# Principal Component Analysis on Graphs

How can somebody apply PCA on a set of graphs? Is it possible to define a meaningful graph kernel for my problem, and then follow the typical procedure on the derived matrix of pairwise distances (kernel PCA) ?

• @DionysisM Unfortunately I don't think thinking about graphs in terms of coordinates will take you very far. It's important to know the difference between a Euclidean space (where you have lengths and distances and you can actually plot points in it) and a metric space (where you only have distances between points and nothing else). $R^n$ is a Euclidean space while graphs live in a metric space, so there is no way you can map graphs onto $R^n$ without extra assumptions. I'm afraid you'll have to get familiar with the abstract mathematical notions of space and metric. – Pedro Mediano May 24 '17 at 8:41