**The setup.** Let's say that we have a set of objects $O_i$ for which we have a dissimilarity measure $M(O_1,O_2)$. With this we can build a distance matrix $D_{ij}$.

Let's also assume that we have NO any reasonable or natural a priory way to assign the objects to vectors in any vector space, the point is to build one.

**Goal:** assign ${O_i}$ to vectors in a Euclidian vector space with small amount of dimensions so that the distance matrix $E_{ij}$ build with Euclidian norm for the assigned vectors was the best possible fit for $D_{ij}$

The desired number of dimension for E is no more than 5. The expected number of objects is measured in thousands, maybe millions.

**Questions:** Is this problem studied in *some* field ? If yes, which field, how is the problem named and what should I learn to write a code solving the problem? If no, what would be the most relevant fields ?