K-means clustering - PyTorch API

The pykeops.torch.generic_argmin() routine allows us to perform bruteforce nearest neighbor search with four lines of code. It can thus be used to implement a large-scale K-means clustering, without memory overflows.


For large and high dimensional datasets, this script outperforms its NumPy counterpart as it avoids transfers between CPU (host) and GPU (device) memories.


Standard imports:

import time

import torch
from matplotlib import pyplot as plt

from pykeops.torch import Genred

use_cuda = torch.cuda.is_available()
dtype = 'float32' if use_cuda else 'float64'
torchtype = {'float32': torch.float32, 'float64': torch.float64}

Simple implementation of the K-means algorithm:

def KMeans(x, K=10, Niter=10, verbose=True):
    N, D = x.shape  # Number of samples, dimension of the ambient space

    # Define our KeOps kernel:
    nn_search = Genred(
        'SqDist(x,y)',            # A simple squared L2 distance
        ['x = Vi({})'.format(D),  # target points of dimension D, indexed by "i"
         'y = Vj({})'.format(D)], # source points of dimension D, indexed by "j"
        axis=1,                   # The reduction is performed on the second axis
        dtype=dtype)          # "float32" and "float64" are available

    # K-means loop:
    # - x  is the point cloud,
    # - cl is the vector of class labels
    # - c  is the cloud of cluster centroids
    start = time.time()
    c = x[:K, :].clone()  # Simplistic random initialization

    for i in range(Niter):
        cl  = nn_search(x,c).long().view(-1)  # Points -> Nearest cluster
        Ncl = torch.bincount(cl).type(torchtype[dtype])  # Class weights
        for d in range(D):  # Compute the cluster centroids with torch.bincount:
            c[:, d] = torch.bincount(cl, weights=x[:, d]) / Ncl

    end = time.time()

    if verbose:
        print("K-means example with {} points in dimension {}, K = {}:".format(N, D, K))
        print('Timing for {} iterations: {:.5f}s = {} x {:.5f}s\n'.format(
                Niter, end - start, Niter, (end-start) / Niter))

    return cl, c

K-means in 2D

First experiment with 10,000 points in dimension 2, with 50 classes:

N, D, K = 10000, 2, 50

Define our dataset:

x = torch.randn(N, D, dtype=torchtype[dtype]) / 6 + .5

Perform the computation:

cl, c = KMeans(x, K)


K-means example with 10000 points in dimension 2, K = 50:
Timing for 10 iterations: 0.02305s = 10 x 0.00230s

Fancy display:

plt.scatter(x[:, 0].cpu(), x[:, 1].cpu(), c=cl.cpu(), s= 30000 / len(x), cmap="tab10")
plt.scatter(c[:, 0].cpu(), c[:, 1].cpu(), c='black', s=50, alpha=.8)
plt.axis([0,1,0,1]) ; plt.tight_layout() ; plt.show()

K-means in dimension 100

Second experiment with 1,000,000 points in dimension 100, with 1,000 classes:

if use_cuda:
    N, D, K = 1000000, 100, 1000
    x = torch.randn(N, D, dtype=torchtype[dtype])
    cl, c = KMeans(x, K)


K-means example with 1000000 points in dimension 100, K = 1000:
Timing for 10 iterations: 19.63705s = 10 x 1.96371s

Total running time of the script: ( 0 minutes 36.969 seconds)

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