Efficient comparison of 100.000 vectors

First, preprocess your vector list to make each vector normalized.. unit magnitude. Notice now that your comparison function T() now has magnitude terms that become constant, and the formula can be simplified to finding the largest dot product between your test vector and the values in the database.

Now, think of a new function D = the distance between two points in 60D space. This is classic L2 distance, take the difference of each component, square each, add all the squares, and take the square root of the sum. D(A, B) = sqrt( (A-B)^2) where A and B are each 60 dimensional vectors.

This can be expanded, though, to D(A, B) = sqrt(A * A -2*dot(A,B) + B * B). A and B are unit magnitude, then. And the function D is monotonic, so it won't change the sort order if we remove the sqrt() and look at squared distances. This leaves us with only -2 * dot(A,B). Thus, miniumizing distance is exactly equivalent to maximizing dot product.

So the original T() classificiation metric can be simplified into finding the highest dot product between the nornalized vectors. And that comparison is shown equivalent to finding the closest points to the sample point in 60-D space.

So now all you need to do is solve the equivalent problem of "given a normalized point in 60D space, list the 20 points in the database of normalized sample vectors which are nearest to it."

That problem is a well understood one.. it's K Nearest Neighbors. There are many algorithms for solving this. The most common is classic KD trees .

But there's a problem. KD trees have an O(e^D) behavior.. high dimensionality quickly becomes painful. And 60 dimensions is definitely in that extremely painful category. Don't e