Manifold learning is a type of nonlinear dimensionality reduction technique that assumes high-dimensional data lies on a lower-dimensional manifold embedded in the higher-dimensional space. The goal is to uncover this manifold structure and represent the data in fewer dimensions while preserving its intrinsic geometry.

Unlike linear methods like PCA, manifold learning captures complex, curved structures in data. Popular algorithms include t-SNE, UMAP, Isomap, and Locally Linear Embedding (LLE). These methods focus on preserving local neighborhoods or global geodesic distances, making them well-suited for visualizing complex datasets like images, speech, or embeddings.

Manifold learning is often used for data exploration, denoising, clustering, or as a preprocessing step before classification. However, it can be sensitive to parameters (e.g., perplexity, number of neighbors) and doesn’t always generalize well to unseen data unless combined with models that support out-of-sample inference.

It assumes the data is continuous and smooth, which may not hold in every setting.