Binary Indexes

Overview

Faiss supports indexing binary vectors (with Hamming distance), with the IndexBinaryFlat, IndexBinaryIVF and IndexBinaryHNSW and IndexBinaryHash/IndexBinaryMultiHash indexes (all inheriting from IndexBinary).

Those indexes store the vectors as arrays of bytes, so that a vector of size d takes only d / 8 bytes in memory. Note that at the moment, only vectors with sizes multiple of 8 are supported. Of course, you can round up the vector length if needed.

The input to the add() and search() methods are also byte arrays ("uint8_t" in C++, "uint8" in numpy). The returned indices are 64-bit ints, distances are 32-bit ints.

From Faiss 1.6.3, most index types also support range_search.

IndexBinaryFlat

The "flat" binary index performs an exhaustive search.

The exhaustive search is carefully optimized especially for 256-bit vectors that are quite common. The Hamming distance computations are optimized using popcount CPU instructions.

Batching is applied on the query and the database side to avoid cache misses.

The values of hamming_batch_size and faiss::IndexBinaryFlat#query_batch_size can be customized to adjust the batch sizes but the default values were found to be close to optimal for a large range of settings.

The examples show how to pass in binary data and how to query the index.

In C++

#include <faiss/IndexBinaryFlat.h>

// Dimension of the vectors, assumed to be a multiple of 8.
int d = 256;

// Vectors to be indexed, each represented by d / 8 bytes, layed out sequentially,
// i.e. the i-th vector starts at db[i * (d / 8)].
int nb = ...;
std::vector<uint8_t> db(nb * (d / 8));
// initialize db

// Vectors to be queried from the index. 
int nq = ...;
std::vector<uint8_t> queries(nq * (d / 8));

// Initializing index.
faiss::IndexBinaryFlat index(d);

// Adding the database vectors.
index.add(nb, db.data());

// Number of nearest neighbors to retrieve per query vector.
int k = ...;

// Output variables for the queries.
std::vector<int32_t> distances(nq * k);
std::vector<faiss::Index::idx_t> labels(nq * k);

// Querying the index
index.search(nq, queries.data(), k, distances.data(), labels.data());

// distances[i * k + j] contains the distance from the i-th query vector to its j-th nearest neighbor.
// labels[i * k + j] contains the id of the j-th nearest neighbor of the i-th query vector.

In Python

import faiss

# Dimension of the vectors.
d = 256

# Vectors to be indexed, each represented by d / 8 bytes in a nb
# i.e. the i-th vector is db[i].
nb = ...
db = np.empty((nb, d // 8), dtype='uint8')
...initialize db...

# Vectors to be queried from the index.
nq = ...
queries = np.empty((nq, d // 8), dtype='uint8')
...initialize queries...

# Initializing index.
index = faiss.IndexBinaryFlat(d)

# Adding the database vectors.
index.add(db)

# Number of nearest neighbors to retrieve per query vector.
k = ...;

# Querying the index
D, I = index.search(queries, k)

# D[i, j] contains the distance from the i-th query vector to its j-th nearest neighbor.
# I[i, j] contains the id of the j-th nearest neighbor of the i-th query vector.

IndexBinaryIVF

The "IVF" (Inverse Vector File) flavor speeds up the search by clustering the vectors. This clustering is done using a second (binary) index for quantization (usually a flat index). This is equivalent to the IndexIVFFlat of the floating-point indexes.

Examples:

In C++

#include <faiss/IndexBinaryIVF.h>

// Dimension of the vectors.
int d = 256;

// Vectors to be indexed, each represented by d / 8 bytes, layed out sequentially,
// i.e. the i-th vector starts at db[i * (d / 8)].
int nb = ...;
std::vector<uint8_t> db(nb * (d / 8);

// Vectors to train the quantizer.
int nt = ...;
std::vector<uint8_t> training(nt * (d / 8));

// Vectors to be queried from the index.
int nq = ...;
std::vector<uint8_t> queries(nq * (d / 8));

// Initializing the quantizer.
faiss::IndexBinaryFlat quantizer(d);

// Number of clusters.
int nlist = ...;

// Initializing index.
faiss::IndexBinaryIVF index(&quantizer, d, nlist);
index.nprobe = 4; // Number of nearest clusters to be searched per query. 

