Unsupervised Learning
No labels — the goal is to discover structure that's already latent in the data.
Clustering
k-Means: pick cluster centers, assign each point to its nearest center, recompute centers as the mean of assigned points, repeat until stable. Simple and fast, but requires choosing upfront and assumes roughly spherical, similarly-sized clusters. See K-Means & Hierarchical Clustering, In Full Depth for what K-Means is actually optimizing (it's the unsupervised analog of squared-error regression) and the elbow method for choosing .
Hierarchical clustering: builds a tree of clusters (a dendrogram) by either repeatedly merging the closest pairs (agglomerative) or splitting (divisive). Doesn't require choosing in advance — you cut the tree at whatever level makes sense. Covered in the same page above, including the four linkage criteria (single/complete/average/Ward) that decide how "distance between clusters" is measured.
DBSCAN and HDBSCAN: group points that are densely packed together, marking sparse points as noise/outliers. Unlike k-Means, they can find arbitrarily shaped clusters and don't need specified — but DBSCAN does need density parameters tuned, and HDBSCAN removes even that. See DBSCAN & HDBSCAN, In Full Depth for the core/border/noise point definitions and why density-based clustering handles non-convex shapes natively.
Gaussian Mixture Models and Spectral Clustering: GMM gives soft, probabilistic cluster membership instead of K-Means' hard assignment (it's essentially unsupervised QDA); Spectral Clustering handles non-convex shapes via graph eigenvectors instead of density. See GMM & Spectral Clustering, In Full Depth for the Expectation-Maximization derivation and a full four-way comparison table across all the clustering methods on this page.
Dimensionality Reduction
PCA (Principal Component Analysis): projects data onto the directions of maximum variance — the eigenvectors of the data's covariance matrix (see Linear Algebra). Fast, deterministic, and the standard first move for compressing features or visualizing high-dimensional data, though it only captures linear structure. Kernel PCA extends it to nonlinear structure via the same kernel trick as SVM; Truncated SVD skips mean-centering to handle sparse data like text. See PCA, Kernel PCA & Truncated SVD, In Full Depth for the eigenvector derivation, scree plots for choosing how many components to keep, and how PCA connects directly to SVD.
ICA (Independent Component Analysis): separates mixed signals into statistically independent sources — the "cocktail party problem." A fundamentally different goal from PCA's variance-maximization. See ICA, t-SNE & UMAP, In Full Depth for the non-Gaussianity trick that makes it work.
t-SNE and UMAP: nonlinear dimensionality reduction, mainly used for visualizing high-dimensional data (like embeddings) in 2D/3D. They preserve local neighborhood structure well, but the resulting axes aren't interpretable and distances between distant clusters shouldn't be over-interpreted. See ICA, t-SNE & UMAP, In Full Depth for exactly what these plots can and can't be trusted to show.
Association Rule Mining
Finding "if X, then usually Y" patterns in transactional data — the algorithms behind "customers who bought this also bought that." See Association Rule Mining: Apriori & FP-Growth, In Full Depth for support/confidence/lift, the Apriori principle for pruning an otherwise-intractable search space, and FP-Growth's faster tree-based alternative.
Topic Modeling
Discovering the themes running through a text collection with no labels — LDA (Latent Dirichlet Allocation, a completely different algorithm from the LDA classifier above despite the shared name) models documents as topic mixtures via a Bayesian generative process; BERTopic clusters modern embeddings instead. See Topic Modeling: LDA & BERTopic, In Full Depth for the full generative story and why embedding-based BERTopic captures synonyms that bag-of-words LDA structurally cannot.
Anomaly Detection
Identifying points that don't fit the normal pattern of the data — fraud transactions, defective products, network intrusions. Approaches range from simple statistical thresholds (points far from the mean), to density-based methods (isolation forests, DBSCAN's noise points), to autoencoders (trained to reconstruct normal data well; anomalies reconstruct poorly). See Anomaly Detection: Isolation Forest, LOF & One-Class SVM, In Full Depth for why randomly-split trees isolate anomalies faster than normal points, and a full comparison across all four approaches.
Next: Model Evaluation & Metrics — how to know whether any of these models are actually good.