hypernonsense

Using Locality Sensitive hashing to find the nearest points to a query point in extremely high dimensional space.


Keywords
database, vector, hash, data-structures, search
License
MIT

Documentation

Hypernonsense

An implementation of Locality Sensitive hashing with random projection.

Locality sensitive hashing allows you to query a very large set of points in extremely high dimensional space to find the nearest points to a query point.

This is useful when working with word vectors where the cosine distance between words is the similarity of those words. You can use a hypernonsense to find the most similar words to a given point in word space.

Usage

Hypernonsense contains two types of index. The basic hyperindex is very fast to generate results but is fairly inaccurate. The multiindex contains more than one hyperindex and aggregates the results to improve accuracy.

hyperindex

// We're working in 300 dimensional space
const dimension : usize = 300;

// How many planes should the space be split by. More planes increases speed but decreases accuracy
// A good starting value is: 2 ^ planes * 10 == number of points
const planes : u8 = 10;

// Create the index
let mut index = HyperIndex::new(dimension, planes, &mut thread_rng());

// Populate the index with random data
let mut rng = thread_rng();
for key in 0..10000usize {

    // Generate a random vector
    let v = random_unit_vector(dimension, &mut rng);
    
    // The `key` can be any type - When you query the hyperindex you will get back a set of keys. In this case we'll just use the index.    
    index.add((key, v));
}

// Find approximately the nearest vectors to a random query vector. The key we used was `usize` so we get back a `Vec<usize>`
let result : Option<&Vec<usize>> = index.group(random_unit_vector(dimension, &mut rng));

Results from the hyperindex will be very fast to retrieve (it's O(planes)). However the quality of results will be very poor, points are prearranged into groups and any points which happen to lie near to one of the hyperplanes will not retrieve all of the closest points. When querying from a hyperindex it will return a reference to the internals of the index, which is a Vec of (approximately) the nearest keys in an arbitrary order.

multiindex

// We're working in 300 dimensional space
const dimension : usize = 300;

// How many sub-indices should there be. More indices increases accuracy, but decreases speed and increases memory consumption.
const indices : u8 = 10

// How many planes should the space be split by. More planes increases speed but decreases accuracy
// A good starting value is: 2 ^ planes * 10 == number of points
const planes : u8 = 10;

// Create the index
let mut index = MultiIndex::new(dimension, 10, 10, &mut thread_rng());

// Populate index
// ...exactly the same as the hyperindex example

// Find the approximately nearest vectors to a random query vector. The key we used was `usize` so we get back a `Vec<DistanceNode<usize>>`
// This requires us to supply the number of points we want and a distance metric to choose them by
const nearest_count : usize = 100;
let result : Vec<DistanceNode<i32>> = index.nearest(&random_unit_vector(dimension, &mut rng), nearest_count, |point, key| {
    return distance(point, get_vector_by_key(key));
});

The multiindex solves the poor quality of results from a single hyperindex by querying multiple hyperindex instances simultaneously and aggregating their results together. This allows you to directly trade off speed to accuracy by increasing the indices count. When querying from a multiindex you can specify the number of items to retrieve (100 in this example) and the distance metric to order them by.

Tweaking Parameters

When using this you must be aware that it is a probabilistic data structure - results that it returns are approximately correct. You should experiment with the two parameters until you achieve a level of speed and accuracy that you are happy with.

Planes

The hyperindex is split into regions of space between the random hyperplanes it generates, when you query the index you simply get back a list of points in the same region.

If you don't have very many hyperplanes you will get back very large result sets and the index isn't really helping you. The limit of this is zero hyperplanes, in which case every query will return the entire set!

If you have too many hyperplanes each group will have a very small number of points in it and the quality of results will suffer as it becomes increasingly likely that the correct answer will have been classified into a different group. Once 2 ^ planes >= data_points it is likely that every point will be in a group on it's own and the index is almost useless.

Sub Index Count

The multiindex contains multiple hyperindex instances each split with the same number of planes, but with different (randomised) plane orientations. When you query the multiindex it queries all the sub-indices and merges the results together. This approach increases the accuracy of the query by taking the best results (according to the distance metric) from each sub query. Increasing the sub index count increases memory consumption and query time.

If you don't have very many sub-indices you will basically just be querying a hyperindex and the distance metric will be useless.