A commonly heard sentence in unsupervised Machine learning is
High dimensional inputs typically live on or near a low dimensional manifold
What is a dimension? What is a manifold? What is the difference?
Can you give an example to describe both?
Manifold from Google/Wikipedia:
In mathematics, a manifold is a topological space that resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
Dimesion from Google/Wikipedia:
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
What does the Google/Wikipedia even mean in layman terms? It sounds like some bizarre definition like most machine learning definition?
They are both spaces, so what's the difference between a Euclidean space (i.e. Manifold) and a dimension space (i.e. feature-based)?