I don’t think they throw out structural information (like adjacency of pixels). Since each pixel corresponds to an independent dimension, the adjacency is still

I don’t think they throw out structural information (like adjacency of pixels). Since each pixel corresponds to an independent dimension, the adjacency is still contained in those coordinates: (a,b,...) is not the same as (b,a,...). So, as long as all images have the same dimension, it’s OK. If you had both 100x100 images and 1x10,000 images in the collection, that would mess up everything! As we know from linear algebra, if a collection is linearly dependent, you can find a subcollection that adds up to 0! In other words, everything cancels out and you end up with a blank photo. Is it possible? If the dimension is too low (the images are small), yes. If the collection is large (a lot of images), maybe. What if it is small? (It is in fact!) In a very extreme case you may need the negative for each image to cancel it: same shape with dark vs. light hair, skin, eyes, teeth (?). Interesting stuff...