This has a lot of practical applications. For example Artsy (https://www.artsy.net) builds a K-nearest neighbor graph for its artworks. For example, scroll down to related results in Warhol's "Mushroom Soup" in https://www.artsy.net/artwork/andy-warhol-mushroom-soup to find Damien Hirst's "Chicken from Last Supper". The data is done by humans, but the related algorithm is based on K-nearest neighbors.
We started with this basically what's in the article, then used Locality Sensitive Hashing (http://www.mit.edu/~andoni/LSH) as a real-time approximation and today we use NNDescent from this priceton paper: http://www.cs.princeton.edu/cass/papers/www11.pdf