Unsupervised Learning

By the end, you can

• Explain what makes a learning problem unsupervised and contrast it with supervised learning.
• Trace one full round of k-means (ASSIGN + UPDATE) and compute a new centroid mean by hand.
• Explain why k-means converges and why it can still return a suboptimal clustering.
• Read an elbow plot and identify the appropriate value of k.
• Describe how hierarchical clustering builds a dendrogram and how cutting the tree selects the number of clusters.
• Explain distance concentration (curse of dimensionality) and why it motivates dimensionality reduction before clustering.
• Describe what PC1 and PC2 represent in PCA and explain how projecting onto them reduces dimensions while retaining variance.
• Distinguish PCA (linear) from t-SNE/UMAP (nonlinear) and identify when each is appropriate.
• Explain how unsupervised clustering detects anomalies and give a real-world example.