Unsupervised Learning

Clustering

1. Clustering FramingGroups without labels: what clustering promises, and its honest ambiguity.1–2 h
2. k-MeansAssign, then move: the alternating loop that carves clouds into k groups.1–2 h
3. Mixture Models IntuitionSoft assignment: points belong by degree, and the EM idea alternates softly too.1–2 h
4. Hierarchical ClusteringNested clusterings as a tree: agglomerative merging and choosing where to cut the dendrogram.1–2 h
5. Density-Based ClusteringClusters as dense regions: DBSCAN finds arbitrary shapes and labels outliers as noise.1–2 h
6. Gaussian Mixture ModelsSoft clustering with Gaussian components fitted by EM: responsibilities, ellipses, and likelihood.1–2 h

Reduction

1. Dimensionality Reduction FramingWhy fewer dimensions: visualization, compression, and the information price.1–2 h
2. Principal Component AnalysisThe directions that carry variance: projection geometry plus variance accounting.1–2 h
3. Latent RepresentationsCompressed codes that reconstruct: bottlenecks, codes, and reconstruction loss.1–2 h
4. Matrix Factorization and the SVDLow-rank structure: the SVD as the best rank-k approximation, the engine behind PCA, recommenders, and LoRA.1–2 h
5. Probabilistic PCA and Factor AnalysisPCA as a latent-variable model: a low-dimensional Gaussian cause plus noise, the ancestor of the VAE.1–2 h
6. Manifold Learning and Nonlinear Embeddingst-SNE, UMAP, and friends: neighbourhood-preserving maps and how to avoid over-reading them.1–2 h

Anomalies

1. Anomaly DetectionRare by density: normal regions, thresholds, and the cost of crying wolf.1–2 h