Dimensionality reduction is an unsupervised task in which the goal is to represent high-dimensional data in lower-dimensional space while preserving the underlying structure.
Manifold Assumption
This may be achieved from Manifolds. There is such an assumption within Machine Learning which states that high-dimensional data lies close to lower-dimensional manifold. In other words, while the data may exist in high-dimensional space, the meaningful features of the data can be captured in a lower-dimensional space. This is essential to dimensionality reduction.
Manifold Learning Algorithms
Manifold learning is a class of techniques in machine learning which aim to discover and model the underlying manifold structure of the data. The objective of doing this is to reduce dimensionality, visualize high-dimensional data, and denoise data.