Manifold learning is the process of estimating the structure of a manifold from a set of samples, also referred to as observations or instances, taken from the manifold. It is a subfield of machine learning that operates in continuous domains and learns from observations that are represented as points in a Euclidean space, referred to as the ambient space. This type of learning, to Mitchell, is termed instance-based or memory-based learning . The goal of such learning is to discover the underlying relationships between observations, on the assumption that they lie in a limited part of the space, typically a manifold, the intrinsic dimensionality of a manifold of which is an indication of the degrees of freedom of the underlying system.
Manifold learning has attracted considerable attention of the machine learning community, due to a wide spectrum of applications in domains such as pattern recognition, data mining, biometrics, function approximation, and...
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