# Natural Language Toolkit: K-Means Clusterer
#
# Copyright (C) 2001-2015 NLTK Project
# Author: Trevor Cohn <tacohn@cs.mu.oz.au>
# URL: <http://nltk.org/>
# For license information, see LICENSE.TXT
from __future__ import print_function, unicode_literals, division
import copy
import random
import sys
try:
import numpy
except ImportError:
pass
from nltk.cluster.util import VectorSpaceClusterer
from nltk.compat import python_2_unicode_compatible
@python_2_unicode_compatible
[docs]class KMeansClusterer(VectorSpaceClusterer):
"""
The K-means clusterer starts with k arbitrary chosen means then allocates
each vector to the cluster with the closest mean. It then recalculates the
means of each cluster as the centroid of the vectors in the cluster. This
process repeats until the cluster memberships stabilise. This is a
hill-climbing algorithm which may converge to a local maximum. Hence the
clustering is often repeated with random initial means and the most
commonly occurring output means are chosen.
"""
[docs] def __init__(self, num_means, distance, repeats=1,
conv_test=1e-6, initial_means=None,
normalise=False, svd_dimensions=None,
rng=None, avoid_empty_clusters=False):
"""
:param num_means: the number of means to use (may use fewer)
:type num_means: int
:param distance: measure of distance between two vectors
:type distance: function taking two vectors and returing a float
:param repeats: number of randomised clustering trials to use
:type repeats: int
:param conv_test: maximum variation in mean differences before
deemed convergent
:type conv_test: number
:param initial_means: set of k initial means
:type initial_means: sequence of vectors
:param normalise: should vectors be normalised to length 1
:type normalise: boolean
:param svd_dimensions: number of dimensions to use in reducing vector
dimensionsionality with SVD
:type svd_dimensions: int
:param rng: random number generator (or None)
:type rng: Random
:param avoid_empty_clusters: include current centroid in computation
of next one; avoids undefined behavior
when clusters become empty
:type avoid_empty_clusters: boolean
"""
VectorSpaceClusterer.__init__(self, normalise, svd_dimensions)
self._num_means = num_means
self._distance = distance
self._max_difference = conv_test
assert not initial_means or len(initial_means) == num_means
self._means = initial_means
assert repeats >= 1
assert not (initial_means and repeats > 1)
self._repeats = repeats
self._rng = (rng if rng else random.Random())
self._avoid_empty_clusters = avoid_empty_clusters
[docs] def cluster_vectorspace(self, vectors, trace=False):
if self._means and self._repeats > 1:
print('Warning: means will be discarded for subsequent trials')
meanss = []
for trial in range(self._repeats):
if trace: print('k-means trial', trial)
if not self._means or trial > 1:
self._means = self._rng.sample(list(vectors), self._num_means)
self._cluster_vectorspace(vectors, trace)
meanss.append(self._means)
if len(meanss) > 1:
# sort the means first (so that different cluster numbering won't
# effect the distance comparison)
for means in meanss:
means.sort(key=sum)
# find the set of means that's minimally different from the others
min_difference = min_means = None
for i in range(len(meanss)):
d = 0
for j in range(len(meanss)):
if i != j:
d += self._sum_distances(meanss[i], meanss[j])
if min_difference is None or d < min_difference:
min_difference, min_means = d, meanss[i]
# use the best means
self._means = min_means
def _cluster_vectorspace(self, vectors, trace=False):
if self._num_means < len(vectors):
# perform k-means clustering
converged = False
while not converged:
# assign the tokens to clusters based on minimum distance to
# the cluster means
clusters = [[] for m in range(self._num_means)]
for vector in vectors:
index = self.classify_vectorspace(vector)
clusters[index].append(vector)
if trace: print('iteration')
#for i in range(self._num_means):
#print ' mean', i, 'allocated', len(clusters[i]), 'vectors'
# recalculate cluster means by computing the centroid of each cluster
new_means = list(map(self._centroid, clusters, self._means))
# measure the degree of change from the previous step for convergence
difference = self._sum_distances(self._means, new_means)
if difference < self._max_difference:
converged = True
# remember the new means
self._means = new_means
[docs] def classify_vectorspace(self, vector):
# finds the closest cluster centroid
# returns that cluster's index
best_distance = best_index = None
for index in range(len(self._means)):
mean = self._means[index]
dist = self._distance(vector, mean)
if best_distance is None or dist < best_distance:
best_index, best_distance = index, dist
return best_index
[docs] def num_clusters(self):
if self._means:
return len(self._means)
else:
return self._num_means
[docs] def means(self):
"""
The means used for clustering.
"""
return self._means
def _sum_distances(self, vectors1, vectors2):
difference = 0.0
for u, v in zip(vectors1, vectors2):
difference += self._distance(u, v)
return difference
def _centroid(self, cluster, mean):
if self._avoid_empty_clusters:
centroid = copy.copy(mean)
for vector in cluster:
centroid += vector
return centroid / (1+len(cluster))
else:
if not len(cluster):
sys.stderr.write('Error: no centroid defined for empty cluster.\n')
sys.stderr.write('Try setting argument \'avoid_empty_clusters\' to True\n')
assert(False)
centroid = copy.copy(cluster[0])
for vector in cluster[1:]:
centroid += vector
return centroid / len(cluster)
def __repr__(self):
return '<KMeansClusterer means=%s repeats=%d>' % \
(self._means, self._repeats)
#################################################################################
def demo():
# example from figure 14.9, page 517, Manning and Schutze
from nltk.cluster import KMeansClusterer, euclidean_distance
vectors = [numpy.array(f) for f in [[2, 1], [1, 3], [4, 7], [6, 7]]]
means = [[4, 3], [5, 5]]
clusterer = KMeansClusterer(2, euclidean_distance, initial_means=means)
clusters = clusterer.cluster(vectors, True, trace=True)
print('Clustered:', vectors)
print('As:', clusters)
print('Means:', clusterer.means())
print()
vectors = [numpy.array(f) for f in [[3, 3], [1, 2], [4, 2], [4, 0], [2, 3], [3, 1]]]
# test k-means using the euclidean distance metric, 2 means and repeat
# clustering 10 times with random seeds
clusterer = KMeansClusterer(2, euclidean_distance, repeats=10)
clusters = clusterer.cluster(vectors, True)
print('Clustered:', vectors)
print('As:', clusters)
print('Means:', clusterer.means())
print()
# classify a new vector
vector = numpy.array([3, 3])
print('classify(%s):' % vector, end=' ')
print(clusterer.classify(vector))
print()
if __name__ == '__main__':
demo()