[bjano]

They are using openface: https://cmusatyalab.github.io/openface/#openface

The library gets the picture as input and spits out a 128-element vector. The more similar the vectors are for two pictures the more likely they are of the same person.

You don't need to train it, there is a pretrained version available.

[rzzzt]

This reminded me of a news article I read about "eigenfaces" as a facial recognition method way back; here's its corresponding Wikipedia page: https://en.wikipedia.org/wiki/Eigenface

[Senji]

Really, there would be "eigenshapes" for any arbitrary configuration of 3D space. That we can smoothly transition from one face to the next in a higher dimensional matrix is no surprise.