[iradik]

This is how it can be done without any EXIF/GPS data with a fairly dumb algorithm.

It's a picture of a baby at a hospital.

There are probably hundreds of baby photos being taken per day at that hospital being posted to FB. Some have GPS and some don't.

The images that do have GPS, get recognized and lumped together as the same "entity" since they all look the same.

FB then looks up where she lives, then looks for any photos that don't have a location (like her baby photo), then tries to match it with any photos within a 50 mi proximity to her hometown. Bingo finds 90% match on the baby pic in the hospital, and asks user for verification. She says YES, then this pic gets lumped together with all the other entities. FB also asks more often since it's "right".

[hyperbovine]

A slightly more sophisticated approach would be to use the all /other/ data they have on her to predict what hospital she is likely to choose. Why stop with just her hometown?

[iradik]

Sure let's speculate they have a function that returns a guessed gps coordinate at time t. Again there are dumb implementations for this. Can take a time decaying and time-of-day/day-of-week weighted mode of your recognized locations. I imagine it'd be fairly accurate.