Algorithms for manifold learning

Manifold learning is a popular recent approach to nonlinear dimensionality reduction. Algorithms for this task are based on the idea that the dimensionality of many data sets is only artificially high; though each data point consists of perhaps thousands of features, it may be described as a function of only a few underlying parameters. That is, the data points are actually samples from a low-dimensional manifold that is embedded in a high-dimensional space. Manifold learning algorithms attempt to uncover these parameters in order to find a low-dimensional representation of the data. In this paper, we discuss the motivation, background, and algorithms proposed for manifold learning. Isomap, Locally Linear Embedding, Laplacian Eigenmaps, Semidefinite Embedding, and a host of variants of these algorithms are examined.