manifold

Definition

A manifold is a curved low-dimensional surface embedded in a high-dimensional space. The manifold hypothesis says real data lives on one: natural images occupy a vanishing fraction of all possible pixel arrays, so intrinsic dimension sits far below ambient dimension. Dimensionality reduction, representation learning, and generative modeling can all be read as attempts to locate that surface and put usable coordinates on it.

Explainers using this term

• Unsupervised Learning from Scratch — Clustering and Dimensionality ReductionUMAP: Uniform Manifold Approximation and Projection for Dimension Reduction