File kmeans1d.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

void smawk(const idx_t nrows, const idx_t ncols, const float *x, idx_t *argmins)

SMAWK algorithm. Find the row minima of a monotone matrix.

Expose this for testing.

Parameters:

  • nrows – number of rows

  • ncols – number of columns

  • x – input matrix, size (nrows, ncols)

  • argmins – argmin of each row

double kmeans1d(const float *x, size_t n, size_t nclusters, float *centroids)

Exact 1D K-Means by dynamic programming

From “Fast Exact k-Means, k-Medians and Bregman Divergence Clustering in 1D” Allan Grønlund, Kasper Green Larsen, Alexander Mathiasen, Jesper Sindahl Nielsen, Stefan Schneider, Mingzhou Song, ArXiV’17

Section 2.2

https://arxiv.org/abs/1701.07204

Parameters:

  • x – input 1D array

  • n – input array length

  • nclusters – number of clusters

  • centroids – output centroids, size nclusters

Returns:

imbalancce factor