Reading this makes me understand why most people still use the trivial ANN library. The theorems for the optimality of these algorithm are too hard to explain easily. This is the most painful paper I've read in this course so far, and I'm glad I finish it.
In this paper, 3 fast ANN algorithms are proposed. The last one, locality-sensitive hashing, is very similar to the Pyramid Match Hashing by Grauman and Darrell. The point in R^d is first embedded to the Hamming space, and then efficient histogram (hashing) matching can be performed. My main problem is, is there any good reference book to explain the good properties of the Hamming distance? I think that will be more interesting than this paper.
Besides the endless theorems and proofs in the paper (I re-derived some of them...), I don't know how to present this paper. There is no experimental result. I wish my brain could be so smart so I can publish something without doing any experiment....
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