# Natural Language Toolkit: K-Means Clusterer # # Copyright (C) 2001-2023 NLTK Project # Author: Trevor Cohn # URL: # For license information, see LICENSE.TXT import copy import random import sys try: import numpy except ImportError: pass from nltk.cluster.util import VectorSpaceClusterer 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. """ 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 returning 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 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 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 def num_clusters(self): if self._means: return len(self._means) else: return self._num_means 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 "" % (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()