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Manifold learning subsumes techniques conceived for problems where data of interest are assumed to lie on an embedded non-linear manifold within a higher-dimensional space.

Manifold Learning can be thought of as an attempt to generalize linear frameworks like PCA to be sensitive to non-linear structure in data. Though supervised variants exist, the typical manifold learning problem is unsupervised: it learns the high-dimensional structure of the data from the data itself, without the use of predetermined classifications.

Examples of Manifold Learning algorithms include:

  • Isomap
  • Locally Linear Embedding
  • Hessian Eigenmapping
  • Laplacian Eigenmaps
  • Multi-dimensional Scaling (MDS)
  • t-distributed Stochastic Neighbor Embedding (t-SNE)

Reference: http://scikit-learn.org/stable/modules/manifold.html and https://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction#Manifold_learning_algorithms

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