// Training the quantizer.
index.train(nt, training.data());

// Adding the database vectors.
index.add(nb, db.data());

// Number of nearest neighbors to retrieve per query vector.
int k = ...;

// Output variables for the queries.
std::vector<int32_t> distances(nq * k);
std::vector<faiss::idx_t> labels(nq * k);

// Querying the index
index.search(nq, queries.data(), k, distances.data(), labels.data());

// distances[i * k + j] contains the distance from the i-th query vector to its j-th nearest neighbor.
// labels[i * k + j] contains the id of the j-th nearest neighbor of the i-th query vector.

In Python

import faiss

# Dimension of the vectors.
d = 256

# Vectors to be indexed, each represented by d / 8 bytes.
# the i-th vector is db[i].
db = ...

# Vectors to train the quantizer.
training = ...

# Vectors to be queried from the index.
queries = ...

# Initializing the quantizer.
quantizer = faiss.IndexBinaryFlat(d)

# Number of clusters.
nlist = ...

# Initializing index.
index = faiss.IndexBinaryIVF(quantizer, d, nlist)
index.nprobe = 4 # Number of nearest clusters to be searched per query. 

# Training the quantizer.
index.train(training)

# Adding the database vectors.
index.add(db)

# Number of nearest neighbors to retrieve per query vector.
k = ...

# Querying the index.
D, I = index.search(queries, k)

# D[i, j] contains the distance from the i-th query vector to its j-th nearest neighbor.
# I[i, j] contains the id of the j-th nearest neighbor of the i-th query vector.

The IndexBinaryHNSW

This is the same method as for the floating point vectors.

Example usage here: TestHNSW

The IndexBinaryHash and IndexBinaryMultiHash

(Faiss 1.6.3 and above)

IndexBinaryHash: A classical method is to extract a hash from the binary vectors and to use that to split the dataset in buckets. At search time, all hashtable entries within nflip Hamming radius of the query vector's hash are visited.

The hash value is the first b bits of the binary vector. At search time, the number of visited buckets is 1 + b + b * (b - 1) / 2 + .... + comb(b, nflip).

IndexBinaryMultiHash: An extension of this method, studied in “Fast Search in Hamming Space with Multi-Index Hashing”, Norouzi et al, CVPR’12, consists in using nhash hash tables built from bits 0:b, b:2*b, … , (nhash-1) * b: nnhash * b`. This is sometimes referred to as LSH because of the multiple hash tables.

A comparison between IndexBinaryHash and IndexBinaryIV is here: Binary hashing index benchmark

Shorter versions using index factory

The faiss::index_binary_factory() allows for shorter declarations of binary indexes. It is especially useful for IndexBinaryIVF, for which a quantizer needs to be initialized.

How to use index_binary_factory:

In C++

Instead of the above initialization code:

// Initializing the quantizer.
faiss::IndexBinaryFlat quantizer(d);

// Number of clusters.
int nlist = 32;

// Initializing index.
faiss::IndexBinaryIVF index(&quantizer, d, nlist);
index.nprobe = 4; // Number of nearest clusters to be searched per query. 

one could write:

#include <faiss/AutoTune.h>
  
// Initializing the quantizer.
faiss::IndexBinaryIVF *index = dynamic_cast<faiss::IndexBinaryIVF *>(faiss::index_binary_factory(d, "BIVF32"));
index->nprobe = 4; // Number of nearest clusters to be searched per query.

In Python

Instead of the above initialization code:

# Initializing the quantizer.
quantizer = faiss.IndexBinaryFlat(d)

# Number of clusters.
nlist = 32

# Initializing index.
index = faiss.IndexBinaryIVF(quantizer, d, nlist)
index.nprobe = 4 # Number of nearest clusters to be searched per query. 

one could write:

# Initializing the quantizer.
index = faiss.index_binary_factory(d, "BIVF32")
index.nprobe = 4 # Number of nearest clusters to be searched per query.

Table of available index_binary_factory strings:

String	Class name	bytes per vector	Comments
BFlat	IndexBinaryFlat	d/8	simple flat index
BIVF1024	IndexBinaryIVF	d/8	IVF with 1024 centroids and a flat quantizer
BHNSW16	IndexBinaryHNSW	d/8 + 16 * 2 * 4	HNSW with branching factor M=16.
BIVF1024_HNSW16	IndexBinaryIVF	d/8	IVF with 1024 centroids and HNSW M=16 used as a quantizer.
BHash32	IndexBinaryHash	d/8	Binary hash index with 32 bit prefix.
BHash4x32	IndexBinaryMultiHash	4*64/8	Multiple binary hash index with 32 bits each.

The bytes per vector are approximate, there is additional memory overhead due to geometric std::vector allocation, the coarse quantizer in the IVF and the HSNW tree.