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Work on "human in the loop" classifiers have been around for a long time.

That said, this is very interesting. The real innovation here is the untrained humans feeding the expert system via simple visual identification. This requires a preestablished taxonomy to be defined, so you won't get any surprises, but it is perfect for any large scale classification that has fine differentiation (like biology).

I'm working on how to seed this system without defining the taxonomy in advance too. This would enable growing a library of classifiers that would eventually be able to do a huge number of fine-grained classification, without saying what those classifiers have to be beforehand. But setting up the taxonomy in advance makes it so you don't end up training two classifiers that do essentially the same thing.
Just spitballing, could you do this by asking humans to differentiate two images that have been classified the same way?

For example, for the pocket square set, once there's a reasonable single cluster, could you randomly choose images (or ask "are these the same?") and ask what is different about the two images.

You may not get a formal taxonomy, but after enough of this, you could have something experts could work on. The problem, of course, is that without expert level insight, you'll get a lot of "that one is prettier".

I've done a similar thing trying to create classifiers for scenes and buildings. It's hard to have a word for 'bottom left corner of a window with bars on it', for example. And for scenes there's no taxonomy in advance. I think it works better than expected (as good as automatic patch discovery methods), but you end up having to train a lot more classifiers because you'll get a number of redundant classifiers.

Something that might be cool is to have a step where the common people try to do the clustering, and an expert corrects them if they do something not useful. Then there'd be a back and forth between experts and crowd people. I haven't really thought that out though.