Concept of Manifolds
•“A manifold is a topological space which is locally Euclidean.”
•In general, any object which is nearly "flat" on small scales is a manifold.
•Euclidean space is a simplest example of a manifold.
•Concept of submanifold.
•Manifolds arise naturally whenever there is a smooth variation of parameters [like pose of the face in previous example]
•The dimension of a manifold is the minimum integer number of co-ordinates necessary to identify each point in that manifold.
Embed data in a higher dimensional
space to a lower dimensional manifold
Concept of
Dimensionality Reduction: