Dimensionality reduction feature extraction principal component analysis manifold hypothesis manifolds manifold learning manifold regularization
Dimensionality reduction is a process of reducing the number of random variables under consideration by obtaining a set of principal variables. In other words, it is a process of reducing the dimension of the feature set, also called the "number of features". Most of the dimensionality reduction techniques can be considered as either feature elimination or extraction. One of the popular methods of dimensionality reduction is principal component analysis (PCA). PCA involves changing higher-dimensional data (e.g., 3D) to a smaller space (e.g., 2D). This results in a smaller dimension of data (2D instead of 3D), while keeping all original variables in the model without changing the data.
The manifold hypothesis proposes that high-dimensional data sets lie along low-dimensional manifolds, and many dimensionality reduction techniques make this assumption, leading to the area of manifold learning and manifold regularization.
