# Isn't graph embedding a step back from non-euclidean space?

As I understand, we use graph embedding to make a euclidean representation of non-euclidean structure - graph. Does it mean that conceptually we just take a step back to, may be, more complex, but still grid processing?

• Can you be more specific? My feeling is that you're mixing up discrete/graph/grid with (non) euclidean-ness. Nodes of a graph may not even have positions, so theyre neither euclidean nor non-euclidean. Unless you're thinking of a case where they do. – bogovicj Jul 8 '20 at 0:01
• @bogovicj I'm beginner here, may be I do really mix up something. My question was about loosing data and loosing the advantages of graph structures. As I understand, we use graphs to hold relations and properties more then position and coordinates. I mean this by non-euclidean-ness. Correct me if I am wrong, an idea of embedding is to map graph structure to linear coordinate system (like plane, or volume, or higher-dimensional linear space). So, this way we just transform an initial data to more simple and space-like format. Doesn't it mean that we loose initial graph advantages? – Nikita Jul 9 '20 at 9:00
• Thanks, that helps. I'll try to write an answer on those points, and we can continue the conversation after if I'm not clear enough / am still missing the point. – bogovicj Jul 9 '20 at 14:45

## Building embeddings is the first step in graph processing.

We mainly use to apply mathematics on something like plane or hyperplane. Almost all mathematical methods can work with linear space, especially linear algebra which we use in neural networks and computer data processing.

So, in fact, embedding is just one of the first steps we need to do in order to apply some math on graph data. We can embed node features to a lower dimension, we can also embed an entire graph to some space we know how to work with. Then apply functions, transformations, whatever we want.

When you are building an embedding, your task is to represent a graph in linear space so that it will keep all the characteristics it has in non-linear "graph" space.

In this article you can read more about different approaches to graph embedding. I will just cite one phrase from there.

Machine learning algorithms are tuned for continuous data, hence why embedding is always to a continuous vector space.