We have been working in a series of slides for the topic of Manifold Learning. We were nicely surprised of the scope of the subjects you need in order to understand this machinery. We believe this is the future!!! For example, Uniform Manifold Approximation and Projection (UMAP) is a nice result from understanding the geometry of the data. And when we compare it with the old t-SNE, an algorithm that uses the KL-divergence in a minimization framework, it is easy to notice that t-SNE has not an structure to store the manifold information which is a terrible drawback. Thus, algorithms based on Manifold Learning can be used to get deeper and detailed representations of the data by the use of light discrete representations (Fuzzy Graphs in the case of UMAP) of manifolds for good representations and speed ups.

Thus, to understand the ideas behind of Manifold Learning, we are starting with the following subjects:

  1. Understanding what is a smooth function in Euclidean spaces
  2. Get the isomorphism between Tangent Vectors and Derivatives at a point \(p\)
  3. The Cotangents
  4. A lot of the algebraic ideas on K-multilinear, Tensors, Wedge Operators
  5. The Topological ideas on Manifolds
  6. Etc

Once the slides are ready, we will post them at the section ML