other distance functions

[erikbern]

I realized today it's pretty easy to generalize to arbitrary distance functions. If every split is just the midpoint normal of two points then you can split by checking whether d(a, x) < d(b, x) where a and b are the points defining the split.

Interestingly this generalizes to crazy shit like edit distance. Would be cool to do a spell checker using Annoy :)

[a1k0n]

Huh, that's true. A tree is a Voronoi diagram then, effectively. So you could use Hamming distance too.... which I actually have a use for, right now. Neat!

[a1k0n]

And actually, then you don't have to store the split planes at all, only pointers to the left/right tree nodes. Which again breaks your fixed tree node size constraint unless leaves are tiny, but if you had dynamic leaf node sizes then the whole tree would be a lot smaller.

If you do that then it would also make sense to reorder the indices so that the roots and interior tree nodes are first, etc, for memory locality purposes.

Another idea I had was to just store the points in the interior nodes and not in the leaves, and push them onto the priority queue while traversing the tree. But that doesn't really help when you have multiple trees and the same points which are interior in one tree end up in a leaf of another tree.

[erikbern]

But Hamming distance is pretty much the same as Euclidean unless you are
saying some leaves could have many items?

Btw did you see https://github.com/houzz/annoy2 ? Will be interesting to
see if the LMDB backend works out - then you don't have to worry about the
fixed size stuff

On Friday, September 11, 2015, Andy Sloane notifications@github.com wrote:

And actually, then you don't have to store the split planes at all, only
pointers to the left/right tree nodes. Which again breaks your fixed tree
node size constraint unless leaves are tiny, but if you had dynamic leaf
node sizes then the whole tree would be a lot smaller.

If you do that then it would also make sense to reorder the indices so
that the roots and interior tree nodes are first, etc, for memory locality
purposes.

Another idea I had was to just store the points in the interior nodes and
not in the leaves, and push them onto the priority queue while traversing
the tree. But that doesn't really help when you have multiple trees and the
same points which are interior in one tree end up in a leaf of another tree.

—
Reply to this email directly or view it on GitHub
#102 (comment).

[a1k0n]

Oh yeah, I hadn't considered hamming as a special case of euclidean. Still, it would be much more compactly represented as bits rather than 0/0.5/1 floats :)

I did see that, yeah. That could enable all kinds of neat stuff.

[erikbern]

You could implement hamming distance by just having T=int64 and add up the bit distance btw

ANyway, closing this...