Hashing Similarity

Question

Normally, the goal of hashing is to turn a continuous function into a discrete one: a small change in the input should cause a large change in the output. However, is there any hashing algorithm that will, (very) roughly speaking, return similar but (still different) hashes for similar inputs?

(An example of the use of this would be to check whether two files are "similar" by checking their hashes for similarity. Of course, some failure is always acceptable.)

Answer 1

Given a distance function that tells you how similar or different are your objects, you can also employ distance permutations: http://www.computer.org/portal/web/csdl/doi/10.1109/TPAMI.2007.70815 or sketches: http://portal.acm.org/citation.cfm?id=1638180

For an implementation of the latter approach: http://obsearch.net

Answer 2

Look at Locality Sensitive Hashing (LSH). That is a probabilistic way of quickly finding a bunch of points near a given one, for example.