Manifold learning

In Chapter 02, Introduction to Semi-Supervised Learning, we discussed the manifold assumption, saying that high-dimensional data normally lies on low-dimensional manifolds. Of course, this is not a theorem, but in many real cases, the assumption is proven to be correct, and it allows us to work with non-linear dimensionality reduction algorithms that would be otherwise unacceptable. In this section, we're going to analyze some of these algorithms. They are all implemented in Scikit-Learn, therefore it's easy to try them with complex datasets.