This crate provides a Rust implementation of the paper by Yu.A. Malkov and D.A Yashunin:

"Efficient and Robust approximate nearest neighbours using Hierarchical Navigable Small World Graphs" (2016,2018) arxiv

The crate provides:

• usual distances as L1, L2, Cosine, Jaccard, Hamming for vectors of standard numeric types, Levenshtein distance on u16.

• Hellinger distance and Jeffreys divergence between probability distributions (f32 and f64). It must be noted that the Jeffreys divergence (a symetrized Kullback-Leibler divergence) do not satisfy the triangle inequality. (Neither Cosine distance !).

• Jensen-Shannon distance between probability distributions (f32 and f64). It is defined as the square root of the Jensen-Shannon divergence and is a bounded metric. See Nielsen F. in Entropy 2019, 21(5), 485.

• A Trait to enable the user to implement its own distances. It takes as data slices of types T satisfying T:Serialize+Clone+Send+Sync. It is also possible to use C extern functions or closures.

• An interface towards C and more specifically to the Julia language. See the companion Julia package HnswAnn.jl and the building paragraph for some help for Julia users.

• Multithreaded insertion and search requests.

• Dump and reload functions (See module hnswio) to store the data and the graph once it is built. These facilities rely partly on Serde so T needs to implement Serialize and Deserialized as derived by Serde. It is also possible to reload only the graph and not the data themselves. A specific type (struct NoData, associated to the NoDist distance is dedicated to this functionality.

• A flattening conversion of the Hnsw structure to keep only neighborhood relationships between points (without their internal data) internal to the Hnsw structure (see module flatten.rs, FlatPoint and FlatNeighborhood). It is thus possible to keep some topology information with low memory usage.

• Filtering: It is possible to add filters so only results which satisfies the filter is in the result set. The filtering is done during the search, so it is not a post filter. There is currently two ways of using the filter, one can add allowed ids in a sorted vector and send as a parameter, or one can define a function which will be called before an id is added to the result set.
  Examples on both these strategies are in the examples or tests directory. One can also implement the trait Filterable for new types, if one would like the filter to be kept in a bitvector, for example.

• Possibilty to use mmap on dumped data (not on graph part) which is useful for large data vectors.

The graph construction and searches are multithreaded with the parking_lot crate (See parallel_insert_data and parallel_search_neighbours functions and also examples files).
Simd Avx2 implementation, currently based on the simdeez crate, is provided for most distances in the f32 heavily used case and for the Hamming distance for i32. See Building.

• The simd provided by the simdeez crate is accessible with the feature "simdeez_f" for x86_64 processors. Compile with cargo build --release --features "simdeez_f" .... To compile this crate on a M1 chip just do not activate this feature. As soon as std::simd lands in rust stable, it will be the default.

• It is nevertheless possible to experiment with std::simd. Compiling with the feature stdsimd (cargo build --release --features "stdsimd"), activates the transitory crate packed_simd, this requires rust nightly. only the Hamming distance with the u32x16 and u64x8 types and DistL1 on f32 are provided.

By default the crate is a standalone project and builds a static libray and executable. To be used with the companion Julia package it is necessary to build a dynamic library. This can be done by just uncommenting (i.e get rid of the #) in file Cargo.toml the line:

#crate-type = ["cdylib"]

and rerun the command: cargo build --release.

This will generate a .so file in the target/release directory.

The algorithm stores points in layers (at most 16), and a graph is constructed to enable a search from less densely populated levels to most densely populated levels by constructing links from less dense layers to the most dense layer (level 0).

Roughly the algorithm goes along runs as follows:

Upon insertion, the level l of a new point is sampled with an exponential law, limiting the number of levels to 16, so that level 0 is the most densely populated layer, upper layers being exponentially less populated as level increases.
The nearest neighbour of the point is searched in lookup tables from the upper level to the level just above its layer (l), so we should arrive near the new point at its level at a relatively low cost. Then the max_nb_connection nearest neighbours are searched in neighbours of neighbours table (with a reverse updating of tables) recursively from its layer l down to the most populated level 0.

