File Clustering.h

namespace faiss

Implementation of k-means clustering with many variants.

Copyright (c) Facebook, Inc. and its affiliates.

This source code is licensed under the MIT license found in the LICENSE file in the root directory of this source tree.

IDSelector is intended to define a subset of vectors to handle (for removal or as subset to search)

PQ4 SIMD packing and accumulation functions

The basic kernel accumulates nq query vectors with bbs = nb * 2 * 16 vectors and produces an output matrix for that. It is interesting for nq * nb <= 4, otherwise register spilling becomes too large.

The implementation of these functions is spread over 3 cpp files to reduce parallel compile times. Templates are instantiated explicitly.

This file contains callbacks for kernels that compute distances.

Throughout the library, vectors are provided as float * pointers. Most algorithms can be optimized when several vectors are processed (added/searched) together in a batch. In this case, they are passed in as a matrix. When n vectors of size d are provided as float * x, component j of vector i is

x[ i * d + j ]

where 0 <= i < n and 0 <= j < d. In other words, matrices are always compact. When specifying the size of the matrix, we call it an n*d matrix, which implies a row-major storage.

I/O functions can read/write to a filename, a file handle or to an object that abstracts the medium.

The read functions return objects that should be deallocated with delete. All references within these objectes are owned by the object.

Definition of inverted lists + a few common classes that implement the interface.

Since IVF (inverted file) indexes are of so much use for large-scale use cases, we group a few functions related to them in this small library. Most functions work both on IndexIVFs and IndexIVFs embedded within an IndexPreTransform.

In this file are the implementations of extra metrics beyond L2 and inner product

Implements a few neural net layers, mainly to support QINCo

Defines a few objects that apply transformations to a set of vectors Often these are pre-processing steps.

Functions

float kmeans_clustering(size_t d, size_t n, size_t k, const float *x, float *centroids)

simplified interface

Parameters:

• d – dimension of the data

• n – nb of training vectors

• k – nb of output centroids

• x – training set (size n * d)

• centroids – output centroids (size k * d)

Returns:

final quantization error

struct ClusteringParameters

#include <Clustering.h>

Class for the clustering parameters. Can be passed to the constructor of the Clustering object.

Subclassed by faiss::Clustering, faiss::ProgressiveDimClusteringParameters

Public Members

int niter = 25

number of clustering iterations

int nredo = 1

redo clustering this many times and keep the clusters with the best objective

bool verbose = false

bool spherical = false

whether to normalize centroids after each iteration (useful for inner product clustering)

bool int_centroids = false

round centroids coordinates to integer after each iteration?

bool update_index = false

re-train index after each iteration?

bool frozen_centroids = false

Use the subset of centroids provided as input and do not change them during iterations

int min_points_per_centroid = 39

If fewer than this number of training vectors per centroid are provided, writes a warning. Note that fewer than 1 point per centroid raises an exception.

int max_points_per_centroid = 256

to limit size of dataset, otherwise the training set is subsampled

int seed = 1234

seed for the random number generator. negative values lead to seeding an internal rng with std::high_resolution_clock.

size_t decode_block_size = 32768

when the training set is encoded, batch size of the codec decoder

bool check_input_data_for_NaNs = true

whether to check for NaNs in an input data

bool use_faster_subsampling = false

Whether to use splitmix64-based random number generator for subsampling, which is faster, but may pick duplicate points.

struct ClusteringIterationStats

Public Members

float obj

objective values (sum of distances reported by index)

double time

seconds for iteration

double time_search

seconds for just search

double imbalance_factor

imbalance factor of iteration

int nsplit

number of cluster splits

struct Clustering : public faiss::ClusteringParameters

#include <Clustering.h>

K-means clustering based on assignment - centroid update iterations

The clustering is based on an Index object that assigns training points to the centroids. Therefore, at each iteration the centroids are added to the index.

On output, the centoids table is set to the latest version of the centroids and they are also added to the index. If the centroids table it is not empty on input, it is also used for initialization.

