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Project | Paper | Tutorial

A 2D example using both k-means and PQk-means Large-scale evaluation

PQk-means [Matsui, Ogaki, Yamasaki, and Aizawa, ACMMM 17] is a Python library for efficient clustering of large-scale data. By first compressing input vectors into short product-quantized (PQ) codes, PQk-means achieves fast and memory-efficient clustering, even for high-dimensional vectors. Similar to k-means, PQk-means repeats the assignment and update steps, both of which can be performed in the PQ-code domain.

For a comparison, we provide the ITQ encoding for the binary conversion and Binary k-means [Gong+, CVPR 15] for the clustering of binary codes.

The library is written in C++ for the main algorithm with wrappers for Python. All encoding/clustering codes are compatible with scikit-learn.

Summary of features

  • Approximation of k-means
  • Tens to hundreds of times faster than k-means
  • Tens to hundreds of times more memory efficient than k-means
  • Compatible with scikit-learn
  • Portable; one-line installation



  • CMake
    • brew install cmake for OS X
    • sudo apt install cmake for Ubuntu
  • OpenMP (Optional)
    • If openmp is installed, it will be automatically used to parallelize the algorithm for faster calculation.

Build & install

You can install the library from PyPI:

pip install pqkmeans

Or, if you would like to use the current master version, you can manually build and install the library by:

git clone --recursive
cd pqkmeans
python install

Run samples

# with artificial data
python bin/ --dataset artificial --algorithm bkmeans pqkmeans --k 100
# with texmex dataset (
python bin/ --dataset siftsmall --algorithm bkmeans pqkmeans --k 100


python test


For PQk-means

import pqkmeans
import numpy as np
X = np.random.random((100000, 128)) # 128 dimensional 100,000 samples

# Train a PQ encoder.
# Each vector is divided into 4 parts and each part is
# encoded with log256 = 8 bit, resulting in a 32 bit PQ code.
encoder = pqkmeans.encoder.PQEncoder(num_subdim=4, Ks=256)[:1000])  # Use a subset of X for training

# Convert input vectors to 32-bit PQ codes, where each PQ code consists of four uint8.
# You can train the encoder and transform the input vectors to PQ codes preliminary.
X_pqcode = encoder.transform(X)

# Run clustering with k=5 clusters.
kmeans = pqkmeans.clustering.PQKMeans(encoder=encoder, k=5)
clustered = kmeans.fit_predict(X_pqcode)

# Then, clustered[0] is the id of assigned center for the first input PQ code (X_pqcode[0]).

Note that an instance of PQ-encoder (encoder) and an instance of clustering (kmeans) can be pickled and reused later.

import pickle

# An instance of PQ-encoder.
pickle.dump(encoder, open('encoder.pkl', 'wb'))
encoder_dumped = pickle.load(open('encoder.pkl', 'rb'))

# An instance of clustering. This can be reused as a vector quantizer later.
pickle.dump(kmeans, open('kmeans.pkl', 'wb'))
kmeans_dumped = pickle.load(open('kmeans.pkl', 'rb'))

For Bk-means

In almost the same manner as for PQk-means,

import pqkmeans
import numpy as np
X = np.random.random((100000, 128)) # 128 dimensional 100,000 samples

# Train an ITQ binary encoder
encoder = pqkmeans.encoder.ITQEncoder(num_bit=32)[:1000])  # Use a subset of X for training

# Convert input vectors to binary codes
X_itq = encoder.transform(X)

# Run clustering
kmeans = pqkmeans.clustering.BKMeans(k=5, input_dim=32)
clustered = kmeans.fit_predict(X_itq)

Please see more examples on a tutorial


  • This repository contains the re-implemented version of the PQk-means with the Python interface. There can be the difference between this repository and the pure c++ implementation used in the paper.
  • We tested this library with Python3, on OS X and Ubuntu 16.04.


  • Keisuke Ogaki designed the whole structure of the library, and implemented most of the Bk-means clustering
  • Yusuke Matsui implemented most of the PQk-means clustering


    author = {Yusuke Matsui and Keisuke Ogaki and Toshihiko Yamasaki and Kiyoharu Aizawa},
    title = {PQk-means: Billion-scale Clustering for Product-quantized Codes},
    booktitle = {ACM International Conference on Multimedia (ACMMM)},
    year = {2017},


  • Evaluation script for billion-scale data
  • Nearest neighbor search with PQTable
  • Documentation
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