## Sammon mapping

Sammon mapping is a way of projecting multi-dimensional data to a lower dimensional space. The idea behind Sammon mapping is to create a projection in which distances between points are kept the same as in the higher-dimensional space. This is probably going to be the most complicated program we have explored in this book.

We will use information from the previous chapters. For example, we will use the optimization routines we explored in the chapter dedicated to the Breeze numerical computing library. Sammon mapping was proposed by John W. Sammon in 1968 with regard to data structure analysis. It is particularly suited for exploratory data analysis, since it maintains (or aims to maintain) the structure of the data after projecting it to a lower dimensional space. To understand how Sammon mapping of a dataset is calculated, see the formula here:

Let's look at it term by term. *E* is called Sammon's stress or Sammon's error. This is the value we will want to minimize. Indices...