The scale parameter of the exponential law depends on the maximum number of connection possible for a point (parameter max_nb_connection) to others.
Explicitly the scale parameter is chosen as : scale=1/ln(max_nb_connection).

The main parameters occuring in constructing the graph or in searching are:

• max_nb_connection (in hnsw initialization) The maximum number of links from one point to others. Values ranging from 16 to 64 are standard initialising values, the higher the more time consuming.

• ef_construction (in hnsw initialization)
  This parameter controls the width of the search for neighbours during insertion. Values from 200 to 800 are standard initialising values, the higher the more time consuming.

• max_layer (in hnsw initialization)
  The maximum number of layers in graph. Must be less or equal than 16.

• ef_arg (in search methods)
  This parameter controls the width of the search in the lowest level, it must be greater than number of neighbours asked but can be less than ef_construction. As a rule of thumb could be between the number of neighbours we will ask for (knbn arg in search method) and max_nb_connection.

• keep_pruned and extend_candidates.
  These parameters are described in the paper by Malkov and Yashunin can be used to modify the search strategy. The interested user should check the paper to see the impact. By default the values are as recommended in the paper.

Some examples are taken from the ann-benchmarks site and recall rates and request/s are given in comments in the examples files for some input parameters. The annhdf5 module implements reading the standardized data files of the ann-benchmarks site, just download the necessary benchmark data files and modify path in sources accordingly. Then run: cargo build --release --features="simdeez_f" --examples .
It is possible in these examples to change from parallel searches to serial searches to check for speeds or modify parameters to see the impact on performance.

With a i9-13900HX 24 cores laptop we get the following results:

1. fashion-mnist-784-euclidean : search requests run at 59900 req/s with a recall rate of 0.977
2. ann-glove-25-angular : search for the first 100 neighbours run with recall 0.979 at 12000 req/s
3. sift1m benchmark: (1 million points in 128 dimension) search requests for the 10 first neighbours runs at 15000 req/s with a recall rate of 0.9907 or at 8300 req/s with a recall rate of 0.9959, depending on the parameters.

Moreover a tiny crate bigann gives results on the first 10 Million points of the BIGANN benchmark and can used to play with parameters on this data. Results give a recall between 0.92 and 0.99 depending on number of requests and parameters.

Some lines extracted from this Mnist benchmark show how it works for f32 and L2 norm

    //  reading data
    let anndata = AnnBenchmarkData::new(fname).unwrap();
    let nb_elem = anndata.train_data.len();
    let max_nb_connection = 24;
    let nb_layer = 16.min((nb_elem as f32).ln().trunc() as usize);
    let ef_c = 400;
    // allocating network
    let mut hnsw =  Hnsw::<f32, DistL2>::new(max_nb_connection, nb_elem, nb_layer, ef_c, DistL2{});
    hnsw.set_extend_candidates(false);
    // parallel insertion of train data
    let data_for_par_insertion = anndata.train_data.iter().map( |x| (&x.0, x.1)).collect();
    hnsw.parallel_insert(&data_for_par_insertion);
    //
    hnsw.dump_layer_info();
    //  Now the bench with 10 neighbours
    let mut knn_neighbours_for_tests = Vec::<Vec<Neighbour>>::with_capacity(nb_elem);
    hnsw.set_searching_mode(true);
    let knbn = 10;
    let ef_c = max_nb_connection;
    // search 10 nearest neighbours for test data
    knn_neighbours_for_tests = hnsw.parallel_search(&anndata.test_data, knbn, ef_c);
    ....

Sannsyn contributed to Drop implementation and FilterT trait. Petter Egesund added the DistLevenshtein distance.

Licensed under either of

• Apache License, Version 2.0, LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0
• MIT license LICENSE-MIT or http://opensource.org/licenses/MIT

at your option.

This software was written on my own while working at CEA.