Subclassed by faiss::Clustering1D

Public Functions

Clustering(int d, int k)

Clustering(int d, int k, const ClusteringParameters &cp)

virtual void train(idx_t n, const float *x, faiss::Index &index, const float *x_weights = nullptr)

run k-means training

Parameters:

• x – training vectors, size n * d

• index – index used for assignment

• x_weights – weight associated to each vector: NULL or size n

void train_encoded(idx_t nx, const uint8_t *x_in, const Index *codec, Index &index, const float *weights = nullptr)

run with encoded vectors

win addition to train()’s parameters takes a codec as parameter to decode the input vectors.

Parameters:

codec – codec used to decode the vectors (nullptr = vectors are in fact floats)

void post_process_centroids()

Post-process the centroids after each centroid update. includes optional L2 normalization and nearest integer rounding

inline virtual ~Clustering()

Public Members

size_t d

dimension of the vectors

size_t k

nb of centroids

std::vector<float> centroids

centroids (k * d) if centroids are set on input to train, they will be used as initialization

std::vector<ClusteringIterationStats> iteration_stats

stats at every iteration of clustering

int niter = 25

number of clustering iterations

int nredo = 1

redo clustering this many times and keep the clusters with the best objective

bool verbose = false

bool spherical = false

whether to normalize centroids after each iteration (useful for inner product clustering)

bool int_centroids = false

round centroids coordinates to integer after each iteration?

bool update_index = false

re-train index after each iteration?

bool frozen_centroids = false

Use the subset of centroids provided as input and do not change them during iterations

int min_points_per_centroid = 39

If fewer than this number of training vectors per centroid are provided, writes a warning. Note that fewer than 1 point per centroid raises an exception.

int max_points_per_centroid = 256

to limit size of dataset, otherwise the training set is subsampled

int seed = 1234

seed for the random number generator. negative values lead to seeding an internal rng with std::high_resolution_clock.

size_t decode_block_size = 32768

when the training set is encoded, batch size of the codec decoder

bool check_input_data_for_NaNs = true

whether to check for NaNs in an input data

bool use_faster_subsampling = false

Whether to use splitmix64-based random number generator for subsampling, which is faster, but may pick duplicate points.

struct Clustering1D : public faiss::Clustering

#include <Clustering.h>

Exact 1D clustering algorithm

Since it does not use an index, it does not overload the train() function

Public Functions

explicit Clustering1D(int k)

Clustering1D(int k, const ClusteringParameters &cp)

void train_exact(idx_t n, const float *x)

inline virtual ~Clustering1D()

virtual void train(idx_t n, const float *x, faiss::Index &index, const float *x_weights = nullptr)

run k-means training

Parameters:

• x – training vectors, size n * d

• index – index used for assignment

• x_weights – weight associated to each vector: NULL or size n

void train_encoded(idx_t nx, const uint8_t *x_in, const Index *codec, Index &index, const float *weights = nullptr)

run with encoded vectors

win addition to train()’s parameters takes a codec as parameter to decode the input vectors.

Parameters:

codec – codec used to decode the vectors (nullptr = vectors are in fact floats)

void post_process_centroids()

Post-process the centroids after each centroid update. includes optional L2 normalization and nearest integer rounding

Public Members

size_t d

dimension of the vectors

size_t k

nb of centroids

std::vector<float> centroids

centroids (k * d) if centroids are set on input to train, they will be used as initialization

std::vector<ClusteringIterationStats> iteration_stats

stats at every iteration of clustering

int niter = 25

number of clustering iterations

int nredo = 1

redo clustering this many times and keep the clusters with the best objective

bool verbose = false

bool spherical = false

whether to normalize centroids after each iteration (useful for inner product clustering)

bool int_centroids = false

round centroids coordinates to integer after each iteration?

bool update_index = false

re-train index after each iteration?

bool frozen_centroids = false

Use the subset of centroids provided as input and do not change them during iterations

int min_points_per_centroid = 39

If fewer than this number of training vectors per centroid are provided, writes a warning. Note that fewer than 1 point per centroid raises an exception.

int max_points_per_centroid = 256

to limit size of dataset, otherwise the training set is subsampled

int seed = 1234

seed for the random number generator. negative values lead to seeding an internal rng with std::high_resolution_clock.

