Let's look at how to use dimensionality reduction algorithms in practice. All of these examples use the same dataset, which contains four normally distributed 2D point sets that have been transformed with Swiss roll mapping, 
, into a 3D space. The following graph shows the result of this mapping. You can find the original dataset and mapping details at http://people.cs.uchicago.edu/~dinoj/manifold/swissroll.html:
This dataset is labeled. Each of the normally distributed parts has its own labels, and we can see these labels as a certain color on the result. We use these colors to show transformation results for each of the algorithms we'll be using in the following samples. This gives us an idea of how the algorithm works. The following sections provide concrete examples of how to use the Dlib...