# Are there methods to learn a projection method into euclidean space, given a set of pairwise distances?

Basically, right now I am trying to do some nearest-neighbour searching on an approach where I don't have points in Euclidean space. To do a nearest-neighbour search currently, I take the query and compare it (with a special similarity function) to each model in the database to find the most similar one.

With this similarity function, I can compute pairwise distances between all points in my database, and I'm interested in whether it's possible to learn a projection into Euclidean space such that any new query can just be projected and nearest neighbour searches can then be performed in that Euclidean space.

Does such a method exist, or am I hoping for a holy grail that hasn't been solved?

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Thanks for this, but Im either misunderstanding your response or you misunderstood the question. These give us a projection based on a matrix of pairwise distances. I can project my initial database into the space fine with this. However, a new, unseen data point cannot be projected without comparing against the entire database with these methods, can it? I want to avoid having to compare against the whole database for each unseen point – water Aug 15 '12 at 19:36