Manifold learning

Manifold learning refers to nonlinear dimensionality reduction techniques that seek to uncover low-dimensional structure in high-dimensional data. Key characteristics:

Assumption that data lies near a low-dimensional manifold.
Nonlinear approaches try to uncover the manifold geometry.
Avoid distortions from linear techniques like PCA.
Algorithms like LLE, Isomap, and t-SNE.
Useful for visualization and preprocessing data.

Applications include:

Reducing dimensions in image, text, genomic, sensory data.
Simplifying complexity while preserving relationships.
Revealing patterns, clusters, and topology.

Challenges include setting appropriate hyperparameters, preserving local and global structure, and determining intrinsic dimensionality.

Overall, manifold learning provides key tools for extracting nonlinear low-dimensional representations spanned by real-world high-dimensional data.