores.

Apply hierarchical clustering and interpret the resulting dendrogram.

Describe Gaussian Mixture Models (GMMs) as a probabilistic clustering method.

Explain the intuition of the Expectation-Maximization (EM) algorithm for fitting GMMs.