In manifold learning technique for dimension reduction, a pairwise distance matrix is taken as input just like for MDS and then using k-nearest neighbors a sparse graph is induced.Then MDS is used on it to produce a low dimensional mapping of the data-points.

My question is what is the difference between the manifold learning and using MDS? MDS is ultimately being used in manifold learning?

Does generating the sparse graph and then applying MDS on it enhance the strength of the reduced data?

It was a nice question. Even i used to think on the same lines and almost every dimensional reduction algorithm, that i had come across, used MDS

But after reading in detail, MDS encompasses much more. It is true that most of the algorithms within the field of Manifold Learning use MDS, but there are some that do not

e.g.

T-distributed Stochastic Neighbor Embedding

Graduated Optimisation

There are many more, but i have not listed them here

I havent myself tried out these algorithms. Let me know if you have some use case