size_t decode_block_size = 32768

when the training set is encoded, batch size of the codec decoder

bool check_input_data_for_NaNs = true

whether to check for NaNs in an input data

bool use_faster_subsampling = false

Whether to use splitmix64-based random number generator for subsampling, which is faster, but may pick duplicate points.

struct ProgressiveDimClusteringParameters : public faiss::ClusteringParameters

Subclassed by faiss::ProgressiveDimClustering

Public Functions

ProgressiveDimClusteringParameters()

Public Members

int progressive_dim_steps

number of incremental steps

bool apply_pca

apply PCA on input

int niter = 25

number of clustering iterations

int nredo = 1

redo clustering this many times and keep the clusters with the best objective

bool verbose = false

bool spherical = false

whether to normalize centroids after each iteration (useful for inner product clustering)

bool int_centroids = false

round centroids coordinates to integer after each iteration?

bool update_index = false

re-train index after each iteration?

bool frozen_centroids = false

Use the subset of centroids provided as input and do not change them during iterations

int min_points_per_centroid = 39

If fewer than this number of training vectors per centroid are provided, writes a warning. Note that fewer than 1 point per centroid raises an exception.

int max_points_per_centroid = 256

to limit size of dataset, otherwise the training set is subsampled

int seed = 1234

seed for the random number generator. negative values lead to seeding an internal rng with std::high_resolution_clock.

size_t decode_block_size = 32768

when the training set is encoded, batch size of the codec decoder

bool check_input_data_for_NaNs = true

whether to check for NaNs in an input data

bool use_faster_subsampling = false

Whether to use splitmix64-based random number generator for subsampling, which is faster, but may pick duplicate points.

struct ProgressiveDimIndexFactory

#include <Clustering.h>

generates an index suitable for clustering when called

Subclassed by faiss::gpu::GpuProgressiveDimIndexFactory

Public Functions

virtual Index *operator()(int dim)

ownership transferred to caller

inline virtual ~ProgressiveDimIndexFactory()

struct ProgressiveDimClustering : public faiss::ProgressiveDimClusteringParameters

#include <Clustering.h>

K-means clustering with progressive dimensions used

The clustering first happens in dim 1, then with exponentially increasing dimension until d (I steps). This is typically applied after a PCA transformation (optional). Reference:

“Improved Residual Vector Quantization for High-dimensional Approximate

Nearest Neighbor Search”

Shicong Liu, Hongtao Lu, Junru Shao, AAAI’15

https://arxiv.org/abs/1509.05195

Public Functions

ProgressiveDimClustering(int d, int k)

ProgressiveDimClustering(int d, int k, const ProgressiveDimClusteringParameters &cp)

void train(idx_t n, const float *x, ProgressiveDimIndexFactory &factory)

inline virtual ~ProgressiveDimClustering()

Public Members

size_t d

dimension of the vectors

size_t k

nb of centroids

std::vector<float> centroids

centroids (k * d)

std::vector<ClusteringIterationStats> iteration_stats

stats at every iteration of clustering

int progressive_dim_steps

number of incremental steps

bool apply_pca

apply PCA on input

int niter = 25

number of clustering iterations

int nredo = 1

redo clustering this many times and keep the clusters with the best objective

bool verbose = false

bool spherical = false

whether to normalize centroids after each iteration (useful for inner product clustering)

bool int_centroids = false

round centroids coordinates to integer after each iteration?

bool update_index = false

re-train index after each iteration?

bool frozen_centroids = false

Use the subset of centroids provided as input and do not change them during iterations

int min_points_per_centroid = 39

If fewer than this number of training vectors per centroid are provided, writes a warning. Note that fewer than 1 point per centroid raises an exception.

int max_points_per_centroid = 256

to limit size of dataset, otherwise the training set is subsampled

int seed = 1234

seed for the random number generator. negative values lead to seeding an internal rng with std::high_resolution_clock.

size_t decode_block_size = 32768

when the training set is encoded, batch size of the codec decoder

bool check_input_data_for_NaNs = true

whether to check for NaNs in an input data

bool use_faster_subsampling = false

Whether to use splitmix64-based random number generator for subsampling, which is faster, but may pick duplicate points.