Manifold learning is one of the most popular approaches to dimensional reduction. The idea is that the data which seems to be high dimensional e.g. thousands of features, actually lies on a low dimensional manifold embedded in the ambient (high dimensional) Euclidean space. The goal of the manifold learning techniques is to ‘learn’ the low dimensional manifold. The manifold learning methods provide a way to extract the underlying parameters of the data, which are much lesser in number that the original dimension, and can explain the intricacies of the data. The assumption is that the data lies along a low-dimensioanal manifold which describes the underlying parameters and the ambient high-dimensional space is the feature space.
https://jverma.github.io/manifold-learning/
Manifold learning is one of the most popular approaches to dimensional reduction. The idea is that the data which seems to be high dimensional e.g. thousands of features, actually lies on a low dimensional manifold embedded in the ambient (high dimensional) Euclidean space. The goal of the manifold learning techniques is to ‘learn’ the low dimensional manifold. The manifold learning methods provide a way to extract the underlying parameters of the data, which are much lesser in number that the original dimension, and can explain the intricacies of the data. The assumption is that the data lies along a low-dimensioanal manifold which describes the underlying parameters and the ambient high-dimensional space is the feature space.