I have a dataset associated with labels. According to https://arxiv.org/pdf/1802.03426.pdf --> UMAP (Uniform Manifold Approximation and Projection) which is a novel manifold learning technique for dimension reduction and the data, I succeeded to create the green and red clouds bellow. The problem I have is they are stick together. For machine learning purposes, it is kinda hard to learn something when the clouds are placed that way.

Is there a topological approach that might be used to create a significant space between clouds?

**UPDATE**

I would be interested by an analytic approach to separated the two clouds. Each cloud can be seen as a compact space.

Here is an example in 2-D. I would like a way to generalize that concept in z-D, where z would be a finite positive integer.

I want to create an algo which will be used with high-frequency speed. So the algo needs to be fast enough. I believe the "Uniform Manifold Approximation and Projection" to be tweakable so that I can preprocess the data and pass it to an LSTM. The idea are is three steps : 1- Reduce the dimensionality, separated the clouds and then pass the data to a LSTM model.

**UPDATE 2**

I am trying an approach, but I am far from certain that it's the best solution.

- Cover each cloud by the smallest possible sphere.
- Extend the intersection of the spheres by an hyperplane.
- Taking away the clouds according to the orthogonal vector to the hyperplane by a distance alpha. alpha might be the furthest point on the orthogonal line inside the intersection of the spheres.